Stability of parametric vibrations of laminated composite plates
The dynamic stability of laminated composite plates subjected to arbitrary periodic loads is studied based on the first-order shear deformation plate theory. The in-plane load is taken to be a combination of periodic biaxial and bending stress. A set of second-order ordinary differential equations with periodic coefficients of Mathieu-Hill type is formed to determine the regions of dynamic instability based on Bolotin's method. Numerical results reveal that the dynamic instability is significantly affected by the modulus ratio, number of layer, static and dynamic load parameters. The effects of various important parameters on the instability region and dynamic instability index are investigated.
A study on the dynamic stability of plates under a follower force
Abstract In this study, a dynamic stability analysis of a plate under a follower force was performed through the finite element method based on the Kirchhoff–Love plate theory and Mindlin plate theory. Four-, nine- and 16-node quadrilateral elements were used. Through the dynamic stability analysis of a thin plate under an in-plane force and a follower force, the calculation results of these elements were compared with the analytical solutions. It is concluded from these observations that the 16-node Mindlin plate element is the best element for the dynamic stability analysis of a shear deformable plate. The dynamic stability analysis was performed for an isotropic, orthotropic and a symmetrically laminated composite plate under a pure follower force using 16-node Mindlin plate element. The effects of shear deformation and rotary inertia were investigated.
Stability of Skew Plates Subjected to Aerodynamic and In-Plane Forces
Abstract In this paper an investigation is presented into the stability of skew plates acted upon by both aerodynamic and in-plane forces simultaneously. The in-plane force is assumed to be small in magnitude compared to the aerodynamic force. Due to this small in-plane force, the system may become unstable before the aerodynamic force reaches its critical value. A finite element formulation is used to obtain the discretized system equations. The system equations are then partially uncoupled and reduced in size by the modal truncation method. Finally, the method of multiple scales is used to determine the transition curves of the system. The effects of system parameters on the boundaries of the unstable regions are studied numerically.