张菊梅, 赵凤群, 党晓敏. 变截面弹性直杆纵振动分析的小波--DQ法[J]. 力学与实践, 2010, 32(4): 71-73. DOI: 10.6052/1000-0879-lxysj2009-267
引用本文: 张菊梅, 赵凤群, 党晓敏. 变截面弹性直杆纵振动分析的小波--DQ法[J]. 力学与实践, 2010, 32(4): 71-73. DOI: 10.6052/1000-0879-lxysj2009-267
WAVELET-DQ METHOD FOR LONGITUDINAL VIBRATION ANALYSIS OF ELASTIC STRAIGHT ROD WITH VARIABLE CROSS-SECTION[J]. MECHANICS IN ENGINEERING, 2010, 32(4): 71-73. DOI: 10.6052/1000-0879-lxysj2009-267
Citation: WAVELET-DQ METHOD FOR LONGITUDINAL VIBRATION ANALYSIS OF ELASTIC STRAIGHT ROD WITH VARIABLE CROSS-SECTION[J]. MECHANICS IN ENGINEERING, 2010, 32(4): 71-73. DOI: 10.6052/1000-0879-lxysj2009-267

变截面弹性直杆纵振动分析的小波--DQ法

WAVELET-DQ METHOD FOR LONGITUDINAL VIBRATION ANALYSIS OF ELASTIC STRAIGHT ROD WITH VARIABLE CROSS-SECTION

  • 摘要: 在经典微分求积(DQ)法基础上, 根据多分辨分析理论, 以尺度函数为基础构造插值基函数, 形成了新的微分方程边值问题的求解方法------小波--DQ法, 并应用该方法分析了变截面弹性直杆的纵振动问题, 给出了其频率方程, 计算出了不同参数下固支--固支, 自由--自由楔形直杆和锥形直杆的固有频率,数值结果表明该方法是一个简单易行高精度的方法,该方法可以推广应用于其他力学问题的数值分析.

     

    Abstract: The wavelet-DQ method combines the classic differential quadrature (DQ) method, the multi-resolution analysis theory, and a constructor of scaling function-basedinterpolation base functions.This is a new method for solving boundary valueproblems of differential equations. This method is applied to analyze the longitudinal vibration of an elastic straight rod with variable cross-section, to obtain thefrequency equation. With different parameters, the natural frequencies ofclamped-clamped, free-free wedge-shaped straight rod and cone-shapedstraight rod are obtained. Numerical results show that the method is simpleand enjoys high-precision. This method can be applied to othermechanical problems in numerical analysis.

     

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