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Title: VIBRATION ANALYSIS OF RECTANGULAR PLATES UNDER FLUID LOADING.
Creator: LEE, TZER CHIA., Florida Atlantic University, Dunn, Stanley E., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: An energy method is presented for predicting the natural frequencies, radiation loss factor and system loss factor of simply supported rectangular plates under fluid loading. Both bare plates and plates with complete damping treatments are considered. Results obtained using the method developed are compared with two other theories. The agreement is generally good. The study points out the need for detailed analyses of plate vibration patterns and their associated radiation output under...
Show moreAn energy method is presented for predicting the natural frequencies, radiation loss factor and system loss factor of simply supported rectangular plates under fluid loading. Both bare plates and plates with complete damping treatments are considered. Results obtained using the method developed are compared with two other theories. The agreement is generally good. The study points out the need for detailed analyses of plate vibration patterns and their associated radiation output under various plate boundary conditions. There also exists a need for carefully conducted experimental work to verify the applicability of the current theory.
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Date Issued: 1981
PURL: http://purl.flvc.org/fcla/dt/14086
Subject Headings: Plates (Engineering)--Vibration
Format: Document (PDF)

Title: Vibrational power flow in thick connected plates.
Creator: McCollum, Michele D., Florida Atlantic University, Cuschieri, Joseph M., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: The total vibrational power flow in connected plate structures is investigated using an analytical "Power Flow" approach. The effects of shear and rotary inertia on the flexural wave transmission and the influence of in-plane wave generation at structural discontinuities are included in the analytical model. In formulating a Power Flow model, the structure is divided into substructures whose responses may be determined analytically to obtain expressions for the input and transfer mobilities...
Show moreThe total vibrational power flow in connected plate structures is investigated using an analytical "Power Flow" approach. The effects of shear and rotary inertia on the flexural wave transmission and the influence of in-plane wave generation at structural discontinuities are included in the analytical model. In formulating a Power Flow model, the structure is divided into substructures whose responses may be determined analytically to obtain expressions for the input and transfer mobilities of the substructures. For the case of plate-type structures joined along a line, the mobilities are functions of both frequency and space. The power transmission between the individual plate substructures is then written as a function of these mobility expressions. The structure of concern in this dissertation consists of two plates connected in an L-configuration. In obtaining the expressions for the mobilities, the vibrational response of the individual plates is determined by solving the appropriate equations of motion. In this study the antisymmetric (flexural) motion is described using Mindlin's (1951) thick plate approximation to the three-dimensional equations of motion. The applicability of this thick plate formulation is limited to frequencies below the frequency of the first antisymmetric mode of thickness-shear vibration of the plate. The symmetric (in-plane) motion of the plates is described using the generalized theory of plane stress which neglects the direct coupling of the in-plane motion with the thickness vibration modes, and is therefore valid only for frequencies which are lower than the frequency of the first mode of pure thickness vibration of the plate. The results for the power transmission in the L-plate obtained using the Power Flow formulation are verified at high frequencies by comparison with the results obtained using the Statistical Energy Analysis (SEA) technique. The SEA formulation for the L-plate is based on Mindlin's equations for flexural motion and the theory of generalized plane stress for in-plane vibration. The results of the Power Flow formulation are verified at low frequencies by the results obtained using a Finite Element model of the L-shaped plate.
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Date Issued: 1988
PURL: http://purl.flvc.org/fcla/dt/11929
Subject Headings: Plates (Engineering)--Vibration
Format: Document (PDF)

Title: VIBRATION ANALYSIS OF RECTANGULAR PLATES WITH COMPLETE CONSTRAINED-LAYER DAMPING TREATMENTS.
Creator: CO, CHI-MIN., Florida Atlantic University, Stevens, Karl K.
Abstract/Description: An energy method for predicting the natural frequencies and loss factors of Rectangular Plates with Complete Constrained-Layer Damping Treatments has been presented. Results obtained using the method developed were compared with those of two former theories. The agreement between the current theory and these two theories was generally good. There is a serious need for carefully conducted experimental work to verify the applicability of the current theory and of the various other laminated...
Show moreAn energy method for predicting the natural frequencies and loss factors of Rectangular Plates with Complete Constrained-Layer Damping Treatments has been presented. Results obtained using the method developed were compared with those of two former theories. The agreement between the current theory and these two theories was generally good. There is a serious need for carefully conducted experimental work to verify the applicability of the current theory and of the various other laminated plate theories in existence. It is believed that the method of analysis presented can be extended to handle plates with partial constrainedlayer damping treatments.
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Date Issued: 1981
PURL: http://purl.flvc.org/fcla/dt/14085
Subject Headings: Plates (Engineering)--Vibration
Format: Document (PDF)

Title: The measurement of structural power flow in thin plate structures.
Creator: Padiyar, Satish., Florida Atlantic University, Cuschieri, Joseph M., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: An analytical and experimental investigation of the flow of vibrational power in a thin, L-shaped, finite plate structure subjected to mechanical and acoustic excitation is presented. In the analytical approach, mobility functions are used to determine the structural intensity vectors at various locations on the plate structure. Simulation results of intensity vectors estimated using three different measurement schemes are compared. The experimentally measured intensity vectors, for the case...
Show moreAn analytical and experimental investigation of the flow of vibrational power in a thin, L-shaped, finite plate structure subjected to mechanical and acoustic excitation is presented. In the analytical approach, mobility functions are used to determine the structural intensity vectors at various locations on the plate structure. Simulation results of intensity vectors estimated using three different measurement schemes are compared. The experimentally measured intensity vectors, for the case of mechanical excitation, using a four accelerometer array, are presented. They are found to match well with the results from the corresponding simulation. Similar results are obtained for the case of acoustic excitation of the L-shaped plate. The general pattern of the structural intensity vectors is found to be in agreement with the expected results.
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Date Issued: 1990
PURL: http://purl.flvc.org/fcla/dt/14678
Subject Headings: Plates (Engineering)--Vibration
Format: Document (PDF)

Title: An experimental study of the response of circular plates subjected to fluid loading.
Creator: Coulson, Robert Kenneth., Florida Atlantic University, Glegg, Stewart A. L.
Abstract/Description: The interaction between vibrating structures and fluids can have a profound influence upon the natural frequencies of the structure's vibration. This study examines one specific structure; a thin circular plate with the rarely studied free edge condition. It starts by considering a completely free plate in a vacuum and then, using receptance matching, utilises this result to determine the effects, on the natural frequencies, of a centrally located driving rod. Then, using the same technique,...
Show moreThe interaction between vibrating structures and fluids can have a profound influence upon the natural frequencies of the structure's vibration. This study examines one specific structure; a thin circular plate with the rarely studied free edge condition. It starts by considering a completely free plate in a vacuum and then, using receptance matching, utilises this result to determine the effects, on the natural frequencies, of a centrally located driving rod. Then, using the same technique, a result for the drive admittance of the fluid loaded plate is adapted to predict the natural frequencies of the same structure when subjected to significant fluid loading. All these results are then compared to those obtained from experiments.
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Date Issued: 1990
PURL: http://purl.flvc.org/fcla/dt/14605
Subject Headings: Plates (Engineering)--Vibration, Acoustical engineering
Format: Document (PDF)

Title: ANALYSIS OF DAMPING LAYER TREATMENTS FOR PLATES USING EXPERIMENTALLY DETERMINED MODE SHAPES.
Creator: JAISING, VINOD R., Florida Atlantic University, Stevens, Karl K.
Abstract/Description: A method of analysis is presented to determine the natural frequencies and loss factors of a plate covered with viscoelastic coating, using experimentally obtained mode shapes. The mode shapes for a square plate clamped on all edges are determined using an HP 5423 A Structural Dynamics Analyzer. A computer program, based on the method of analysis, is developed to determine the natural frequencies and loss factors of a rectangular plate covered with viscoelastic material, and clamped on all...
Show moreA method of analysis is presented to determine the natural frequencies and loss factors of a plate covered with viscoelastic coating, using experimentally obtained mode shapes. The mode shapes for a square plate clamped on all edges are determined using an HP 5423 A Structural Dynamics Analyzer. A computer program, based on the method of analysis, is developed to determine the natural frequencies and loss factors of a rectangular plate covered with viscoelastic material, and clamped on all edges. It was found that, for a fully coated plate, and for a mesh with twenty-five mesh points, the error in the fundamental frequency was approximately 5 percent. A comparison between the mode shapes for the bare plate and for the fully coated plate revealed no significant difference. It was also found that increasing the number of measurement points would not significantly improve the results.
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Date Issued: 1981
PURL: http://purl.flvc.org/fcla/dt/14050
Subject Headings: Plates (Engineering)--Vibration, Damping (Mechanics)
Format: Document (PDF)

Title: EXPERIMENTAL DETERMINATION OF NATURAL FREQUENCIES AND LOSS FACTORS OF A CLAMPED RECTANGULAR PLATE WITH PARTIAL CONSTRAINED LAYER DAMPING TREATMENTS.
Creator: BHAT, RAJENDRA AGHUT., Florida Atlantic University, Stevens, Karl K.
Abstract/Description: An experimental investigation to determine the effectiveness of partial constrained layer damping treatments for a clamped rectangular plate is described. The impulse testing technique was used with a Hewlett Packard '5423A structural Dynamics Analyzer' to determine modal parameters of the first five flexural modes. The results obtained are compared with theoretical results and they are in agreement. The results indicate that partial constrained layer damping treatments, if properly used, can...
Show moreAn experimental investigation to determine the effectiveness of partial constrained layer damping treatments for a clamped rectangular plate is described. The impulse testing technique was used with a Hewlett Packard '5423A structural Dynamics Analyzer' to determine modal parameters of the first five flexural modes. The results obtained are compared with theoretical results and they are in agreement. The results indicate that partial constrained layer damping treatments, if properly used, can be more effective than complete treatments.
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Date Issued: 1983
PURL: http://purl.flvc.org/fcla/dt/14188
Subject Headings: Plates (Engineering)--Vibration, Damping (Mechanics)
Format: Document (PDF)

Title: Power flow analysis of a structure subjected to distributed excitation.
Creator: Cimerman, Benjamin Pierre., Florida Atlantic University, Cuschieri, Joseph M.
Abstract/Description: An analytical investigation based on the Power Flow Method is presented for the prediction of vibrational Power Flow in simple connected structures subjected to various forms of distributed excitations. The principle of the power flow method consists of dividing the global structure into a series of substructures which can be analyzed independently and then coupled through the boundary conditions. Power flow expressions are derived for an L-shaped plate structure, subjected to any form of...
Show moreAn analytical investigation based on the Power Flow Method is presented for the prediction of vibrational Power Flow in simple connected structures subjected to various forms of distributed excitations. The principle of the power flow method consists of dividing the global structure into a series of substructures which can be analyzed independently and then coupled through the boundary conditions. Power flow expressions are derived for an L-shaped plate structure, subjected to any form of distributed mechanical excitation or excited by an acoustic plane wave. In the latter case air loading is considered to have a significant effect on the power input to the structure. Fluid-structure interaction considerations lead to the derivation of a corrected mode shape for the normal velocity, and the determination of the scattered pressure components in the expressions for the Power Flow.
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Date Issued: 1990
PURL: http://purl.flvc.org/fcla/dt/14578
Subject Headings: Structural dynamics, Plates (Engineering)--Vibration
Format: Document (PDF)

Title: Weight function approach for stress analysis of the surface crack in a finite plate subjected to nonuniform stress fields.
Creator: Jani, Jayant Shivkumar., Florida Atlantic University, Arockiasamy, Madasamy, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: The effects of various nonuniform stress fields on the stress intensity factors for the semi-elliptic surface crack (three-dimensional problem) in a finite plate are determined using the weight function approach. The formulation satisfies the linear elastic fracture mechanics criteria and the principle of conservation of energy. Based on the knowledge of stress intensity solutions for the reference load/stress system, the expression for the crack opening displacement function for the surface...
Show moreThe effects of various nonuniform stress fields on the stress intensity factors for the semi-elliptic surface crack (three-dimensional problem) in a finite plate are determined using the weight function approach. The formulation satisfies the linear elastic fracture mechanics criteria and the principle of conservation of energy. Based on the knowledge of stress intensity solutions for the reference load/stress system, the expression for the crack opening displacement function for the surface crack is derived. Using the crack opening displacement function and the reference stress intensity factor, the three-dimensional weight functions and subsequently the stress intensity solutions for the surface crack subjected to nonuniform stress fields are derived. The formulation is then applied to determine the effects of linear, quadratic, cubic, and pure bending stress fields on the stress intensity factor for the surface crack in a finite plate. In the initial stage of the study a two-dimensional problem of an edge-crack emanating from the weld-toe in a T-joint is considered. The effect of parameters such as plate thickness, weld-toe radius, and weld-flank angle on the stress intensity factor for an edge-crack is studied. Finite element analyses of the welded T-joints are performed to study the effects of plate thickness, weld-toe radius and the weld-flank angle on the local stress distribution. The ratio of plate thickness to weld-toe radius ranging from 13.09 to 153.93, and the weld-flank angles of 30, 45, and 60 degrees are considered in the analyses. Based on the results from FEM analyses, a parametric equation for the local stress concentration factor and a polynomial expression for the local stress distribution across the plate thickness are derived using the method of least squares and the polynomial curve-fitting technique.
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Date Issued: 1990
PURL: http://purl.flvc.org/fcla/dt/12254
Subject Headings: Strains and stresses, Plates (Engineering), Fracture mechanics
Format: Document (PDF)

Title: VIBRATION ANALYSIS OF RECTANGULAR PLATES WITH COMPLETE AND PARTIAL CONSTRAINED-LAYER DAMPING TREATMENTS.
Creator: HSU, HONG-YUAN., Florida Atlantic University, Stevens, Karl K.
Abstract/Description: A theoretical analysis for predicting the system loss factors and natural frequencies of rectangular plates with complete and partial constrained-layer damping treatments has been presented. This analysis is based upon an energy approach to the free vibration of plates. Results predicted were compared with those from experiments. Satisfactory agreement has been reached. Both the theoretical and the experimental results presented in this thesis indicate clearly that partial constrained-layer...
Show moreA theoretical analysis for predicting the system loss factors and natural frequencies of rectangular plates with complete and partial constrained-layer damping treatments has been presented. This analysis is based upon an energy approach to the free vibration of plates. Results predicted were compared with those from experiments. Satisfactory agreement has been reached. Both the theoretical and the experimental results presented in this thesis indicate clearly that partial constrained-layer damping treatments can provide effective, or even superior, amounts of damping, and that their use can lead to significant savings in material costs and weight.
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Date Issued: 1983
PURL: http://purl.flvc.org/fcla/dt/14160
Subject Headings: Damping (Mechanics), Vibration, Plates (Engineering)--Vibration
Format: Document (PDF)

Title: A METHOD OF ANALYSIS FOR EVALUATING THE EFFECTIVENESS OF PARTIAL DAMPING LAYER TREATMENTS FOR SQUARE PLATES.
Creator: KUNG, CHUN-HUA., Florida Atlantic University, Stevens, Karl K., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: An energy method for predicting the natural frequency and loss factor for square plates with partial and complete coatings is developed. Both simply-supported and edge-fixed bonndary conditions are considered. An impulse testing technique is used to provide an experimental verification of the analysis for the case of an edge-fixed square plate. The analytical and experimental results are in close agreement, and indicate that partial coatings can provide effective damping treatments.
Date Issued: 1981
PURL: http://purl.flvc.org/fcla/dt/14045
Subject Headings: Plates (Engineering)--Vibration, Damping (Mechanics)
Format: Document (PDF)

Title: Dynamic response of plate structures to external excitations.
Creator: Mani, George., Florida Atlantic University, Yong, Yan, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: The dynamic response of plate structures composed of rigidly connected thin plates subjected to point loads is studied. The finite strip method combined with a new approach for analyzing periodic structures is utilized to obtain substantial reduction in computational efforts. Each strip with various boundary conditions is treated as a waveguide capable of transmitting different wave motions. Wave scattering matrices are defined to characterize wave motions at boundaries, intersection of...
Show moreThe dynamic response of plate structures composed of rigidly connected thin plates subjected to point loads is studied. The finite strip method combined with a new approach for analyzing periodic structures is utilized to obtain substantial reduction in computational efforts. Each strip with various boundary conditions is treated as a waveguide capable of transmitting different wave motions. Wave scattering matrices are defined to characterize wave motions at boundaries, intersection of plates and where type of wave guides are changed. The results obtained from the application of the approach on various plate configurations are presented and discussed.
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Date Issued: 1990
PURL: http://purl.flvc.org/fcla/dt/14661
Subject Headings: Plates (Engineering)--Vibration, Finite strip method, Structural analysis (Engineering)
Format: Document (PDF)

Title: Interaction of acoustic waves generated by coupled finite fluid-loaded plates.
Creator: Kaina, Rachid., Florida Atlantic University, Cuschieri, Joseph M., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: The response of fluid-loaded plates has been extensively studied in the past. However, most of the work deals with either infinite plates or finite plates with particular boundary conditions and the results are generally presented only in the limit of small wavelengths compared with the dimensions of the plates. Furthermore, the problem of coupled finite plates where both the acoustic interaction and structural interaction are included in the solution has not been considered. In this...
Show moreThe response of fluid-loaded plates has been extensively studied in the past. However, most of the work deals with either infinite plates or finite plates with particular boundary conditions and the results are generally presented only in the limit of small wavelengths compared with the dimensions of the plates. Furthermore, the problem of coupled finite plates where both the acoustic interaction and structural interaction are included in the solution has not been considered. In this dissertation the response of two coupled finite plates set in two alternative configurations is considered. The plates are simply supported on two edges, with arbitrary boundary conditions on the remaining two edges. The solutions obtained for the response of the plates include both the structural interaction at the common junction and the acoustic interaction due to the scattered pressure from each of the two plates. The results are presented in terms of the vibrational power flow into and out of each plate component. The solution is based on a formulation developed in the wavenumber domain combined with the Mobility Power Flow method. Using this approach, different substructural elements coupled under different boundary conditions to form a complex global structure can be considered. The detailed spatial and temporal scales of the structure response are not lost when using this method. In obtaining the solution for the scattering from the fluid-loaded plates, a modal decomposition in the direction normal to the simply supported edge is used. A spatial Fourier-transform decomposition is used in the other direction. Due to the finiteness of the plate, eight unknowns parameters are obtained in the transformed result. The solution for these eight unknown parameters is obtained from the boundary conditions and the condition that the response must remain finite. Two analytical approaches are used to solve the final plate integral equation. The first approach consists of an approximation method which obtains a solution based on the solution of the corresponding infinite plate problem. The second approach is a more accurate solution based on the Projection Method for the solution of integral equations. Both of the approaches used in the solution provide accurate predictions at high frequencies. At low frequencies especially for low structural damping or for heavy fluid loading, only the Projection Method gives reliable results. This is attributed to the fact that at low frequencies, the influence of the edges of the plates on the scattering is significant. The overall results obtained from this analysis indicate that the fluid loading and the plate characteristics have a significant influence on the acoustic scattering properties, especially in the case of heavy fluid loading. The application of the method to coupled fluid-loaded plates indicates that the junction enhances the scattering properties. The acoustical interaction between the coupled plates increases the contribution to scattering from subsonic wavenumber components. In the absence of the interaction, only supersonic wavenumbers contribute to the scattering. Inclusion of acousticlal interaction requires both supersonic and subsonic components. The significance of the contribution from the subsonic wavenumber components is dependent on the type of the fluid loading.
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Date Issued: 1993
PURL: http://purl.flvc.org/fcla/dt/12341
Subject Headings: Finite element method, Plates (Engineering), Acoustic emission, Sound--Transmission
Format: Document (PDF)

Title: Vibration tailoring of inhomogeneous beams and circular plates.
Creator: Pentaras, Demetris., Florida Atlantic University, Elishakoff, Isaac, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: The vibrational behavior of inhomogeneous beams and circular plates is studied, utilizing the semi-inverse method developed by I. Elishakoff and extensively discussed in his recent monograph (2005). The main thread of his methodology is that the knowledge of the mode shape is postulated. The candidate mode shapes can be adopted from relevant static, dynamic or buckling problems. In this study, the exact mode shapes are sought as polynomial functions, in the context of vibration tailoring, i.e...
Show moreThe vibrational behavior of inhomogeneous beams and circular plates is studied, utilizing the semi-inverse method developed by I. Elishakoff and extensively discussed in his recent monograph (2005). The main thread of his methodology is that the knowledge of the mode shape is postulated. The candidate mode shapes can be adopted from relevant static, dynamic or buckling problems. In this study, the exact mode shapes are sought as polynomial functions, in the context of vibration tailoring, i.e. designing the structure that possesses the pre-specified value. Apparently for the first time in the literature, several closed-form solutions for vibration tailoring have been derived for vibrating inhomogeneous beams and circular plates. Twelve new closed-form solutions for vibration tailoring have been derived for an inhomogeneous polar orthotropic plate that is either clamped or simply supported around its circumference. Also, the vibration tailoring of a polar orthotropic circular plate with translational spring is analyzed. There is considerable potential of utilizing the developed method for design of functionally graded materials.
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Date Issued: 2006
PURL: http://purl.flvc.org/fcla/dt/13344
Subject Headings: Acoustical engineering, Plates (Engineering)--Vibration--Mathematical models, Buckling (Mechanics), Structural analysis
Format: Document (PDF)

Title: Mobility power flow analysis of an infinite cylindrical shell with an enclosed plate discontinuity.
Creator: Buchmann, Patrick Pierre., Florida Atlantic University, Cuschieri, Joseph M.
Abstract/Description: A mobility power flow approach is used to study the response of an infinitely-long cylindrical shell with an internal plate discontinuity. The shell is excited by either a ring radial force or by a plane acoustic wave. The junction between the shell and the internal plate is assumed to be radially pinned such that in-plane waves of the plate can be neglected. The junction forces are expressed in terms of the mobility functions of the plate and the shell. From knowledge of the junction forces...
Show moreA mobility power flow approach is used to study the response of an infinitely-long cylindrical shell with an internal plate discontinuity. The shell is excited by either a ring radial force or by a plane acoustic wave. The junction between the shell and the internal plate is assumed to be radially pinned such that in-plane waves of the plate can be neglected. The junction forces are expressed in terms of the mobility functions of the plate and the shell. From knowledge of the junction forces and velocities, the power input, the power flow from the shell to the plate, the shell response and the radiated far-field scattered pressure are determined for the circumferential mode n = 0. The results show how the energy propagates from one structure to the other, and present a very clear picture of the characteristics of the scattering pattern from the junction forces.
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Date Issued: 1994
PURL: http://purl.flvc.org/fcla/dt/15113
Subject Headings: Shells (Engineering)--Vibration, Plates (Engineering)--Vibration, Structural dynamics, Vibration
Format: Document (PDF)

Title: Vibration, buckling and impact of carbon nanotubes.
Creator: Pentaras, Demetris., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: Natural frequencies of the double and triple-walled carbon nanotubes are determined exactly and approximately for both types. Approximate solutions are found by using Bubnov-Galerkin and Petrov-Galerkin methods. For the first time explicit expressions are obtained for the natural frequencies of double and triple-walled carbon nanotubes for different combinations of boundary conditions. Comparison of the results with recent studies shows that the above methods constitute quick and effective...
Show moreNatural frequencies of the double and triple-walled carbon nanotubes are determined exactly and approximately for both types. Approximate solutions are found by using Bubnov-Galerkin and Petrov-Galerkin methods. For the first time explicit expressions are obtained for the natural frequencies of double and triple-walled carbon nanotubes for different combinations of boundary conditions. Comparison of the results with recent studies shows that the above methods constitute quick and effective alternative techniques to exact solution for studying the vibration properties of carbon nanotubes. The natural frequencies of the clamped-clamped double-walled carbon nanotubes are obtained; exact solution is provided and compared with the solution reported in the literature. In contrast to earlier investigation, an analytical criterion is derived to establish the behavior of the roots of the characteristic equation. Approximate Bubnov-Galerkin solution is also obtained to compare natural frequencies at the lower end of the spectrum. Simplified version of the Bresse-Timoshenko theory that incorporates the shear deformation and the rotary inertia is proposed for free vibration study of double-walled carbon nanotubes. It is demonstrated that the suggested set yields extremely accurate results for the lower spectrum of double-walled carbon nanotube. The natural frequencies of double-walled carbon nanotubes based on simplified versions of Donnell shell theory are also obtained. The buckling behavior of the double-walled carbon nanotubes under various boundary conditions is studied. First, the case of the simply supported double-walled carbon nanotubes at both ends is considered which is amenable to exact solution., Then, approximate methods of Bubnov-Galerkin and Petrov-Galerkin are utilized to check the efficacy of these approximations for the simply supported double-walled carbon nanotubes. Once the extreme accuracy is demonstrated for simply supported conditions, the approximate techniques are applied to two other cases of the boundary conditions, namely to clamped-clamped and simply supported-clamped double-walled carbon nanotubes. For the first time in the literature approximate expression for the buckling loads are reported for these boundary conditions. The dynamic deflection of a single-walled carbon nanotube under impact loading is analyzed by following a recently study reported on the energy absorption capacity of carbon nanotubes under ballistic impact.
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Date Issued: 2009
PURL: http://purl.flvc.org/FAU/186764
Subject Headings: Nanostructured materials, Buckling (Mechanics), Plates (Engineering), Vibration, Mathematical models, Structural analysis
Format: Document (PDF)

Title: Modal analysis of plates with uncertain properties: Theory and applications.
Creator: Wu, Jingshu., Florida Atlantic University, Stevens, Karl K., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: This dissertation is concerned with modal analysis of plates with properties which vary over the structures. The uncertain geometric and material parameters are treated as random fields which are discretized over individual regions by using a local averaging technique. These discretized properties are then combined with a random perturbation procedure based upon traditional finite element methods. The result is a stochastic finite element method (SFEM) program for modal analysis of plates....
Show moreThis dissertation is concerned with modal analysis of plates with properties which vary over the structures. The uncertain geometric and material parameters are treated as random fields which are discretized over individual regions by using a local averaging technique. These discretized properties are then combined with a random perturbation procedure based upon traditional finite element methods. The result is a stochastic finite element method (SFEM) program for modal analysis of plates. This SFEM method is applied to two problems areas. The first application is to provide a new approach for modal analysis of printed circuit boards wherein the circuit board is modeled as an elastic plate with random spatial variation of its properties. The SFEM program is used to predict the effect of this variation on the natural frequencies and mode shapes of the board. Predicted results are compared with those obtained from modal testing of a circuit board. It is shown that variations between the measured and predicted modal parameters can be accounted for by small random variations in the board properties. This approach offers a simple, realistic, and cost-effective way for prediction of board modal properties. The second application is on vibration control of plates by application of surface viscoelastic damping treatments. Existing works generally treat the geometric and material properties of the damping layer as deterministic parameters, although uncertainties in the values of these parameters are commonplace. No work has been done regarding surface damping treatments with uncertain properties. In this thesis, the modal properties of plates with random spatial variation of the damping layer properties are investigated. The effects of this variation on the system natural frequencies, modal loss factors, and mode shapes are calculated by the SFEM program developed. Results are presented for a cantilever aluminum plate with complete PVC surface damping treatment with uncertain properties. In the SFEM modeling of both PC boards and plates with surface damping treatments, the effects on the system eigenvalues/eigenvectors of the correlation distance of the random property field, the correlation constant between the random fluctuations, and the magnitude of the random property variations, are investigated.
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Date Issued: 1993
PURL: http://purl.flvc.org/fcla/dt/12335
Subject Headings: Modal analysis, Stochastic processes, Finite element method, Plates (Engineering)--Testing
Format: Document (PDF)

Title: A perturbation method for the vibration analysis of beams and plates with free-layer damping treatments.
Creator: Shen, Sueming, Florida Atlantic University, Stevens, Karl K., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: The feasibility of using structural modification techniques to determine the effect of added viscoelastic damping treatments on the modal properties of a distinct eigenvalue system and a degenerate system is investigated. Linear perturbation equations for the changes introduced into the system eigenproperties are derived and applied to several examples involving the flexural vibration of beams and square plates with varying degrees of damping treatment. Both large and small perturbations are...
Show moreThe feasibility of using structural modification techniques to determine the effect of added viscoelastic damping treatments on the modal properties of a distinct eigenvalue system and a degenerate system is investigated. Linear perturbation equations for the changes introduced into the system eigenproperties are derived and applied to several examples involving the flexural vibration of beams and square plates with varying degrees of damping treatment. Both large and small perturbations are considered. An FEM code has been developed to compute the dynamic system parameters which are subsequently used in an iterative method to determine the modal properties. The perturbation approach described can accommodate temperature and frequency-dependent material properties, and the procedures involved are illustrated in the examples considered. Results obtained for these examples are compared with those available from closed form or finite element solutions, or from experiments. Excellent agreement of the results of the present method with those of other contemporary methods demonstrates the validity, overall accuracy, efficiency and convergence rate of this technique. The perturbation approach appears to be particularly well suited for systems with temperature and frequency dependent material properties, and for design situations where a number of damping configurations must be investigated.
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Date Issued: 1989
PURL: http://purl.flvc.org/fcla/dt/12239
Subject Headings: Girders--Vibration, Plates (Engineering)--Vibration, Perturbation (Mathematics), Damping (Mechanics)
Format: Document (PDF)

Plates (Engineering)--Vibration (13)	+ -
Damping (Mechanics) (5)	+ -
Plates (Engineering) (3)	+ -
Vibration (3)	+ -
Acoustical engineering (2)	+ -

Buckling (Mechanics) (2)	+ -
Finite element method (2)	+ -
Structural analysis (2)	+ -
Structural dynamics (2)	+ -
Acoustic emission (1)	+ -
Finite strip method (1)	+ -
Fracture mechanics (1)	+ -
Girders--Vibration (1)	+ -
Mathematical models (1)	+ -
Modal analysis (1)	+ -
Nanostructured materials (1)	+ -
Perturbation (Mathematics) (1)	+ -
Plates (Engineering)--Testing (1)	+ -
Plates (Engineering)--Vibration--Mathematical models (1)	+ -
Shells (Engineering)--Vibration (1)	+ -
Sound--Transmission (1)	+ -
Stochastic processes (1)	+ -
Strains and stresses (1)	+ -
Structural analysis (Engineering) (1)	+ -

Florida Atlantic University (17)	+ -
College of Engineering and Computer Science (11)	+ -
Department of Ocean and Mechanical Engineering (11)	+ -
Stevens, Karl K. (7)	+ -
Cuschieri, Joseph M. (5)	+ -

Pentaras, Demetris. (2)	+ -
Arockiasamy, Madasamy (1)	+ -
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