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Nonlinear vibrations of a polar-orthotropic thin circular plate subjected to circularly moving point load

机译：对圆形移动点载荷进行偏振正向薄圆形板的非线性振动

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摘要

Here, we formulate and study nonlinear vibrations of a thin, polar-orthotropic circular plate subjected to a circularly moving point load at a fixed radius and constant angular velocity. The governing equations and boundary conditions are obtained following Kirchhoff's plate theory, incorporating von Karman nonlinearity, and employing extended Hamilton's principle. The external damping is introduced via Rayleigh dissipation function. The governing equations are solved using mode summation procedure. The mode shapes and the natural frequencies of the polar-orthotropic circular plate are found using Frobenius series method. Mode summation procedure results in coupled nonlinear ordinary differential equations. These equations are solved using the Runge-Kutta method for time response and method of harmonic balance with the arc continuation method for frequency response. The spectrum of the undamped linear vibration response of isotropic and polarorthotropic plates exhibits natural frequencies of plates and angular velocity of the rotating load. The damped response contains the frequency of the angular velocity of the rotating load only. The nonlinear transverse vibrations of the undamped and damped plate due to rotating point load reveal frequency rich spectrums. The frequency response function shows strong modal interactions.
机译：这里，我们在固定半径和恒定角速度下制定和研究经受圆周移动点负载的薄型，偏光正圆形板的非线性振动。在Kirchhoff的盘子理论之后获得了管理方程和边界条件，纳入了von Karman非线性，并雇用延长汉密尔顿的原则。通过瑞利耗散功能引入外部阻尼。使用模式求和程序解决了管理方程。使用Frobenius串联方法发现偏振正圆形板的模式形状和自然频率。模式求和过程导致耦合非线性常微分方程。使用频率响应的时间响应和谐波平衡方法来解决这些等式，以及频率响应的电弧延续方法。各向同性和偏振片的无透明线性振动响应的光谱表现出平板的固有频率和旋转载荷的角速度。阻尼响应仅包含旋转负载的角速度的频率。由于旋转点负荷显示频率丰富的频谱而导致的稳定和阻尼板的非线性横向振动。频率响应函数显示强的模态相互作用。

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