- 作者: 林聰悟
- 作者服務機構: 國立臺灣大學
- 中文摘要: 本文係以動態勁度矩陣法為基礎。首先導出以桿件兩端變位表示之通式化形態函數及獨立桿件之動態勁度矩陣,據以利用平衡關係建立結點之動態勁度矩陣。由結點動態勁度矩陣行列式值等於零之類率方程式可得各自然振動頻率及對應之結點變位幅度比,因而即得各桿件之形態函數。受任意頻率之簡諧力作用時,亦可利用動態勁度矩陣根據外力幅度大小求得各結點之變位幅度。於餘解及特解求得後,根據初始條件即得各自然振動函數之係數。文後另附二程序計劃,一以分析彈性支承連續樑之自然類率及結點變位幅度比,同時並計算受簡諧力作用時之結點變位幅度。另一程序計劃根據程序計劃一之結果及初始條件可得各自然振動函數之係數(即積分常數)。
- 英文摘要: The method of dynamic stiffness matrix is the theoretical basis of this paper.The generalized shape function in terms of end displacements of each member andthe dynamic stiffness matrix of individual member are first derived. Then thedynamic stiffness matrix of joints can be constructed by using equilibrium conditions.Setting the determinant of the dynamic stiffness matrix equal to zero, the frequencyequation of which can results in the solution of each natural frequency and the cor-responding ratio of node displacement amplitude, theretore, the shape function ofeach member can be determined. As the structure subjectied to any harmonic forces,the amplitudes of node displacements can also be solved by dynamic stiffness. matrix.After the homogeneous solution and the particular solution are found, coefficients ofeach vibration function are then determined by using the initial conditions. Two computer programs are attached in the paper. The first program is for theanalysis of natural frequency of elastic-support continuous beam and the ratio ofnode displacement amplitude, and for the computation of the amplitudes of nodsdisplacements under harmonic forces. The second program is for the determinationof the coefficients (integral constants of the general solution) of each vibration func-tion by use of the result from the first program and the initial conditions.
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