Nonlinear vibrations of a polar-orthotropic thin circular plate subjected to circularly moving point load. (15th January 2021)

• Record Type: Journal Article
• Authors: Rai, Amit K.; Gupta, Shakti S.
• Is Part Of: Composite structures. Volume 256(2021)
• Publication Date: 2021-01-15
• Subjects: Nonlinear vibration -- Circular plate -- Polar-orthotropic material -- Moving point load -- Frobenius method -- Harmonic balance -- Frequency response; Composite construction -- Periodicals; Composites -- Périodiques; 624.18
• DOI: 10.1016/j.compstruct.2020.112953
• Languages: English
• ISSNs: 0263-8223

Abstract

Abstract: 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 Kármán 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 polar-orthotropic 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.