Softening-spring nonlinearity in large amplitude vibration of unsymmetric double-layer lattice truss core sandwich beams

In recent years, many novel sandwich structures with multilayer or graded lattice truss cores that exhibited superior structural performance have been proposed. However, only limited works have studied the nonlinear behavior of sandwich structures with unsymmetric lattice truss cores. This paper aims to provide an analytical study on the nonlinear vibration of the unsymmetric double-layer lattice truss core sandwich beams (LTCSBs). The double-layer LTCSB is designed to be unsymmetric and possesses varying material property and structural geometry in each layer. In this study, six unsymmetric cases of LTCSB classified as two categories according to the midplane locations are considered. Subsequently, an analytical model for the unsymmetric double-layer LTCSB is developed based on the Allen's model and von Karman nonlinear theory. The axial displacement of the midplane of LTCSB is considered in the analytical model, therefore the proposed model is more generalized compared with previous models for the symmetric double-layer LTCSB. The Ritz method with a direct iterative procedure is applied to solve the nonlinear governing equations and determine the nonlinear frequencies for the unsymmetric double-layer LTCSB. Finally, the effects of six unsymmetric cases of LTCSBs on the nonlinear frequency ratio versus amplitude curve under three different types of boundary conditions are discussed detailly. An interesting phenomenon of softening-spring nonlinearity is found for hinged-hinged and clamped-hinged sandwich beams with large bending-extension coupling.