This paper reviews most of the recent research done in the field of dynamic stability/ dynamic instability/ parametric excitation /parametric resonance characteristics of structures with special attention to parametric excitation of plate and shell structures. The solution of dynamic stability problems involves derivation of the equation of motion, discretization and determination of dynamic instability regions of the structures. The purpose of this study is to review most of the recent research on dynamic stability in terms of the geometry (plates, cylindrical, spherical and conical shells), type of loading (uniaxial uniform, patch, point loading ….), boundary conditions (SSSS, SCSC, CCCC ….), method of analysis (exact, finite strip, finite difference, finite element, differential quadrature and experimental ….), the method of determination of dynamic instability regions (Lyapunovian, perturbation and Floquet’s methods ), order of theory being applied (thin, thick, 3D, nonlinear….), shell theory used (Sanders’, Love’s and Donnell’s), materials of structures (homogeneous, bimodulus, composite, FGM….) and the various complicating effects such as geometrical discontinuity, elastic support, added mass, fluid structure interactions, non-conservative loading and twisting etc. The important effects on dynamic stability of structures under periodic loading have been identified and influences of various important parameters are discussed. Review on the subject for non-conservative systems in detail will be presented in Part-2.

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Research Advances in the Dynamic Stability Behavior of Plates and Shells: 1987–2005—Part I: Conservative Systems

Dynamic stability of laminated composite plates by the finite element method

Dynamic instability of composite laminated rectangular plates and prismatic plate structures

The presented paper deals with the parametric instability behavior of a simply supported rectangular plate with a crack emanating from one edge, subjected to in-plane compressive periodic edge loading. The problem is reduced to computing the free vibration frequencies and the corresponding mode shapes and substituting them into an integral equation based formula, which leads to a compact matrix form. Once the components of this matrix are found, the rest of the computation, i.e., establishing regions of instability, buckling loads and modified frequencies, is straightforward and fast. Several plates, each with a different dimension and crack length size are analyzed using this approach. The comparison of results with those of finite element models is found to be in close agreement.

Parametric instability of edge cracked plates

Parametric instability characteristics of rectangular plates subjected to localized edge loading (compression or tension)

Convergent finite element equations for dynamic stability of plates dependent on vibration and buckling modes

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Ahmed E. Salam

Papers

Dynamic Stability of Plates by Finite Elements