| 李俊永,吕和祥.弹性力学状态变量体系下带有初应力的振动问题[J].计算力学学报,2010,27(4):716~720 |
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| 弹性力学状态变量体系下带有初应力的振动问题 |
| Vibration problem of theory of elasticity in Hamilton system under initial stress |
| 投稿时间：2008-08-27 |
| DOI：10.7511/jslx20104025 |
| 中文关键词: 振动 临界载荷 固有频率 精细积分 Hamilton |
| 英文关键词:vibration critical load natural frequency precise integration method Hamilton |
| 基金项目: |
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| 摘要点击次数: 1365 |
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| 中文摘要: |
| 通过在Hellinger-Reissner广义势能中引入应变的非线性项,推导出了弹性力学Hamilton体系下的具有初应力的振动方程,并运用精细积分给出了两端简支的梁、组合梁和四边简支板及组合板在初应力下振动频率。本文结果是严格弹性力学意义(没有引入任何几何变形假设)下的精确解,为衡量各种计入剪切变形的薄板、中厚板理论的准确性提供了一个标准。 |
| 英文摘要: |
| In this paper, by considering the nonlinear term in Hellinger-Reissner variational principle, the vibration formulation with initial stress in Hamilton system was derived. As examples, frequencies with initial stress of a beam, composite beam, plate and composite plate were studied in precise integration method. The results were the exact solutions based on the exact elasticity theory (not considering any geometrical hypothesis). This paper provides a standard for both thin plates and moderately thick plates theory considering the effect of shear deformation. |
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