Free vibration analysis of curved lattice sandwich beams

Abstract

In this paper, the effects of initial curvature and lattice core shape on the bending vibration of sandwich beams are investigated. The three-dimensional (3D) sandwich beam is simulated by combining a two-dimensional (2D) cross-sectional analysis with a one-dimensional (1D) nonlinear beam analysis. The sandwich beam is composed of two identical isotropic faces covering a lattice core. Four different lattice core structures are used to take into account the effect of core unit cell shape on the dynamic properties of the sandwich beam. The nonlinear governing equations of the sandwich beam are Discretized using a time-space scheme. Numerical results show that the lattice unit cell shape affects both in-plane and out of plane stiffness values and hence changes the dynamic behavior of the beam. Furthermore, it is observed that by changing the density ratio of the beam, modes veer away from each other at a specific value of density ratio for specific unit cell types. Moreover, the initial curvature of the beam is shown to affect the dynamics of the beam especially lower modes. Finally, it is obtained that the dynamics of the beam is different when it is initially curved or curved due to an applied end follower moment.