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A wave solution for energy dissipation and exchange at nonclassical boundaries of a traveling string

机译：行进绳子非自治区边界的能量耗散和交换的波解

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摘要

The finite length model of a traveling string can be used to study the lateral vibrations in many engineering devices. The vibrational energy exchange mechanism and its characteristics are very complex, due to the axial movement and the different boundary conditions. A finite length translating tensioned string model with mixed boundary conditions is considered here in order to study the exchange of vibrational energy during the reflection process. The boundary conditions are respectively at one end a spring-dashpot and the other a fixed boundary, together forming one kind of mixed boundary conditions. An analytical solution and energy expressions for the propagating wave are presented using a reflected wave superposition method. Firstly, a complete cycle of boundary reflections in the string is provided. To simplify the process for obtaining the response, each cycle is divided into three time intervals. Applying D'Alembert's principle and the reflection properties, expressions for the reflected waves under these mixed boundary conditions are derived with the vibrational response solved for three time intervals. The accuracy and efficiency of the proposed method are confirmed numerically by comparison to simulations produced using a Newmark-β method solution. The comparison shows that the reflected wave superposition method solution is achievable for higher translational speeds, even the critical speed, which is not attainable from most numerical methods. The subsequent energy analytical expressions for a traveling string with these mixed boundary conditions are obtained in terms of the superposition of the traveling waves and their reflections. The properties of vibration energy exchange as a function of the translational velocity, the type of boundary and level of damping are discussed. Numerical simulation results proved that the viscous damper results in energy dissipation at the boundary, and the choice of the magnitude and direction of the translational string velocity can affect the energy of the traveling wave.
机译：行驶串的有限长度模型可用于研究许多工程设备中的横向振动。由于轴向运动和不同的边界条件，振动能量交换机制及其特性非常复杂。这里考虑了具有混合边界条件的有限长度平移张紧的串模型，以便在反射过程中研究振动能的交换。边界条件分别在一个端部是弹簧划线和另一个固定边界，一起形成一种混合边界条件。使用反射波叠加法提出了用于传播波的分析溶液和能量表达。首先，提供了字符串中的边界反射的完整循环。为了简化获得响应的过程，每个循环分为三个时间间隔。应用D'Anumbert的原理和反射特性，在这些混合边界条件下的反射波的表达源于三个时间间隔解决的振动响应。通过与使用纽马克-β方法解决方案产生的模拟来确定所提出的方法的准确性和效率。比较表明，对于更高的平移速度，即使是临界速度，也可以实现反射波叠加方法解决方案，这是临界速度，这是不可达到大多数数值方法的临界速度。随后具有这些混合边界条件的行进串的随后的能量分析表达式是根据行驶波的叠加和它们的反射的。讨论了作为平移速度的函数的振动能量交换的性质，讨论了衰减的类型和阻尼水平。数值模拟结果证明，粘性阻尼器导致边界处的能量耗散，并且平移串速度的幅度和方向的选择可以影响行波的能量。

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  • 来源
    《Mechanical systems and signal processing》 |2021年第3期|107272.1-107272.16|共16页
  • 作者

    E.W. Chen; J.F. Yuan; N.S. Ferguson; K. Zhang; W.D. Zhu; Y.M. Lu; H.Z. Wei;

  • 作者单位

    School of Mechanical Engineering Hefei University of Technology Hefei 230009 China;

    School of Mechanical Engineering Hefei University of Technology Hefei 230009 China;

    Institute of Sound and Vibration Research University of Southampton Southampton SO17 1BJ England UK;

    School of Mechanical Engineering Hefei University of Technology Hefei 230009 China;

    Department of Mechanical Engineering University of Maryland Baltimore County Baltimore MD 21250 USA;

    School of Mechanical Engineering Hefei University of Technology Hefei 230009 China;

    School of Mechanical Engineering Hefei University of Technology Hefei 230009 China;

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  • 正文语种 eng
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  • 关键词

    Energy exchange; Traveling string; Nonclassical boundaries; Reflection properties; Wave superposition;

    机译：能量交换;旅行弦;非分化边界;反思属性;波峰叠加;

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