双模量泡沫铝芯夹层梁的自由振动分析

Free vibration analysis of bimodulous aluminum foam core laminated beam

对模量泡沫铝芯夹层梁的固有振动问题进行了研究。利用双模量的材料应力-应变方程,推导出了双模量材料剪切弹性模量计算公式,证明了双模量梁中性轴位置不受作用在梁上的横向载荷的影响。在考虑剪切变形的基础上,建立了双模量泡沫铝芯夹层梁的强迫振动控制方程,推导出了双模量泡沫铝芯夹层梁固有振动问题的振型函数及固有频率计算公式,并分析了剪切变形及泡沫铝芯夹层的拉压弹性模量对双模量泡沫铝芯夹层梁固有振动频率的影响。研究表明:泡沫铝芯夹层梁固有振动时,其固有振动波形是不连续的,奇数波型与偶数波型之间存在间断点;剪切变形及泡沫铝芯夹层的拉压弹性模量对双模量泡沫铝芯夹层梁固有振动的影响是不能忽略的。

The free vibration of bimodulous aluminum foam core laminated beam is studied in this paper. Using pure shear state unit body of bimodulous material, the expression of shear elastic modulus of bimodulous material is derived. That the transverse load has no effect on the position of the neutral axis of bimodulous beam under arbitrary boundary conditions is proved, and the position of the neutral axis of bending bimodulous aluminum foam core laminated beam is determined. By considering shear effects, the vibration differential equation of bimodulous aluminum foam core laminated beam is established, expressions of mode shapes and natural frequencies of vibration problem of bimodulous aluminum foam core laminated beam are derived, and the influence of shear effects and modulus of elasticity in tension and compression of aluminum foam core sandwich on free vibration natural frequencies of bimodulous aluminum foam core laminated beam is analyzed. The results show that the vibration waveform is discontinuous, discontinuous point exists between the odd number wave type and vibration mode,when the bimodulous aluminum foam core laminated beam is freely vibrating. The influence of shear effects and modulus of elasticity in tension and compression of aluminum foam core on free vibration of bimodulous aluminum foam core laminated beam can't be ignored.