A Non-uniform Equivalent Model for Free Vibration Analysis of Sandwich Composite Panels with Trapezoidal Lattice Core

Free vibration characteristics of the trapezoidal lattice sandwich composite panels are investigated based on a novel equivalent plate model.

The equivalent shear modulus and the relative density of the graded lattice core are assumed to be thickness-dependent and these material properties are calculated based on the single-cell equivalence theory and the continuity assumption. Under the framework of the higher-order shear deformation theory (HSDT), the unknown displacement functions are expressed in terms of standard Fourier series and auxiliary functions to avoid discontinuities on the edges of lattice sandwich plate. Artificial spring technique is utilized to simulate arbitrary boundary conditions and the unknown coefficients in the displacement functions are obtained by Rayleigh–Ritz variational method.

The accuracy of the present method can be verified by comparing the obtained results with FEM results and those from literature. On this basis, a detailed parametric study concerning the effect of boundary conditions, aspect ratio a/b, tilt angle θ, and lamination schemes on the vibration frequencies of the trapezoidal lattice sandwich plate is also performed.