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    張偉杰
    (河南理工大學(xué)土木工程學(xué)院，焦作454000)

[摘要] 應(yīng)用Hamilton變分原理推導(dǎo)出變截面Timoshenko懸臂梁在諧波位移激勵(lì)下強(qiáng)迫振動(dòng)的控制微分方程及相應(yīng)的邊界條件，并用常微分方程求解器( Ordinary Differential Equation Solver)進(jìn)行求解，同時(shí)求得等截面及變截面Timoshenko懸臂梁自由振動(dòng)的前三階振動(dòng)頻率和相應(yīng)的振型，計(jì)算結(jié)果通過(guò)解析解以及SAP2000有限元程序進(jìn)行校核。數(shù)值算例表明：該方法具有收斂速度快、精度高等特點(diǎn)，從而為工程中塔式結(jié)構(gòu)的動(dòng)力特性分析提供理論參考。
[關(guān)鍵詞] 變截面懸臂梁；Timoshenko梁；常微分方程求解器；自由振動(dòng)；共振響應(yīng)

ODE solution of dynamic characteristics of Timoshenko cantilever beams with variable cross-section
Zhang Weijie
( School of Civil Engineering, Henan Polytechnic University, Jiaozu0 454000, China)

Abstract: The differential equations and corresponding boundary conditions of Timoshenko cantilever beams with variable cross-section which impelled by harmonic displacement were developed by Hamilton variational principle and solved by Ordinary Differential Equation Solver. At the same time, the first three natural frequencies and corresponding mode shapes of the Timoshenko cantilever beams with same or variable cross-section were obtained. In order to illustrate the accuracy and practical usefulness of this method, numerical solutions by this study were presented and compared with exact solutions and solutions by SAP2000. The presented method is simple in convergent and sufficiently accurate, so as to provide theoretical reference in the analysis of dynamic characteristics of tower structures in civil engmeenng.
Keywords: cantilever with variable cross-section, Timoshenko beam; Ordinary Differential Equation Solver, free vibration; the resonant response