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Postbuckling And Free Vibrations Of Composite Beams

机译：复合梁的后屈曲和自由振动

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An exact solution for the postbuckling configurations of composite beams is presented. The equations governing the axial and transverse deformations of a composite laminated beam accounting for the mid-plane stretching are derived. The inplane inertia and damping are neglected, and hence the two equations are reduced to a single nonlinear fourth-order partial-integral-differential equation governing the transverse deformations. We find out that the governing equation for the postbuckling of symmetric or asymmetric composite beams has the same form as that of beams made of an isotropic material. Composite beams with fixed-fixed, fixed-hinged, and hinged-hinged boundary conditions are considered. A closed-form solution for the postbuckling deformation is obtained as a function of the applied axial load, which is beyond the critical buckling load. To study the vibrations that take place in the vicinity of a buckled equilibrium position, we exactly solved the linear vibration problem around the first buckled configuration. Solving the resulting eigen-value problem results in the natural frequencies and their associated mode shapes. Both the static response represented by the postbuckling analysis and the dynamic response represented by the free vibration analysis in the postbuckling domain strongly depend on the lay-up of the laminate. Variations of the beam's midspan rise and the fundamental natural frequency of the postbuckling domain vibrations with the applied axial load are presented for a variety of lay-up laminates. The ratio of the axial stiffness to the bending stiffness was found to be a crucial parameter in the analysis. This control parameter, through the selection of the appropriate lay-up, can be manipulated to help design and optimize the static and dynamic behavior of composite beams.
机译：提出了复合梁屈曲后结构的精确解决方案。推导了控制中平面拉伸的复合层合梁轴向和横向变形的方程式。由于忽略了平面惯性和阻尼，因此两个方程式简化为控制横向变形的单个非线性四阶偏积分方程。我们发现对称或非对称组合梁的后屈曲控制方程具有与各向同性材料制成的梁相同的形式。考虑具有固定-固定，固定-铰接和铰接-铰接边界条件的复合梁。根据所施加的轴向载荷获得了后屈曲变形的封闭形式解，该载荷超出了临界屈曲载荷。为了研究在弯曲的平衡位置附近发生的振动，我们精确地解决了第一个弯曲结构周围的线性振动问题。解决所产生的特征值问题将导致固有频率及其相关的模态形状。在屈曲后域中，由后屈曲分析表示的静态响应和由自由振动分析代表的动态响应都强烈取决于层压板的铺层。对于各种叠层层压板，梁的中跨上升和后屈曲域振动的基本固有频率随施加的轴向载荷而变化。发现轴向刚度与弯曲刚度之比是分析中的关键参数。通过选择适当的铺层，可以控制此控制参数，以帮助设计和优化复合梁的静态和动态性能。

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