Abstract Dynamic response of beams on elastic foundations is of great theoretical significance in the field of engineering. Galerkin truncation method is the most commonly used powerful method to study the vibration of these structures. The number of truncation terms affects the convergence of the analysis and determines the accuracy of the dynamic responses. However, there is still no basis for how to choose the appropriate number of truncation terms. In this paper, two effective schemes based on the natural frequency of the corresponding linear conservative system are proposed to determine the convergent terms of the Galerkin truncation. Since determining the natural frequencies of the corresponding linear conservative system are much easier, the convergence determination method is convenient for application. Based on the dynamic response of the sandwich beam on nonlinear foundations under a moving load, the feasibility of the two schemes for determining the convergent term is confirmed. Moreover, the effects of system parameters on the two schemes are presented. In short, this paper provides two simple and easy schemes for selecting the Galerkin truncation terms in the research of the dynamic response of elastic structures resting on elastic foundations.

中文翻译：

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非线性基础上夹层梁动力响应的伽辽金截断收敛项

摘要 弹性地基梁的动力响应在工程领域具有重要的理论意义。伽辽金截断法是研究这些结构振动最常用的有力方法。截断项的数量会影响分析的收敛性并决定动态响应的准确性。但是，如何选择合适的截断项数仍然没有依据。本文提出了两种基于相应线性保守系统固有频率的有效方案来确定Galerkin截断的收敛项。由于确定相应线性保守系统的固有频率容易得多，因此收敛确定方法便于应用。基于夹层梁在移动荷载作用下非线性地基上的动力响应，验证了两种确定收敛项的方案的可行性。此外，还介绍了系统参数对两种方案的影响。总之，本文提供了两种简单易行的方案，用于在弹性地基上弹性结构的动力响应研究中选择伽辽金截断项。