地基梁的振动特性在工程领域及科学界备受关注。将黏弹性Pasternak地基与Timoshenko梁进行组合，对地基梁横向自由振动特性进行研究。基于回传射线矩阵法，推导出复系数一元四次的频率方程，并对其进行求解得到Pasternak地基上两端简支的Timoshenko梁的自振频率及衰减系数的解析解；根据单一局部坐标系下的边界条件推导了模态函数解析表达式，进一步根据正交归一化条件对未知参数进行求解。通过具体算例验证了基于回传射线矩阵法所得的粘弹性Pasternak地基上Timoshenko梁横向自由振动特性解析解的正确性。
Abstract
Vibration characteristics of foundation beams receive much attention in engineering and scientific fields. Here, transverse free vibration characteristics of a simply supported Timoshenko beam on a viscoelastic Pasternak foundation were studied. Firstly, based on the reverberation-ray matrix method, the quartic frequency equation with complex coefficients was derived and solved, the analytical solutions to natural frequencies and attenuation coefficients of the simply supported Timoshenko beam on a viscoelastic Pasternak foundation were obtained. Then, the analytical expressions for modal functions of the beam were solved according to the boundary conditions under a single local coordinate system, unknown parameters were further solved according to the orthogonal normalization conditions. Finally, the correctness of the analytical solutions to transverse free vibration characteristics of the beam based on the reverberation-ray matrix method was verified with a specific example.
关键词
黏弹性Pasternak地基 /
Timoshenko梁 /
横向自由振动特性 /
解析解 /
回传射线矩阵法
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Key words
viscoelastic Pasternak foundation /
Timoshenko beam /
transverse free vibration characteristics /
analytical solution /
reverberation-ray matrix method
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