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首页> 外文期刊>International journal of non-linear mechanics >Non-linear forced periodic oscillations of laminates with curved fibres by the shooting method
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Non-linear forced periodic oscillations of laminates with curved fibres by the shooting method

机译：射束法对弯曲纤维层合板的非线性强迫周期性振动

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Large-amplitude forced vibration, before damage onset, of variable stiffness composite laminated plates with curvilinear fibres are studied. The fibre paths considered change linearly in relation to one Cartesian coordinate. The plates are rectangular and with clamped edges. The displacement field is modelled by a third order shear deformation theory and the equations of motion, in the time domain, are obtained using a p-version finite element method. The in-plane inertia is neglected, still taking into consideration the in-plane displacements, and the model is statically condensed. The condensed model is transformed to modal coordinates in order to have a reduced model with a smaller number of degrees-of-freedom. A shooting method using fifth-order Runge-Kutta method, as well as adaptive stepsize control, is used to find periodic solutions of the equations of motion. Frequency-response curves of composite laminates with different curvilinear fibre angles and various thicknesses are plotted and compared. Tsai-Wu criterion is employed in order to predict the damage onset. When it is detected that damaged started, the continuation method is interrupted and no further points of the response curve are computed. The reason behind this interruption is that the model does not include the effects of damage. Examples of bifurcations are presented and studied in detail, using projections of trajectories in a phase plane and Fourier spectra. The time histories and frequency spectra of steady-state stresses are plotted for VSCL plates with different fibre angles. The steady-state stresses are also displayed for bifurcated branches of the solutions, Crown Copyright (C) 2015 Published by Elsevier Ltd. All rights reserved.
机译：研究了具有曲线纤维的变刚度复合层合板在破坏发生之前的大振幅强迫振动。所考虑的光纤路径相对于一个笛卡尔坐标线性变化。这些板是矩形的，并带有夹紧的边缘。利用三阶剪切变形理论对位移场进行建模，并使用p版本有限元方法获得时域中的运动方程。忽略平面内惯性，仍然考虑平面内位移，并且模型被静态压缩。压缩后的模型将转换为模态坐标，以使简化后的模型具有较少的自由度。使用五阶Runge-Kutta方法的射击方法以及自适应步长控制，用于找到运动方程的周期解。绘制并比较了具有不同曲线纤维角度和不同厚度的复合材料层压板的频率响应曲线。采用蔡吴准则以预测损伤发作。当检测到损坏开始时，继续方法被中断，并且不再计算响应曲线的其他点。这种中断的原因是该模型不包括损坏的影响。使用相平面中的轨迹投影和傅立叶光谱，详细介绍和研究了分叉的例子。绘制了具有不同纤维角的VSCL板的稳态应力的时间历史和频谱。还显示解决方案的分支分支的稳态应力，Elsevier Ltd.出版的Crown版权所有（C）2015。保留所有权利。

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