Efficient Higher-Order Shear Deformation Theories for Instability Analysis of Plates Carrying a Mass Moving on an Elliptical Path

Journal of Solid Mechanics

مقاله 8، دوره 11، شماره 4، اسفند 2019، صفحه 790-808   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.22034/jsm.2019.668763

نویسندگان

E Torkan¹؛ M Pirmoradian^{* 2}

¹Young Researchers and Elite Club, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Isfahan,Iran

²Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Isfahan, Iran

چکیده

The dynamic performance of structures under traveling loads should be exactly analyzed to have a safe and reasonable structural design. Different higher-order shear deformation theories are proposed in this paper to analyze the dynamic stability of thick elastic plates carrying a moving mass. The displacement fields of different theories are chosen based upon variations along the thickness as cubic, sinusoidal, hyperbolic and exponential. The well-known Hamilton’s principle is utilized to derive equations of motion and then they are solved using the Galerkin method. The energy-rate method is used as a numerical method to calculate the boundary curves separating the stable and unstable regions in the moving mass parameters plane. Effects of the relative plate thickness, trajectories radii and the Winkler foundation stiffness on the system stability are examined. The results obtained in this research are compared, in a special case, with those of the Kirchhoff’s plate model for the validation.                    

کلیدواژه‌ها

Mass–plate interaction؛ Higher-order shear deformation theories؛ Parametric vibration؛ Parametric resonance؛ Energy-rate method

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