Nonlinear vibrations of a clamped rectangular plate with initial deflection and initial edge displacement— Part II: Experiment
TL;DR: Theoretical analyses for nonlinear vibrations of a clamped rectangular plate under a uniformly distributed periodic load, with the effect of both initial deflection and initial edge displacement taken into consideration, are presented in this paper.
Abstract: Theoretical analyses are presented for nonlinear vibrations of a clamped rectangular plate under a uniformly distributed periodic load, with the effect of both initial deflection and initial edge displacement taken into consideration The dynamic analog of the Marguerre equations is used and the steady-state solutions are obtained by first applying the Galerkin method and then the harmonic balance method Actual calculations are carried out for the square plate under the assumption of the three degrees-of-freedom system and the frequency response characteristics and typical waveforms are determined under various initial edge displacements including initially buckled cases Effects of both initial deflection and initial edge displacement on the static deflection as well as the lower natural frequencies are also clarified
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Abstract: A review of the recent developments in the analysis of laminated beams and plates with an emphasis on shear effects and buckling is presented. A discussion of various shear-deformation theories for plates and beams is given. The available theories are derived assuming a variation of either the in-plane displacement components or the stress components or both in the thickness coordinate. A review of the recently developed finite elements to analyze thin and thick laminated beams and plates is given next. These elements have been derived using the displacement methods, or the mixed methods or the hybrid methods. Recent studies on the buckling and postbuckling behavior of perfect and geometrically imperfect plates are described next. These behaviors have been studied using analytical, numerical, and experimental techniques. Finally, a review of the various studies on the delamination buckling and growth in beams and plates is given. Once again, the studies have been conducted using analytical, numerical, and experimental techniques. The energy release rates have been determined using closed-form solutions or using numerical differentiation. Mention also is made of studies on multiple delaminations and on dynamic response of composite laminates under impact loads.
490 citations
TL;DR: A review of the recent developments in the analysis of laminated beams and plates with an emphasis on vibrations and wave propagations is presented in this paper, where a significant effort has been spent on developing appropriate continuum theories for modeling the composite materials.
Abstract: A summary of the recent developments in the analysis of laminated beams and plates with an emphasis on vibrations and wave propagations in presented. First, a review of the recent studies on the free-vibration analysis of symmetrically laminated plates is given. These studies have been conducted for various geometric shapes and edge conditions. Both analytical (closed-form, Galerkin, Rayleigh-Ritz) and numerical methods have been used. Because of the importance of unsymmetrically laminated structural components in many applications, a detailed review of the various developments in the analysis of unsymmetrical ly laminated beams and plates also is given. A survey of the nonlinear vibrations of the perfect and geometrically laminated plates is presented next. It is seen that due to the bending-stretching coupling, the nonlinear behavior of the unsymmetrically laminated perfect and imperfect plates, depending upon the boundary conditions, may be hardening or softening type. Similar behavior also is observed for imperfect isotropic and laminated plates. Lastly, the developments in studying the wave propagation in laminated materials are reviewed. It is seen that a significant effort has been spent on developing appropriate continuum theories for modeling the composite materials. Some recent studies on the linear and nonlinear transient response of laminated materials also are described.
288 citations
TL;DR: In this paper, the authors investigated the nonlinear vibration of imperfect shear deformable laminated rectangular plates comprising a homogeneous substrate and two layers of functionally graded materials (FGMs).
144 citations
TL;DR: In this article, the nonlinear partial differential equations of nonlinear vibration for a functionally graded plate in a general state of non-uniform initial stress is presented, which includes the effects of transverse shear deformation and rotary inertia.
126 citations
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381 citations
TL;DR: In this paper, approximate solutions for the nonlinear bending vibrations of thin plates are presented for the cases of rectangular and circular plates subjected to various boundary conditions, and the effects of large amplitudes on both the free and forced vibrations are clarified.
Abstract: Approximate solutions for the nonlinear bending vibrations of thin plates are presented for the cases of rectangular and circular plates subjected to various boundary conditions, and the effects of large amplitudes on both the free and forced vibrations are clarified
263 citations
258 citations
TL;DR: In this paper, einfluss von Vorspannungen auf die freien und erzwungenen nichtlinearen Schwingungen von Balken and rechteckigen Platten wird mittels einer einfachen Erweiterung der Losungen fur Falle ohne VorsPannung untersucht.
Abstract: Der Einfluss von Vorspannungen auf die freien und erzwungenen nichtlinearen Schwingungen von Balken und rechteckigen Platten wird mittels einer einfachen Erweiterung der Losungen fur Falle ohne Vorspannung untersucht. Es wird eine einzige Koordinatenfunktion benutzt; es werden einfach aufgelegte und eingespannte Falle betrachtet; und die Diskussion wird auch auf den uberkritischen Bereich ausgedehnt.
208 citations
TL;DR: In this article, the authors used the dynamic analogue of the von Karman equations to study the symmetric response of a circular plate to a harmonic excitation when the frequency of the excitation is near one of the natural frequencies.
106 citations