Vibration analysis of FGM anisogrid lattice plates with one width fold based on the continuous model using the GDQE method

This research tests the idea of folding on the free vibration response of anisogrid lattice plates. It is assumed that the oblique and straight ribs with functionally graded materials (FGMs) construct the lattice plate. The stiffness and mass of the whole plate are computed by employing the global continuous model based on the shear deformable orthotropic plates. Then a width fold is created in the plate to check its effect on improving the system's natural frequencies. An element-based 2D generalized differential quadrature method recently developed solves this problem. This method divides the physical domain into simple domains (patching) and distributes a series of nodes on each patch (quadrature scheme). The motion equations of each patch are derived using Hamilton's principle. Next, the displacement and stress resultant continuity conditions are satisfied between common nodes. After that, the obtained global equations are solved, and the natural frequencies of such structures are calculated. After validating the response with the available literature, the influence of composite characteristics and geometry on the folded FGM lattice plate is distinguished.