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Investigating the thermal environment effects on geometrically nonlinear vibration of smart functionally graded plates

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Abstract

An analytical solution for a sandwich circular FGM plate coupled with piezoelectric layers under one-dimensional heat conduction is presented. All materials of the device may be of any functional gradients in the direction of thickness. The solution exactly satisfies all the equilibrium conditions and continuity conditions for the stress, displacement and electric displacement as well as electric potential on the interfaces between adjacency layers. A nonlinear static problem is solved first to determine the initial stress state and pre-vibration deformations of the FG plate that is subjected to in-plane forces and applied actuator voltage in thermal environment in the case of simply supported boundary conditions. By adding an incremental dynamic state to the pre-vibration state, the differential equations that govern the nonlinear vibration behavior of pre-stressed piezoelectric coupled FGM plates are derived. The role of thermal environment as well as control effects on nonlinear static deflections and natural frequencies imposed by the piezoelectric actuators using high input voltages are investigated. Numerical examples are provided and simulation results are discussed. Numerical results for FGM plates with a mixture of metal and ceramic are presented in dimensionless forms. The good agreement between the results of this paper and those of the finite element (FE) analyses validated the presented approach. In a parametric study the emphasis is placed on investigating the effect of varying the applied actuator voltage and thermal environment as well as gradient index of FG plate on the dynamics and control characteristics of the structure.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Tehran, Tehran, Iran

    Farzad Ebrahimi, Abbas Rastgoo & Mansoor Nikkhah Bahrami

Authors
  1. Farzad Ebrahimi
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  2. Abbas Rastgoo
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  3. Mansoor Nikkhah Bahrami
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Correspondence to Farzad Ebrahimi.

Additional information

This paper was recommended for publication in revised form by Associate Editor Eung-Soo Shin

Farzad Ebrahimi received his B.S. and M.S. in Mechanical Engineering from the University of Tehran, Iran. He is currently working on his Ph.D. thesis under the title of “Vibration analysis of smart functionally graded plates” at the Smart Materials and Structures Lab in the Faculty of Mechanical Engineering of the University of Tehran. His research interests include vibration analysis of plates and shells, smart materials and structures and functionally graded materials.

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Ebrahimi, F., Rastgoo, A. & Bahrami, M.N. Investigating the thermal environment effects on geometrically nonlinear vibration of smart functionally graded plates. J Mech Sci Technol 24, 775–791 (2010). https://doi.org/10.1007/s12206-010-0102-4

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  • DOI: https://doi.org/10.1007/s12206-010-0102-4

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