Accurate Free Vibration Analysis of Stepped Orthotropic Rectangular Cantilevered Plates Under the Framework of Symplectic Mechanics

An accurate free vibration analysis of stepped orthotropic rectangular cantilever plates is performed to obtain the natural frequencies and vibration mode shapes. Two cases of cantilever boundaries are taken into account.

A Hamiltonian-based method is employed to find analytical free vibration solutions of stepped orthotropic rectangular cantilever plates. The overall plate is divided into multiple regions with uniform thickness, and each region can be further divided into two sub-problems based on a fully sliding clamped orthotropic plate. After that, the Hamilton system is established for the equal thickness region, and analytical solutions are obtained by using the symplectic series and a superposition technique of boundary conditions.

Numerical examples illustrate the accuracy of the proposed analytical solutions and investigate the effects of key influencing factors on the free vibration characteristics of stepped orthotropic rectangular cantilever plates. Furthermore, the obtained analytical solutions may serve as benchmark solutions for the validation of numerical methods.

1. Analytical free vibration solutions of stepped orthotropic rectangular cantilever plates are obtained with the framework of symplectic mechanics.

2. Highly accurate natural frequencies and analytical vibration mode shapes are obtained simultaneously.

3. The position of clamped edge, step length ratio, step thickness ratio and number of steps are key influencing factors for the adjustment of free vibration characteristics of the stepped cantilever plate.