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首页> 外文期刊>Journal of Sound and Vibration >On shear deformable beam theories: The frequency and normal mode equations of the homogeneous orthotropic bickford beam
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On shear deformable beam theories: The frequency and normal mode equations of the homogeneous orthotropic bickford beam

机译：关于剪切可变形梁理论：正交各向异性均质Bickford梁的频率和正模方程

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This paper provides a step forwards the construction and documentation of the frequency equations and the characteristic Functions of a general three-degrees-of-freedom theory that describes the plane motion of shear deformable elastic beams. The governing equations of this shear deformable beam theory (G3DOFBT) involve a general shape function of the transverse beam co-ordinate parameter, the a posteriori choice of which specifies the distribution of the transverse shear strain or stress along the beam thickness. Different choices of this shape function produce, as particular cases. the corresponding governing equations of different beam theories. These include the differential equations of the Euler-Bernoulli beam theory as: well as the corresponding equations of the shear deformable theories due to Timoshenko and Bickford. Other examples can also be found by considering the shear deformable beam theories produced as one-dimensional versions of relevant refined plate theories. Since corresponding developments of the Timoshenko beam theory are already available in the literature, the Bickford theory is considered as the pilot beam theory in this study. The frequency equations, the characteristic functions and the orthogonality conditions of this theory, which assumes a through-thickness parabolic distribution of the transverse shear strain or stress, are constructed analytically for all the classical sets of boundary conditions applied at the beam ends. Some preliminary numerical results are also presented and discussed for beams having both their ends simply supported or clamped. (C) 2001 Academic Press. [References: 44]
机译：本文为进一步介绍频率方程和一般三自由度理论的特征函数的结构和文档，该理论描述了可剪切变形弹性梁的平面运动。该剪切可变形梁理论的控制方程式（G3DOFBT）涉及横梁坐标参数的一般形状函数，其后验选择指定沿横梁厚度的横剪应变或应力的分布。在特定情况下，会产生不同的形状函数选择。不同梁理论的相应控制方程。这些包括Euler-Bernoulli梁理论的微分方程，以及：Timoshenko和Bickford引起的剪切可变形理论的相应方程。通过将剪切可变形梁理论视为相关精炼板理论的一维形式而产生，也可以找到其他示例。由于Timoshenko束理论的相应发展已在文献中提供，因此本研究将Bickford理论视为先导束理论。对于梁端的所有经典边界条件，通过解析构造了该理论的频率方程，特征函数和正交性条件，该条件假定了横向剪切应变或应力的全厚度抛物线分布。还给出了一些初步的数值结果，并讨论了其两端简单支撑或夹紧的梁。 （C）2001学术出版社。 [参考：44]

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