Abstract For the analyze of forced and free vibrations of composites with periodically varying interfaces, we develop an energetic boundary function method. Three types of beams under different homogeneous boundary conditions and a sequence of boundary functions for each type beam are given, which automatically satisfy the homogeneous boundary conditions. Then we derive an energy equation and construct the energetic boundary functions by further satisfying the energy equation. The solution of forced vibration is expressed in terms of energetic boundary functions as the numerical bases, and then we can derive the linear system to decide the expansion coefficients by a simple collocation technique. To find out the natural frequencies of composite beams we iteratively solve the varying linear systems which include the unknown natural frequencies, and at each iteration we employ the Rayleigh quotient to calculate the natural frequencies until convergence. Through numerical tests we find that the energetic boundary function methods are highly efficient and very accurate for solving the proposed vibration problems of composite beams.

中文翻译：

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用能量边界函数搭配法求解组合梁的受迫和自由振动

摘要 为了分析具有周期性变化界面的复合材料的受迫振动和自由振动，我们开发了一种能量边界函数方法。给出了不同齐次边界条件下的三种类型的梁和每种类型梁的一系列边界函数，它们自动满足齐次边界条件。然后我们推导出能量方程并通过进一步满足能量方程来构造能量边界函数。强迫振动的解以能量边界函数为数值基础表示，然后我们可以通过简单的搭配技术推导出线性系统来确定膨胀系数。为了找出组合梁的固有频率，我们迭代求解包含未知固有频率的变化线性系统，并且在每次迭代中，我们使用瑞利商来计算自然频率直到收敛。通过数值试验，我们发现能量边界函数方法对于解决所提出的组合梁振动问题非常有效且非常准确。