含裂纹简支梁的非线性振动研究

摘要

研究含裂纹的简支梁在移动质量车辆模型作用下的非线性动力响应。根据哈密尔顿能量原理，考虑梁的几何非线性和裂纹处的释放能影响，推导出在移动质量车辆模型和含裂纹的简支梁相互耦合作用下车桥系统的非线性运动方程，利用数值方法求解方程。探讨了裂纹对简支梁桥非线性动力响应的影响，分析裂纹长度和位置变化，车速及车重等对裂纹损伤桥梁的非线性振动特性的影响。%The nonlinear vibration response of the simply supported cracked beams subjecting to moving mass model was analyzed. With consideration of geometrical nonlinearity and crack release energy,the systematic nonlinear vibration equation on vehicle-bridge coupled was derived under moving mass model according to Hamilton ’s principle. The nonlinear equation was solved with numerical method,and the effects of location and depth of crack,vehicle velocity,vehicle mass on nonlinear dynamic behaviors for the simply supported cracked beams were discussed.