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A Novel Exact Plate Theory for Bending Vibrations Based on the Partial Differential Operator Theory

Author

Listed:
  • Chuanping Zhou

    (School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China
    School of Mechatronics Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
    Hangzhou Changchuan Technology Co., Ltd., Hangzhou 310018, China)

  • Maofa Wang

    (School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Xiao Han

    (Hangzhou Changchuan Technology Co., Ltd., Hangzhou 310018, China)

  • Huanhuan Xue

    (School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Jing Ni

    (School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China)

  • Weihua Zhou

    (College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China)

Abstract

Thick wall structures are usually applied at a highly reduced frequency. It is crucial to study the refined dynamic modeling of a thick plate, as it is directly related to the dynamic mechanical characteristics of an engineering structure or device, elastic wave scattering and dynamic stress concentration, and motion stability and dynamic control of a distributed parameter system. In this paper, based on the partial differential operator theory, an exact elasto-dynamics theory without assumptions for bending vibrations is presented by using the formal solution proposed by Boussinesq–Galerkin, and its dynamic equations are obtained under appropriate gauge conditions. The exact plate theory is then compared with other theories of plates. Since the derivation of the dynamic equation is conducted without any prior assumption, the proposed dynamic equation of plates is more exact and can be applied to a wider frequency range and greater thickness.

Suggested Citation

  • Chuanping Zhou & Maofa Wang & Xiao Han & Huanhuan Xue & Jing Ni & Weihua Zhou, 2021. "A Novel Exact Plate Theory for Bending Vibrations Based on the Partial Differential Operator Theory," Mathematics, MDPI, vol. 9(16), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1920-:d:613156
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