拉压弹性模量不等材料简支梁在横向载荷作用下的线性振动问题

Linear Vibration of Simply-supported Beam with Different Tension-compression Moduli Subjected to Transverse Loads

采用Hamilton原理,假设线性振动为简谐响应形式,把偏微分振动控制方程化为无量纲常微分方程组.考虑横向载荷作用的大挠度,研究拉压性能不同时简支梁的线性振动规律.利用打靶法数值求解了简支梁线性振动时,横向载荷引起的弯曲挠度、中性轴位置变化以及微幅振动时的固有频率.结果表明:固有频率随着弹性模量比值非线性变化,横向载荷较大时呈现出非单调性.横向载荷的作用引起梁的抗弯刚度变化,固有频率也明显变化.

According to the Hamilton theory, and assuming linear vibration in the form of harmonic response, the partial differential equation of vibration control is transformed into the dimensionless equations of ordinary differen- tials. Considering the action of transverse loads, we studied the rules of the linear vibration of the beam with differ- ent tension-compression performances. The method of shooting is used to solve the linear vibration of the simply- supported beam, the bending deflection caused by transverse loads, the change of the neutral axis position and the natural frequency of micro vibration. Research shows that the natural frequency changes with elastic modulus ratio in nonlinear changes, and it becomes non-monotonic when transverse loads are bigger. The effect of transverse loads causes the change of bending stiffness of the beam, and the natural frequency also changes obviously.