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

Abstract

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 …), method of determination of dynamic instability regions (Lyapunovian, perturbation, and Floquet’s methods), order of theory being applied (thin, thick, three-dimensional, 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, nonconservative 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. A review of the subject for nonconservative systems in detail will be presented in Part 2. This review paper cites 156 references.

Dynamic instability analysis of rotating delaminated tapered composite plates subjected to periodic in-plane loading

“…Sahu and Datta [22] reviewed the recent research on dynamic stability in terms of the geometry, type of loading, boundary conditions, method of analysis and method of determination of dynamic instability regions with the effect on the dynamic stability of structures under periodic loading. Lee [23] investigated the finite element dynamic stability analysis of laminated composite skew structures under uniaxial pulsating forces based on the higher-order shear deformation theory (HSDT).…”

Methodology Research of Stability of Shallow Orthotropic Shells of Double Curvature Under Dynamic Loading

“…), и исследование поведения оболочек из таких материалов является акту-альной задачей [5][6][7][8][9][10][11][12]. Основными задачами исследования оболочеч-ных конструкций при динамическом нагруже-нии являются исследования их устойчивости, прочности и колебаний, о чем свидетель-ствуют обзорные статьи и монографии [13][14][15][16][17][18][19][20].…”

Dynamical stability and parametrical vibrations of the laminated plates with complex shape

“…where U is total potential energy taking into account the influence of forces in the median plane: 11 …”

“…The use of composite materials requires complex analytical and numerical methods in order to predict accurately their response to external loading. A recent review of current developments in non-linear vibration analysis and dynamic stability of the laminated plates and shells has been presented in references [6,9,11,13,14], ets. From presented review it follows that buckling problems with non-uniform pre-buckle stress state are of special interest.…”