Free Vibration Analysis of Sandwich Micro Beam with Piezoelectric Based on Modified Couple Stress Theory and Surface Effects

Subject Areas : Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering

Mohammad khajekhabaz ¹ , Ali Eftekhari ² , Mohammad Hashemian ³

1 - Khomeinishahr branch, Islamic Azad Uni., Esfahan, Iran.
2 - Khomeinishahr branch, Islamic Azad Uni., Esfahan, Iran.
3 - Islamic Azad University, Khomeinishahr Branch

Received: 2018-01-14 Accepted : 2018-06-11 Published : 2018-07-11

Keywords: Free vibration analysis, Micro-beam, Modified couple stress elasticity theory, Gurtin- Murdoch surface theory,

Abstract :

In this paper, the free vibration analysis of sandwich micro beam with piezoelectric layers based on the modified couple stress and surface elasticity theories are investigated. The Hamilton’s principle is employed to derive the sandwich micro beam with piezoelectric based on modified couple stress theory incorporating with Gurtin- Murdoch surface theory. The generalized differential quadrature method is used to discretize the partial differential equation into the ordinary differential equation. The effect of various parameters such as thickness to material length scale parameter ratio, the surface residual stress, Young's modulus of surface layer, surface mass density and surface piezoelectric constant are investigated by comparing the results obtained using the modified couple and classical theories. Numerical results of this problem evaluate the effect of micro length scale parameters on natural frequency. The results show that surface parameter effects are significant when the model is small, but can be neglected with increasing model size.

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