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Nonlinear dynamics and vibration of reinforced piezoelectric scale-dependent plates as a class of nonlinear Mathieu–Hill systems: parametric excitation analysis

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Abstract

This work is motivated by little research in the nonlinear dynamic instability of the reinforced piezoelectric nanoplates. This paper, using an analytical approach, presents bifurcations in the nonlinear dynamic instability of the reinforced piezoelectric nanoplates caused by the parametric excitation. An axial parametric load is applied to excite the system, while the reinforced piezoelectric nanoplate is under an applied electric voltage, simultaneously. The governing equations of motion for the reinforced piezoelectric nanoplate embedded on a visco-Pasternak foundation are derived using the nonlocal elasticity theory, Hamilton’s principle, and nonlinear von Karman theory. A class of nonlinear the Mathieu–Hill equation is established to determine the bifurcations and the regions of the nonlinear dynamic instability. The numerical results are performed, while the emphasis is placed on investigating the effect of the applied electric voltage, visco-Pasternak foundation coefficients, and the parametric excitation. It is found that the damping coefficient is responsible of the bifurcation point variation, while the amplitude response depends on the term of the natural frequency.

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Authors and Affiliations

  1. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Ali Shariati

  2. Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Ali Shariati

  3. Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, 3414896818, Iran

    S. Hamed S. Hosseini & Farzad Ebrahimi

  4. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    Ali Toghroli

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  1. Ali Shariati
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  3. Farzad Ebrahimi
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  4. Ali Toghroli
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Shariati, A., Hosseini, S.H.S., Ebrahimi, F. et al. Nonlinear dynamics and vibration of reinforced piezoelectric scale-dependent plates as a class of nonlinear Mathieu–Hill systems: parametric excitation analysis. Engineering with Computers 37, 2285–2301 (2021). https://doi.org/10.1007/s00366-020-00942-y

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