Current Search: Lin, Y. K. (x)
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 Title
 Stochastic analysis of an ecosystem of two competing species.
 Creator
 Cai, GuoQiang, Lin, Y. K.
 Date Issued
 200608
 PURL
 http://purl.flvc.org/fau/fd/FAUIR000098
 Format
 Citation
 Title
 Deterministic, stochastic and convex analyses of one and twodimensional periodic structures.
 Creator
 Zhu, Liping., Florida Atlantic University, Lin, Y. K., Elishakoff, Isaac, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

The periodic structures considered in the dissertation are onedimensional periodic multispan beams, and twodimensional periodic grillages with elastic interior supports. The following specific topics are included: (1) Deterministic VibrationExact solutions are obtained for free vibrations of both multispan beams and grillages, by utilizing the wave propagation concept. The wave motions at the periodic supports/nodes are investigated and the dispersion equations are derived from which...
Show moreThe periodic structures considered in the dissertation are onedimensional periodic multispan beams, and twodimensional periodic grillages with elastic interior supports. The following specific topics are included: (1) Deterministic VibrationExact solutions are obtained for free vibrations of both multispan beams and grillages, by utilizing the wave propagation concept. The wave motions at the periodic supports/nodes are investigated and the dispersion equations are derived from which the natural frequencies of the periodic structures are determined. The emphasis is placed on the calculation of mode shapes of both types of periodic structures. The general expressions for mode shapes with various boundary conditions are obtained. These mode shapes are used to evaluate the exact dynamic response to a convected harmonic loading. (2) Stochastic VibrationA multispan beam under stochastic acoustic loading is considered. The exact analytical expressions for the spectral densities are derived for both displacement and bending moment by using the normal mode approach. Nonlinear vibration of a multispan beam with axial restraint and initial imperfection are also investigated. In the latter case, the external excitation is idealized as a Gaussian white nose. An expression for the joint probability density function in the generalized coordinates is obtained and used to evaluate the mean square response of a multispan beam system. (3) Convex Modeling of Uncertain Excitation FieldIt is assumed that the parameters of the stochastic excitation field are uncertain and belong to a multidimensional convex set. A new approach is developed to determine the multidimensional ellipsoidal convex set with a minimum volume. The most and least favorable responses of a multispan beam are then determined for such a convex set, corresponding to a stochastic acoustic field. The procedure is illustrated in several examples.
Show less  Date Issued
 1994
 PURL
 http://purl.flvc.org/fcla/dt/12366
 Subject Headings
 Grillages (Structural engineering), GirdersVibration, Wavemotion, Theory of, Vibration
 Format
 Document (PDF)
 Title
 Nonlinear stochastic systems.
 Creator
 Cai, GuoQiang, Florida Atlantic University, Lin, Y. K., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

This thesis is concerned with nonlinear dynamical systems subject to random or combined random and deterministic excitations. To this end, a systematic procedure is first developed to obtain the exact stationary probability density for the response of a nonlinear system under both additive and multiplicative excitations of Gaussian white noises. This procedure is applicable to a class of systems called the class of generalized stationary potential. The basic idea is to separate the...
Show moreThis thesis is concerned with nonlinear dynamical systems subject to random or combined random and deterministic excitations. To this end, a systematic procedure is first developed to obtain the exact stationary probability density for the response of a nonlinear system under both additive and multiplicative excitations of Gaussian white noises. This procedure is applicable to a class of systems called the class of generalized stationary potential. The basic idea is to separate the circulatory probability flow from the noncirculatory flow, thus obtaining two sets of equations for the probability potential. It is shown that previously published exact solutions are special cases of this class. For those nonlinear systems not belonging to the class of generalized stationary potential, an approximate solution technique is developed on the basis of weighted residuals. The original system is replaced by the closest system belonging to the class of generalized stationary potential, in the sense that the statistically weighted residuals are zero for some suitably selected weighting functions. The consistency of the approximation technique is proved in terms of certain statistical moments. The above exact and approximate solution techniques are extended to two types of nonlinear systems: one subjected to nonGaussian impulsive noise excitations and another subjected to combined harmonic and broadband random excitations. Approximation procedures are devised to obtain stationary probabilistic solutions for these two types of problems. Monte Carlo simulations are performed to substantiate the accuracy of the approximate solution procedures.
Show less  Date Issued
 1992
 PURL
 http://purl.flvc.org/fcla/dt/12293
 Subject Headings
 Nonlinear theories, Stochastic systems, Stochastic processes
 Format
 Document (PDF)
 Title
 Numerical path integration of stochastic systems.
 Creator
 Yu, Jinshou., Florida Atlantic University, Lin, Y. K., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

The present dissertation is focused on the numerical method of path integration for stochastic systems. The existing procedures of numerical path integration are reexamined. A comparison study is made of the results obtained using various interpolation schemes. The amounts of computation time and relative accuracies of the existing procedures are tested with different mesh sizes and different time step sizes. A new numerical procedure based on GaussLegendre integration formula is proposed,...
Show moreThe present dissertation is focused on the numerical method of path integration for stochastic systems. The existing procedures of numerical path integration are reexamined. A comparison study is made of the results obtained using various interpolation schemes. The amounts of computation time and relative accuracies of the existing procedures are tested with different mesh sizes and different time step sizes. A new numerical procedure based on GaussLegendre integration formula is proposed, which requires no explicit numerical interpolation. The probability evolution is represented in terms of the transition probabilities among Gauss points in various subintervals. Each transition probability is assumed to be Gaussian, and it can be obtained from the moment equations. Gaussian closure is used to truncate the moment equations in the case of a nonlinear system. The computation parameters of the new procedure, such as size of timestep and number of subintervals, can be determined in a systematic manner. The approximate Gaussianity of the transition probability obtained from the moment equations is first tested by comparing it with the simulation results, from which a proper timestep size is selected. The standard deviation of the transition probability in each direction of the state space can then be obtained from the moment equations, and is used to determine the size of the subintervals in that direction. The new numerical path integration procedure is applied to several onedimensional and twodimensional stochastic systems, for which the responses are homogeneous Markov processes. It is shown that the new procedure is not only accurate and efficient, but also numerically stable and highly adaptable. The new procedure is also applied to a nonlinear stochastic system subjected to both sinusoidal and random excitations. The system response in this case is a nonhomogeneous Markov process. The algorithm is adapted for this case, so that recomputation of the transition probability density at every time step can be avoided.
Show less  Date Issued
 1997
 PURL
 http://purl.flvc.org/fcla/dt/12506
 Subject Headings
 Stochastic systems, Numerical integration, Markov processes
 Format
 Document (PDF)
 Title
 Theoretical and experimental investigations of motion stability of longspan bridges in turbulent flow.
 Creator
 Li, Qiang, Florida Atlantic University, Lin, Y. K., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

The motion stability of longspan bridges under turbulent wind is studied. A new stochastic theory, developed on the basis of a new wind turbulence model, is applied to experimentally measured bridge deck models to determine the stochastic stability boundaries. The new turbulence model has a finite meansquare value and a versatile spectral shape, and is capable of closely matching a target spectrum, such as the Dryden or the von Karman spectrum, by changing the parameters of the model. The...
Show moreThe motion stability of longspan bridges under turbulent wind is studied. A new stochastic theory, developed on the basis of a new wind turbulence model, is applied to experimentally measured bridge deck models to determine the stochastic stability boundaries. The new turbulence model has a finite meansquare value and a versatile spectral shape, and is capable of closely matching a target spectrum, such as the Dryden or the von Karman spectrum, by changing the parameters of the model. The bridge motion is represented as a linear system of single degree of freedom in torsion. A bridge is generally subject to two types of wind loads: the buffeting loads and the selfexcited loads. Only the selfexcited loads are considered in the investigation, since the buffeting loads, which appear as inhomogeneous terms in the differential equation of motion, do not affect the motion stability of a linear system. In the absence of turbulence, the onset of flutter instability occurs at a critical wind velocity at which a pair of complexconjugate eigenvalues of the combined structuralfluid system becomes purely imaginary. The corresponding eigenvectors describe the interaction between the structure and the surrounding fluid. Upon the introduction of turbulence, the composition of the structural and fluid components is changed. Since the turbulence portion of the flow fluctuates randomly in time, a new state of balance between the energy inflow from fluid to structure, and the energy outflow from structure to fluid, can only be reached in the statistical sense, or equivalently, in the sense of longtime average under the ergodicity assumption. It is the random deviation from the deterministic flutter mode that renders either the stabilizing or destabilizing effect possible. The asymptotic sample stability boundary of the motion is obtained. The aerodynamic constants for the theoretical analysis are measured experimentally in a forced vibration test conducted in a water channel, with water substituting for air as the working fluid. For a particular bridge deck model, the computed stability boundary shows that the presence of turbulence in the wind flow can be either stabilizing or destabilizing depending on the peak frequency and bandwidth of the turbulence spectrum.
Show less  Date Issued
 1993
 PURL
 http://purl.flvc.org/fcla/dt/12324
 Subject Headings
 Bridges, Longspan, Turbulence
 Format
 Document (PDF)
 Title
 GALLOPING OF AN ELASTICALLY SUPPORTED BLUFF BODY IN TURBULENT FLOW.
 Creator
 Li, Qiang, Florida Atlantic University, Lin, Y. K., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

The phenomenon of flowinduced vibration is found in many engineering systems. The fluid flow generates forces on the structure that cause motion of the structure. In turn, the structural motion changes the angle of attack between the flow and the structure, hence the forces on the structure. Furthermore, turbulence generally exists in a natural fluid flow; namely, the fluid velocity contains a random part. Thus, the problem is formulated as a nonlinear system under random excitations. This...
Show moreThe phenomenon of flowinduced vibration is found in many engineering systems. The fluid flow generates forces on the structure that cause motion of the structure. In turn, the structural motion changes the angle of attack between the flow and the structure, hence the forces on the structure. Furthermore, turbulence generally exists in a natural fluid flow; namely, the fluid velocity contains a random part. Thus, the problem is formulated as a nonlinear system under random excitations. This thesis is focused on one type of motion known as galloping. A mathematical model for the motion of an elastically supported square cylinder in turbulent flow is developed. The physical nonlinear equation is converted to ideal stochastic differential equations of the Ito type using the stochastic averaging method. The probability density for the motion amplitude and the values for the most probable amplitudes are obtained for various mean flow velocities and turbulence levels.
Show less  Date Issued
 1987
 PURL
 http://purl.flvc.org/fcla/dt/14361
 Subject Headings
 Random vibrationMathematical models, Turbulence, Fluid dynamics
 Format
 Document (PDF)
 Title
 Control of response of tall multistory buildings under wind excitation.
 Creator
 Qiu, Xin., Florida Atlantic University, Lin, Y. K., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

Theoretical investigation is carried out into the extent to which floor accelerations of a windexcited tall building can be reduced by increasing damping in those components in a building which are generally regarded to be nonstructural elements, and by using active control. The wind loads are modeled as stochastic processes, which are correlationstationary in time. Only the drag wind forces are considered in the analyses. The spectral densities and crossspectral densities of two commonly...
Show moreTheoretical investigation is carried out into the extent to which floor accelerations of a windexcited tall building can be reduced by increasing damping in those components in a building which are generally regarded to be nonstructural elements, and by using active control. The wind loads are modeled as stochastic processes, which are correlationstationary in time. Only the drag wind forces are considered in the analyses. The spectral densities and crossspectral densities of two commonly used models, proposed by Davenport and by Simiu, are compared. The Davenport spectrum is used in the numerical calculation for illustration purposes. Several structural models are discussed: an ideal spatially periodic model, an ideal piecewise spatially periodic model, a nominal spatially periodic model with random disorder in periodicity, and an ideal spatially periodic model equipped with an active mass damper control system. The problems are formulated using the transfer matrix approach in the frequency domain. Analytical solutions are obtained for the spectral densities and the meansquare values of the floor accelerations and those of the active control force. Numerical examples are given for illustration.
Show less  Date Issued
 1997
 PURL
 http://purl.flvc.org/fcla/dt/12495
 Subject Headings
 Tall buildingsAerodynamics, Windpressure, Damping (Mechanics)
 Format
 Document (PDF)
 Title
 A new methodology in accelerated testing of mechanical heart valve prostheses.
 Creator
 Wu, Changfu., Florida Atlantic University, Lin, Y. K., Cai, GuoQiang, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

Mechanical heart valve (MHV) prosthesis is used commonly for clinical replacement of a diseased or dysfunctional natural valve. It is expected to operate uninterruptedly in the human chest for at least 10 years. Classified as Class III medical devices, MHVs of a new design are required by the Food and Drug Administration (FDA) to undergo accelerated durability test for up to 600 million cycles, before a premarket approval (PMA) can be considered. Knowledge of potential damage/failure...
Show moreMechanical heart valve (MHV) prosthesis is used commonly for clinical replacement of a diseased or dysfunctional natural valve. It is expected to operate uninterruptedly in the human chest for at least 10 years. Classified as Class III medical devices, MHVs of a new design are required by the Food and Drug Administration (FDA) to undergo accelerated durability test for up to 600 million cycles, before a premarket approval (PMA) can be considered. Knowledge of potential damage/failure mechanisms is of practical interest in assessing the results obtained from accelerated testing. During such tests, an MHV is subjected to higher stresses at higher cycling frequency, and to more severe hydrodynamic environment than those under normal physiological conditions. Three primary factors contributable to damage/failure of an MHV are investigated, namely, contact stresses, water hammer effect, and cavitation. Parametric study is conducted on the contactinduced damage, using the model of a ballindentation test. Four possible modes of contact damage are identified. Schemes for the selection of appropriate coating parameters to minimize contact stresses in a valve component are discussed. Experimental results of dynamic stresses on a leaflet are presented. The water hammer effect at the instant of valve closure is studied. The destructive force of cavitation is investigated, by incorporating bubble dynamics in a damage tolerance analysis. Cavitation is found to have a greater effect on potential valve damage/failure during accelerated testing. A new measure, cavitation impulse (CI), is introduced to quantify the intensity of MHV cavitation. It is defined as the area under the trace of the highfrequency pressure bursts generated by collapses of cavitation bubbles. CI is modeled as a stationary stochastic process with a discrete parameter (beats), the probability structure of which is estimated from the experimental data. Each CI accounts for both the magnitude and the timeduration of the impinging high pressure of cavitation; therefore, it correlates more closely with cavitation damage on MHV components, thus the timetofailure (life) of an MHV undergoing testing.
Show less  Date Issued
 2003
 PURL
 http://purl.flvc.org/fau/fd/FADT12077
 Subject Headings
 Heart valve prosthesis, Cavitation, Accelerated life testing
 Format
 Document (PDF)
 Title
 Stability and response of suspension bridges under turbulent wind excitation.
 Creator
 Sternberg, Alex., Florida Atlantic University, Lin, Y. K., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

This research addresses the linear flutter theory for bridges. A new model for the selfexcited loads is proposed in which oscillatory variation in the loads due to motioninduced vortex activity in the wake, is accounted for. The addition of complex exponential terms generalizes the traditional Prony series representation of the indicial function for the selfexcited loads. Turbulence in the flow direction is included in the selfexcited loads. Hence the system is parametrically excited and...
Show moreThis research addresses the linear flutter theory for bridges. A new model for the selfexcited loads is proposed in which oscillatory variation in the loads due to motioninduced vortex activity in the wake, is accounted for. The addition of complex exponential terms generalizes the traditional Prony series representation of the indicial function for the selfexcited loads. Turbulence in the flow direction is included in the selfexcited loads. Hence the system is parametrically excited and its governing equations have randomly varying coefficients. The state vector of the response is approximated by a Markov vector process. Stochastic averaging is utilized to convert the physical equations into Ito's stochastic differential equations which govern the Markov vector process. Ito's differential rule is then used to construct the equations for the second statistical moments. Motion stability of the system is interpreted as stability of the first and second statistical moments. The computed stability boundaries for the first and second moments are shown to be crucially dependent upon the coupled loads. Unfortunately, parameters for the indicial functions calculated indirectly from the frequencydomain flutter derivatives, are nonunique. Nevertheless, it can be concluded that a bridge deck that exhibits oscillatory selfexcited load behavior is generally less stable (in the mean square) than one with nonoscillatory behavior. The new model that captures the oscillatory behavior concisely, reduces the critical wind speed by more than 10%. Buffeting loads result essentially from the vertical turbulence component. In the present thesis the buffeting loads are expressed as convolution integrals, that account for past history of the fluid flow. Thus the buffeting model considered is based on unsteady aerodynamics rather than the quasisteady model that has been traditionally used in many previous analyses. The time domain unsteady buffeting response analysis, that also incorporates the randomly varying parameters of the selfexcited loads, is the first of its kind. In the illustrative examples, the unsteady buffeting effect is shown to be significant on a singledegreeoffreedom system, whereas it is comparatively less significant with a coupled twodegreeoffreedom system.
Show less  Date Issued
 1988
 PURL
 http://purl.flvc.org/fcla/dt/11921
 Subject Headings
 Suspension bridgesStability, Winds
 Format
 Document (PDF)
 Title
 Stochastic earthquake ground motion modeling.
 Creator
 Zhang, Ruichong., Florida Atlantic University, Lin, Y. K., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

A model for earthquake ground motion is developed in this dissertation using principles of geophysics and stochastics. The earth is idealized as being composed of horizontally stratified layers, with uniform physical properties for each layer. The seismic source is assumed to be the result of shear dislocation propagating on a fault line, which is further discretized into a series of point sources at equal intervals. The fundamental problem of the ground motion in a layered medium due to a...
Show moreA model for earthquake ground motion is developed in this dissertation using principles of geophysics and stochastics. The earth is idealized as being composed of horizontally stratified layers, with uniform physical properties for each layer. The seismic source is assumed to be the result of shear dislocation propagating on a fault line, which is further discretized into a series of point sources at equal intervals. The fundamental problem of the ground motion in a layered medium due to a point source at a given source location is first considered. The governing equations of threedimensional wave motion in a uniform layer are presented and solved in both Cartesian and cylindrical coordinates. Wave propagation in a multilayered medium is then analyzed in detail, in which the wave scattering matrices are introduced so that stability and accuracy in numerical calculation can be guaranteed. A detailed review of the mechanism of seismic point source is also provided. Based on the fundamental solution for a point source, an earthquake model is constructed by superposing the solutions associated with a series of point sources along a line which are activated sequentially at random times. Statistical characteristics of earthquake ground motion is then obtained by applying a generalized version of the randompulsetrain theory and its evolutionary spectral representation. Finally the effects of uneven interface on the earthquake ground motion is also analyzed using a firstorder perturbation approach.
Show less  Date Issued
 1992
 PURL
 http://purl.flvc.org/fcla/dt/12290
 Subject Headings
 Earth movements, Earthquakes, Stochastic processes
 Format
 Document (PDF)
 Title
 Response of secondary systems to seismic excitation.
 Creator
 HoLung, Joseph Anthony., Florida Atlantic University, Lin, Y. K., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

In this dissertation the response of secondary systems to seismic excitation is investigated. A secondary system is a piece of equipment or a lighter appendage to a more massive primary structure which receives external excitations indirectly through its host structure. Assumption of linear behavior for both primary and secondary system is made in most parts in the analysis. Parametric excitations due to vertical ground motion and hysteretic behavior of the primary system under severe loading...
Show moreIn this dissertation the response of secondary systems to seismic excitation is investigated. A secondary system is a piece of equipment or a lighter appendage to a more massive primary structure which receives external excitations indirectly through its host structure. Assumption of linear behavior for both primary and secondary system is made in most parts in the analysis. Parametric excitations due to vertical ground motion and hysteretic behavior of the primary system under severe loading are treated in two separate chapters. A general procedure is first developed to formulate the system of equations for a combined primarysecondary linear system in which secondary systems are attached to a primary system at an arbitrary number of locations. Successive chapters are devoted to studying the effects of different factors on the behavior of a particular type of the combined system; namely, a multistory primary structure supporting a secondary equipment, idealized as a singledegreeoffreedom linear oscillator. We list the following major findings of this study: (1) The two approximation procedures to calculate the response of a secondary system to seismic excitations developed in this dissertation are accurate and efficient, and can be applied to light or moderately heavy equipments. (2) Parametric studies suggest that greater amplification occurs as an equipment is tuned to lower building modes. (3) The equipment response is sensitive to the equipment mass, damping in the building, and the location of the equipment. (4) Soil compliancy can affect equipment response significantly. A greater number of modes should be employed when soilstructure interaction effects are important. (5) Protective devices between the equipment and the supporting floor of a building can reduce the equipment response by an order of magnitude. In this dissertation we consider cushioning devices constructed of linear, viscoelastic materials. (6) Vertical ground motion and gravity effect can both increase equipment response. (7) If a building is forced into the nonlinear regime due to intense seismic excitations, the equipment response can be quite sensitive to the parameters of the nonlinear model.
Show less  Date Issued
 1988
 PURL
 http://purl.flvc.org/fcla/dt/11915
 Subject Headings
 Seismology, Earthquake engineering
 Format
 Document (PDF)