On the Vibration of Beams or Rods Carrying a Concentrated Mass
On the Vibration of Beams or Rods Carrying a Concentrated Mass
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DOI：
10.1115/1.3636537
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发表时间：
1963-06
期刊：
影响因子：
--
通讯作者：
Yu Chen
中科院分区：
文献类型：
--
作者：
Yu Chen
本文对带有集中质量的梁或杆的振动问题给出了一个新的公式，其中在微分方程中用狄拉克δ函数来描述集中质量的影响。首先用分离变量法求解描述自由振动的齐次微分方程，然后用拉普拉斯变换法求解所得到的常微分方程，得到问题的特征函数。将梁视为变密度梁，导出了梁的非线性关系，并将其用于求解一般的初值问题和强迫振动问题。
A new formulation is given to the problem of vibration of beams or rods carrying a concentrated mass in which the Dirac δ-function is used in the differential equation to describe the effect of a concentrated mass. The homogeneous differential equation which describes the free vibration is solved first by separation of variables and the resulting ordinary differential equation is then solved by Laplace transform to yield the eigenfunctions of the problem. Orthogonality relation, derived by treating the beam as a variable-density beam, is used to solve the general initial-value problem as well as the forced-vibration problem.