This paper develops a time-varying model for battery tabs based on the parametric excitation of Euler-Bernoulli beams. The instability caused by combination resonance under a high-frequency longitudinal load is considered. A Galerkin procedure is used to discretize the time-dependent problem into the Mathieu equation. The critical axial load is obtained from the transition curve of combination resonance. The effectiveness of the stability analysis was verified by numerical simulations involving longitudinal and bending loads.

中文翻译：

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参数激励下超声焊接的不稳定性研究

本文基于Euler-Bernoulli光束的参数激发，建立了电池接线片的时变模型。考虑了在高频纵向载荷下由组合共振引起的不稳定性。使用Galerkin过程将与时间有关的问题离散化为Mathieu方程。临界轴向载荷是从组合共振的过渡曲线获得的。通过涉及纵向和弯曲载荷的数值模拟，验证了稳定性分析的有效性。