<p>In this paper, the nonlinear free vibration behavior of the composite functionally gradient piezoelectric semiconductor (FGPS) rectangular beam resting on the Pasternak foundation is studied on the basis of the nonlinear strain–displacement relation and the theory of piezoelectric semiconductor. The nonlinear constitutive equations are presented, and the strain energy, kinetic energy and virtual work of the composite FGPS beam are derived. On account of the condition of charge continuity and Hamilton’s principle, the governing equations of the system are obtained. The author provides several numerical examples to display the effect of the initial electron concentration, functionally gradient index, thermal load, elastic foundation parameter and geometric parameter on the nonlinear vibration frequency and damping characteristic of the composite FGPS beam. The main innovation of the paper is that the different performances between the linear vibration responses and the nonlinear vibration responses are illustrated. Also, the thermal effect has a momentous influence on the natural frequency, but an unimportant influence on the damping characteristic of the composite FGPS beam.</p>

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Nonlinear free vibration of composite functionally gradient piezoelectric semiconductor beam under thermal load

  • Yaxi Yan,
  • Changsong Zhu,
  • Xueqian Fang

摘要

In this paper, the nonlinear free vibration behavior of the composite functionally gradient piezoelectric semiconductor (FGPS) rectangular beam resting on the Pasternak foundation is studied on the basis of the nonlinear strain–displacement relation and the theory of piezoelectric semiconductor. The nonlinear constitutive equations are presented, and the strain energy, kinetic energy and virtual work of the composite FGPS beam are derived. On account of the condition of charge continuity and Hamilton’s principle, the governing equations of the system are obtained. The author provides several numerical examples to display the effect of the initial electron concentration, functionally gradient index, thermal load, elastic foundation parameter and geometric parameter on the nonlinear vibration frequency and damping characteristic of the composite FGPS beam. The main innovation of the paper is that the different performances between the linear vibration responses and the nonlinear vibration responses are illustrated. Also, the thermal effect has a momentous influence on the natural frequency, but an unimportant influence on the damping characteristic of the composite FGPS beam.