Free and forced vibration analysis of pyramid lattice sandwich plate based on the dimensional reduction model

Abstract

Due to the high porosity and periodicity of a pyramid lattice core, the dynamic behaviors of a pyramid lattice sandwich plate (PLSP) show new characteristics. In this work, the equivalent stiffness of a PLSP was obtained by homogenizing over the unit cell, and input to an equivalent two-dimensional (2D) reduced-order model constructed from the framework of a variational asymptotic method, based on which the calculation of natural frequencies and the frequency domain analysis of forced vibration were carried out. The accuracy and efficiency of the proposed model were verified by numerical examples of free and forced vibration under different boundary conditions, including frequency domain analysis, steady-state time domain analysis, and analysis of the local field recovered from the maximum resonance response at the peak and trough times. We also investigated the influence of the pyramid lattice core’s structural parameters on the first three natural frequencies and the maximum resonance response, which can provide a useful reference for the fatigue life expectation of a PLSP under a periodic load.