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 Title
 Dynamic response and stability of viscoelastic structures by interval mathematics.
 Creator
 Duan, Dehe., Florida Atlantic University, Elishakoff, Isaac
 Abstract/Description

It is demonstrated in this thesis that the interval mathematics is a powerful tool to deal with uncertain phenomena especially when the uncertainty in bounded. In this thesis, we apply interval mathematics to several engineering problems, apparently for the first time in the world literature. The following topics are included: (1) The application of interval mathematics in several applied mechanics problems. A brief review of basis concepts is given, and some problems are presented to...
Show moreIt is demonstrated in this thesis that the interval mathematics is a powerful tool to deal with uncertain phenomena especially when the uncertainty in bounded. In this thesis, we apply interval mathematics to several engineering problems, apparently for the first time in the world literature. The following topics are included: (1) The application of interval mathematics in several applied mechanics problems. A brief review of basis concepts is given, and some problems are presented to illustrate the application of interval mathematics. (2) The stability and dynamic response of viscoelastic plate are studied. The effect of viscoelastic parameters on critical velocity is elucidated. (3) The application of QiuChenElishakoff theorem in uncertain string and beam problems is investigated.
Show less  Date Issued
 1994
 PURL
 http://purl.flvc.org/fcla/dt/15090
 Subject Headings
 Interval analysis (Mathematics), Viscoelasticity, Fractional calculus
 Format
 Document (PDF)
 Title
 Convex identification and nonlinear random vibration analysis of elastic and viscoelastic structures.
 Creator
 Fang, Jianjie, Florida Atlantic University, Elishakoff, Isaac, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

This dissertation deals with the identification of boundary conditions of elastic structures, and nonlinear random vibration analysis of elastic and viscoelastic structures through a new energybased equivalent linearization technique. In the part of convex identification, convex models are utilized to represent the degree of uncertainty in the boundary condition modification. This means that the identification is actually the identification of the convex model to which the actual boundary...
Show moreThis dissertation deals with the identification of boundary conditions of elastic structures, and nonlinear random vibration analysis of elastic and viscoelastic structures through a new energybased equivalent linearization technique. In the part of convex identification, convex models are utilized to represent the degree of uncertainty in the boundary condition modification. This means that the identification is actually the identification of the convex model to which the actual boundary stiffness profile belongs. Two examples are presented to illustrate the application of the method. For the beam example the finite element analysis is performed to evaluate the frequencies of a beam with any specific boundary conditions. For the plate example, the Bolotin's dynamic edge effect method, generalized by Elishakoff, is employed to determine the approximate natural frequencies and normal modes of elastically supported isotropic, uniform rectangular plates. In the part of nonlinear random analysis, first a systematic finite element analysis procedure, based on the element's energy formulation, through conventional stochastic linearization technique, is proposed. The procedure is applicable to a wide range of nonlinear random vibration problem as long as element's energy formulations are presented. Secondly, the new energybased stochastic linearization method in finite element analysis setting is developed to improve the conventional stochastic linearization technique. The entire formulation is produced in detail for the first time. The theory is applied to beam problem subjected to spacewise and timewise white noise excitations. Finally, the new energybased stochastic linearization technique is applied to treat nonlinear vibration problems of viscoelastic beams.
Show less  Date Issued
 1996
 PURL
 http://purl.flvc.org/fcla/dt/12467
 Subject Headings
 Elasticity, Viscoelasticity, Structural dynamicsMathematical models, VibrationMathematical models
 Format
 Document (PDF)