复合材料组合梁的分布参数传递函数法分析模型

Analysis Model of Composite Combined Beams by Distributed Parameter Transfer Function Method

应用分布参数传递函数法分析了复合材料组合梁在轴压载荷作用下的振动与稳定性问题。通过引入对偶变量，利用Ｌｅｇｒｅｎｄｒｅ 变换和Ｌａｐｌａｃｅ 变换，建立了可进入Ｈａｍ ｉｌｔｏｎ 体系的混合能量变分原理，并推导出了结构在复频域内的状态空间控制方程， 从而得到了任意边界条件下组合梁振动与稳定性问题的传递函数精确解。分析了一阶和高阶横向剪切变形、转动惯量、细长比、材料各向异性等多种因素对组合梁固有频率和屈曲载荷的影响。文中最后给出了数值算例， 验证了本方法的有效性和适应性。

In this paper, the distributed parameter transfer function method is applied to analyzing the vibration and stability of composite combined beams under axial compression. The Hamiltonian formalism of a modified mixed variational principle about the symptic variables is established using Legrendre transformation with spatial variable as independent variable instead of time. The state-space equations in Laplace transform domain is derived from using Hamilton's principle and Laplace transform. The unified and closed form transfer function solutions are obtained for vibration frequencies and buckling loads under arbitrary boundary restrictions. The influences of the first and high order shear deformation, torsion deformtion, rotary inertia, length to thickness ratio and material anisotropy on natural frequencies and buckling loads are investigated. Numerical examples are provided to demonstrate the efficiency and suitability of the methodology.