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

Document Type: Research Paper


Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran


The aim of the paper is to analyze nonlinear electro-magneto vibration of a double-piezoelectric composite microplate-system (DPCMPS) based on nonlocal piezoelasticity theory. The two mi-croplates are assumed to be connected by an enclosing elastic medium which is simulated by 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 calculate mechanical properties of composite. Using nonlinear strain-displacement relations and considering charge equation for coupling between electrical and mechanical fields, the motion equations are derived based on energy method and Hamilton's principle. These equa-tions can't be solved analytically due to their nonlinear terms. Hence, 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 condition. The frequency ratio of DPCMPS is investigated 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 indicate that with increasing volume fraction of the CNTs, the frequency of the structure increases. This study might be useful for the design and smart control of nano/micro devices such as MEMS and NEMS.