黏弹性 Pasternak 地基上修正 Timoshenko 梁 横向自振特性分析
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TU471+.2;TU348

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甘肃省科技计划资助项目(23JRRA1374);2022 年甘肃省高等教育教学成果培育项目(197)


Analysis of transverse free vibration characteristics of modified Timoshenko beam on viscoelastic Pasternak foundction
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    摘要:

    基于修正 Timoshenko 梁理论,建立黏弹性 Pasternak 地基上修正 Timoshenko 梁的横向振动控制方程,运用回 传射线矩阵法推导出黏弹性 Pasternak 地基上两端简支修正 Timoshenko 梁自振频率和衰减系数的解析解,结合二 分法和黄金分割法计算了经典边界条件下黏弹性 Pasternak 地基上修正 Timoshenko 梁的自振特性,对比分析了考 虑剪切变形引起的转动惯量、梁长及不同的边界条件对结构自振特性的影响。研究表明:黏弹性 Pasternak 地基上 修正 Timoshenko 梁的各阶自振频率和衰减系数小于经典 Timoshenko 梁的各阶自振频率和衰减系数;梁越短,剪切 变形引起的转动惯量对结构自振频率和衰减系数的影响越大,且对高阶的影响明显大于低阶;边界约束条件越强, 振动能量衰减越明显。

    Abstract:

    Based on the modified Timoshenko beam theory, the transverse vibration governing equation of the modified Timoshen? ko beam on the viscoelastic Pasternak foundation is established. The analytical solutions of the natural frequency and attenuation co? efficient of the modified Timoshenko beam simply supported at both ends in the viscoelastic Pasternak foundation are derived with the reverberation-ray matrix method. The natural vibration characteristics of the modified Timoshenko beam on the viscoelastic Pasternak foundation under classical boundary conditions are calculated by dichotomy and golden section method. The effects of moment of inertia caused by shear deformation, beam length and different boundary conditions on the natural vibration characteris? tics of the structure are compared and analyzed. The results show that the natural frequency and attenuation coefficient of the modi? fied Timoshenko beam on the viscoelastic Pasternak foundation are smaller than those of the classical Timoshenko beam; the short? er the beam, the more significant the influence of the moment of inertia caused by shear deformation on the natural frequency and at? tenuation coefficient of the structure, and the influence on the higher order is obviously greater than that on the low order; the stron? ger the boundary constraint condition, the more obvious the vibration energy attenuation.

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柳 伟,汪过兵,赵志鹏,赵晓军.黏弹性 Pasternak 地基上修正 Timoshenko 梁 横向自振特性分析[J].振动工程学报,2024,37(8):1330~1338.[LIU Wei, WANG Guo-bin, ZHAO Zhi-peng, ZHAO Xiao-jun. Analysis of transverse free vibration characteristics of modified Timoshenko beam on viscoelastic Pasternak foundction[J]. Journal of Vibration Engineering,2024,37(8):1330~1338.]

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  • 在线发布日期: 2024-09-09
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