Abstract—

The unsteady vibrations of a simply supported Timoshenko beam are investigated by taking into account the mass transfer under the action of a distributed transverse load. To formulate the problem, the Timoshenko beam model obtained using the d’Alembert principle from the elastic diffusion equations for a continuum is used. To solve the obtained problem, the integral Laplace transform in time and the expansion into Fourier series are used. By passing to the classical problem of unsteady vibrations of an elastic beam, the influence of mass transfer on the displacement field inside the beam is analyzed.

中文翻译：

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简支Timoshenko梁振动的非定常弹性扩散模型。

摘要-

通过考虑在横向分布载荷作用下的传质，研究了简单支撑的蒂莫申科梁的非稳态振动。为了解决这个问题，使用了由d'Alembert原理从连续体的弹性扩散方程获得的Timoshenko梁模型。为了解决所获得的问题，使用时间上的积分拉普拉斯变换和扩展成傅立叶级数。通过讨论弹性梁非稳态振动的经典问题，分析了传质对梁内部位移场的影响。