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首页> 外文期刊>Mathematical Problems in Engineering >Nonlinear Vibration of an Elastic Soft String: Large Amplitude and Large Curvature
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Nonlinear Vibration of an Elastic Soft String: Large Amplitude and Large Curvature

机译：弹性软弦的非线性振动：大振幅和大曲率

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摘要

Mechanical nonlinear vibration of slender structures, such as beams, strings, rods, plates, and even shells occurs extensively in a variety of areas, spanning from aerospace, automobile, cranes, ships, offshore platforms, and bridges to MEMS/NEMS. In the present study, the nonlinear vibration of an elastic string with large amplitude and large curvature has been systematically investigated. Firstly, the mechanics model of the string undergoing strong geometric deformation is built based on the Hamilton principle. The nonlinear mode shape function was used to discretize the partial differential equation into ordinary differential equation. The modified complex normal form method (CNFM) and the finite difference scheme are used to calculate the critical parameters of the string vibration, including the time history diagram, configuration, total length, and fundamental frequency. It is shown that the calculation results from these two methods are close, which are different with those from the linear equation model. The numerical results are also validated by our experiment, and they take excellent agreement. These analyses may be helpful to engineer some soft materials and can also provide insight into the design of elementary structures in sensors, actuators and resonators, etc.
机译：细长结构的机械非线性振动，例如梁，弦，杆，板，甚至是壳体，广泛发生在从航空航天，汽车，起重机，船舶，海上平台到MEMS / NEMS的各个领域。在本研究中，已经系统地研究了具有大振幅和大曲率的弹性弦的非线性振动。首先，基于汉密尔顿原理，建立了承受强烈几何变形的弦力学模型。使用非线性模式形状函数将偏微分方程离散为常微分方程。改进的复数范式形式（CNFM）和有限差分方案用于计算琴弦振动的关键参数，包括时程图，配置，总长度和基频。结果表明，这两种方法的计算结果相近，与线性方程模型的计算结果不同。数值结果也通过我们的实验验证，并且它们之间具有极好的一致性。这些分析可能有助于设计某些软材料，还可以提供对传感器，执行器和谐振器等中基本结构设计的了解。

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