Abstract

This paper investigates electro-magneto-elastic free vibration responses of piezomagnetic cylindrical nano panel subjected to electro-magneto-mechanical loads based on third-order theory. Third-order shell theory is used for description of the displacement field. The zero transverse shear strains are obtained using the third-order displacement field. Hamilton’s principle is employed to obtain the governing equations of motion. The nano panel is subjected to a coupling of magnetic and electric loads, including a linear function along with the thickness direction and a 2D function along with the axial and circumferential directions. To account the effect of nanoscale in governing equations, the Eringen nonlocal elasticity theory is used. The numerical results are obtained to investigate the impact of significant parameters such as axial and circumferential mode numbers, the nanoscale parameter, applied electromagnetic potentials, and length-to-radius ratio. It is concluded that an increase in initial electric potential and a decrease in magnetic potential lead to an increase in natural frequencies of the nano panel.

中文翻译：

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压电纳米板高阶电磁弹性自由振动分析

摘要

本文基于三阶理论研究了压电圆柱纳米板在电磁机械载荷作用下的电磁弹性自由振动响应。三阶壳理论用于描述位移场。零横向剪切应变是使用三阶位移场获得的。哈密​​顿原理用于获得运动的控制方程。纳米面板受到磁负载和电负载的耦合，包括沿厚度方向的线性函数和沿轴向和圆周方向的二维函数。为了考虑纳米尺度在控制方程中的影响，使用了 Eringen 非局部弹性理论。获得数值结果以研究重要参数的影响，例如轴向和圆周模式数、纳米级参数、施加的电磁势和长度半径比。结论是初始电势的增加和磁势的降低导致纳米板的固有频率增加。