Free and forced vibration analysis of tri-directional functionally graded porous doubly-curved nanoshells integrated with magneto-electro-elastic layers

This paper introduces, for the first time, a meshfree approach to examine the natural and forced vibration properties of a tri-directional functionally graded porous doubly-curved nanoshell, which incorporates magneto-electro-elastic layers, situated on a visco-elastic foundation. The shell is composed of three different layers of materials, including a core layer made of tri-directional functionally graded porous material and two surface layers made of magneto-electro-elastic materials. The equilibrium equations of the nanoshell are formulated using the higher-order shear theory and the nonlocal elastic theory, and then the meshfree method and Newmark’s direct integration technique are used to ascertain the transient reactions of the nanoshell. The unique point of this study is that the investigated nonlocal coefficients vary in space like other mechanical properties of the material. A series of numerical comparisons is performed to assess the model and method’s performance, followed by a set of numerical studies to analyze the impact of input parameters on the shell’s natural and forced vibration responses. These results are expected to yield specific mechanical insights into the magneto-mechanical coupling of nanometer-scale shell structures and materials with multi-directionally varying mechanical properties that include magneto-elastic-elastic layers, thereby aiding in the computational design of practical micro/nanoelectromechanical structures.