CAJ | 학술논문

考虑吊重的摆动，将重物－桥吊耦合系统简化为移动质量＋吊重在简支梁上运动模型，基于 Lagrange 方程，推导了移动质量＋吊重－简支梁耦合系统运动微分方程。采用 Runge-Kutta 积分法对微分方程组进行数值求解，分析了移动质量加速度、吊重质量所占比重、吊绳长度等因素对梁体振动响应的影响。数值计算结果表明：对于重物－桥吊耦合系统，若不考虑吊重摆动，采用移动质量过桥模型将会低估梁体振动响应，并且在移动质量与吊重质量之和一定的情况下，吊重质量所占比重越大，梁体的振动响应越大；移动质量加速度对梁体的振动影响不能忽略，尤其是对梁体的加速度响应影响很大。
고필조중적파동，장중물－교조우합계통간화위이동질량＋조중재간지량상운동모형，기우 Lagrange 방정，추도료이동질량＋조중－간지량우합계통운동미분방정。채용 Runge-Kutta 적분법대미분방정조진행수치구해，분석료이동질량가속도、조중질량소점비중、조승장도등인소대량체진동향응적영향。수치계산결과표명：대우중물－교조우합계통，약불고필조중파동，채용이동질량과교모형장회저고량체진동향응，병차재이동질량여조중질량지화일정적정황하，조중질량소점비중월대，량체적진동향응월대；이동질량가속도대량체적진동영향불능홀략，우기시대량체적가속도향응영향흔대。
Considering the swing of a suspension weight,a suspension weight-bridge crane coupled system was simplified to a model of a mass with a suspension weight both moving on a simply supported beam,and its differential equation of motion was derived based on Lagrange equation.Runge-Kutta numerical integration method was used for numerically solving.Some influence factors on the system vibration response were analyzed,they were acceleration of moving mass,length of wire and ratio of mass of suspension weight to the total mass of the system.The results showed that without considering the swing of the suspension weight,the vibration response of the beam may be underestimated by using the model of the beam subjected to moving masses;when the mass sum of the moving mass and the suspension weight is fixed,the greater the mass of the suspension weight,the larger the vibration response of the beam;the acceleration of the moving mass has a great influence on the beam vibration.