Abstract In this paper, a fractional viscoelastic model is presented for vibration analysis of a fully simply supported plate excited by the supports movement. To govern the steady-state condition for the plate vibration, the lower limit of the integral in Riemann-Liouville fractional derivative is assumed in minus infinity. The Voigt viscoelastic model is employed for describing the damping effects. Considering the Kirchhoff hypothesis the governing equation of the viscoelastic plate is derived. An analytical solution for the dynamic response of the fractional viscoelastic plate under the support excitation is proposed. The effect of fractional derivative order and damping coefficient on the amplitude-frequency characteristic of the plate is investigated. Also, the obtained natural frequencies for elastic plate (by setting the fractional derivative order to zero) and classical viscoelastic plate (by setting the fractional derivative order to zero) are compared with existing results in the literature.

中文翻译：

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支撑运动激发的薄板振动分析的分数粘弹性模型

摘要 在本文中，提出了一个分数粘弹性模型，用于由支架运动激发的全简支板的振动分析。为了控制板振动的稳态条件，假设黎曼-刘维尔分数阶导数积分的下限为负无穷大。Voigt 粘弹性模型用于描述阻尼效应。考虑到基尔霍夫假设，推导出粘弹性板的控制方程。提出了支座激励下分数粘弹性板动力响应的解析解。研究了分数阶导数和阻尼系数对板幅频特性的影响。还，