Three-dimensional free vibration of arbitrarily shaped laminated micro-plates with sliding interfaces within couple stress theory

摘要

Free vibration of laminated micro plates with arbitrary geometry and boundary conditions consisting of several micro layers with free sliding/frictional sliding/perfect interfaces is of interest. The inter layer bond in the direction normal to the interfaces is perfect, and thus the corresponding displacement component is continuous across the interfaces. The mentioned in-plane interface conditions may be realized by varying the stiffness of the sliding inter layer spring of vanishing thickness. For free sliding and perfect interface conditions the stiffness -> 0 and infinity, respectively. Couple stress theory as a useful higher order continuum theory is utilized to formulate the problem. Subsequently, the corresponding Hamiltonian is presented. The three components of the displacement field in each layer are given by three distinct expressions; each expression consists of the product of a base function and three dimensional polynomials with unknown coefficients. The base functions are chosen according to the geometries of the system and the corresponding layer and to satisfy the homogeneous essential boundary conditions. For the enforcement or the displacement continuity in the direction normal to the interfaces, an appropriate series with unknown coefficients pertinent to each layer is added. The influences of the level of inter-layer imperfection and couple stress on the dynamical characteristics including the angular frequencies of free vibration and the corresponding mode shapes are addressed. (C) 2014 Elsevier Ltd. All rights reserved.