On the Use of a Lattice Model for Analyzing of In-Plane Vibration of Thin Plates

In this paper, a novel approach for simulating in-plane vibration of thin plates is proposed. It is based on the spectral element method (SEM) used within a lattice modeling framework. First, derivation of a frequency dependent dynamic stiffness matrix for a spectral beam element is presented. Then, the lattice modeling concept is introduced. In the model, the two-dimensional plate is discretized as a set of (one dimensional) spectral beam elements connected at the ends. The proposed approach is then used for modal analysis of rectangular plates of different aspect ratios (1 and 2) and boundary conditions (completely free and clamped). Simulated natural frequencies and modal shapes are compared to results available in the literature. It was found that the proposed model can reasonably reproduce low natural frequencies (in most cases within 10%) and modal shapes. Future work will focus on the use of the model as an aid in non-destructive testing of structures.