| 变截面黏弹性直杆纵振时复频率分析的差分解法 |
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| 引用本文： | 李会侠,赵凤群.变截面黏弹性直杆纵振时复频率分析的差分解法[J].力学与实践,2001,23(5):39-41. |
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| 作者姓名： | 李会侠 赵凤群 |
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| 作者单位： | 西安理工大学理学院 |
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| 基金项目： | 陕西省自然科学基金项目（99SL07）资助 |
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| 摘 要： | 从一维黏弹性本构方程出发，导出了黏弹性变截面直杆纵向振动微分方程的一般形式，采用了有限差分法，并以二阶矩阵表示的递推形式，建立了该问题的复特征值方程组。两种Maxwell黏弹性变截面（指数指数、线性函数）直杆的数值计算表明，该方法运算简单，计算精度高，能适用于求解任意变截面黏弹性直属的纵向自由振动问题。
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| 关 键 词： | 纵向振动 微分方程 黏弹性杆 有限差分法 复频率 二阶矩阵 Maxwell黏弹性变截面杆 |
| 修稿时间： | 2000年9月4日 |
THE COMPLEX FREQUENCY ANALYSIS OF FREE LONGITUDINAL VIBRATION OF VISCOELASTIC STRAIGHT ROD WITH VARYING CROSS-SECTION BY USING FINITE DIFFERENCE METHOD |
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| LI Huixia,ZHAO Fengqun.THE COMPLEX FREQUENCY ANALYSIS OF FREE LONGITUDINAL VIBRATION OF VISCOELASTIC STRAIGHT ROD WITH VARYING CROSS-SECTION BY USING FINITE DIFFERENCE METHOD[J].Mechanics and Engineering,2001,23(5):39-41. |
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| Authors: | LI Huixia ZHAO Fengqun |
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| Abstract: | Based on uniaxial viscoelastic constitu- tive law, a general differential equation of motion for free longitudinal vibration of viscoelastic straight rod with varying crosssection and the differential equations of motion for its commonly used model are derived. Then, using finite difference method and the- recurrence formula represented by two-order matrix, the complex eigenequations under various classical boundary conditions are established. The numerical calculations for viscoelastic straight rod with varying cross-section in exponential and linear functions show that this method not only is simpler and enjoys higher accuracy but also can be used to investigate the free longitudinal vibration prob- lem of the viscoelastic straight rod with arbitrarily varying crosssection function. |
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| Keywords: | viscoelastic rod longitudinal vibra- tion finite difference method |
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