Open Access

ARTICLE

Effect of Residual Stresses on Wave Propagation in Adhesively Bonded Multilayered MEMS Structures

M. Kashtalyan^1,2, Y.A. Zhuk³
1 Corresponding author. E-mail: m.kashtalyan@abdn.ac.uk, tel/fax: +44-1224-272519.
2 Centre for Micro- and Nanomechanics (CEMINACS), School of Engineering, University of Aberdeen, Aberdeen, AB24 3UE, Scotland.
3 Timoshenko Institute of Mechanics, 3, Nesterov str., Kiev 03057, Ukraine.

Computer Modeling in Engineering & Sciences 2010, 57(1), 1-30. https://doi.org/10.3970/cmes.2010.057.001

Abstract

The paper investigates propagation of stationary plane longitudinal and transverse waves along the layers in adhesively bonded multilayered structures for MEMS applications in the presence of residual stresses. The multilayered structure is assumed to consist of the infinite amount of the periodically recurring layers made of two different materials possessing significantly dissimilar properties: conductive metal layer and insulating adhesive layer. It is assumed that the mechanical behaviour of both materials is nonlinear elastic and can be described with the help of the elastic Murnaghan potential depending on the three invariants of strain tensor. The problem is formulated in the framework of the three-dimensional linearized elasticity theory of finite initial deformations. The influence of the residual stresses in each layer and of the ratio of the layer thicknesses on the normalized velocity of propagation of the stationary plane wave is examined and discussed. It is found that for some multilayered structures there exist such values of the ratio of the layer thicknesses that wave velocities do not depend on the magnitude of residual stresses but are equal to the corresponding wave velocities in the unstressed structure.

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Keywords

microelectromechanical systems, multilayered structure, three-dimen -sional linearized elasticity theory, initial stresses, longitudinal wave; transverse wave; wave velocity

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