Nonlinear Magneto-Nonlocal Vibration Analysis of Coupled Piezoelectric Micro-Plates Reinforced with Agglomerated CNTs

The aim of this article is to analyze nonlinear electro-magneto vibration of a double-piezoelectric composite microplate-system (DPCMPS) pursuant to the nonlocal piezoelasticity theory. The two microplates are assumed to be connected by an enclosing elastic medium, which is simulated by the Pasternak foundation. Both of piezoelectric composite microplates are made of poly-vinylidene fluoride (PVDF) reinforced by agglomerated carbon nanotubes (CNTs). The Mori-Tanaka model is employed to compute the mechanical properties of composite. Applying nonlinear strain-displacement relations and contemplating charge equation for coupling between electrical and mechanical fields, the motion equations are derived in consonance to the energy method and Hamilton's principle. These equations can't be solved analytically as a result of their nonlinear terms. Hence, the differential quadrature method (DQM) is employed to solve the governing differential equations for the case when all four ends are clamped supported and free electrical boundary conditions. The frequency ratio of DPCMPS is inspected for three typical vibrational states, namely, out-of-phase, in-phase and the case when one microplate is fixed in the DPCMPS. A detailed parametric study is conducted to scrutinize the influences of the small scale coefficient, stiffness of the internal elastic medium, the volume fraction of the CNTs, agglomeration and magnetic field. The results reveal that with increasing volume fraction of the CNTs, the frequency of the structure increases. This study might be beneficial for the design and smart control of nano/micro devices such as MEMS and NEMS.