基于铁木辛柯梁理论,结合哈密尔顿变分原理推导了粘弹性复合材料梁的振动平衡方程.首先,通过与公开发表的文献的计算数据对比,来验证方程推导的正确性.其次,研究了粘弹性层厚度对阻尼层复合材料梁结构的自由振动的影响.结果表明:随着阻尼层厚度的增大,前四阶固有频率逐渐降低,损耗因子值逐渐增大;但是当梁的总厚度不变时,前四阶固有频率呈现急剧下降的趋势;损耗因子在阻尼层厚度值小于总厚度的一半时基本不变,变化较平缓,但是当厚度大于总厚度的一半时,整体构件的损耗因子值急剧增大.%Based on Timoshenko beam theory, combined with Hamilton variation principle, vibration equation of composite sandwich beam was deduced.First,by comparing with the data of the published literature,the correctness of the equation is verified.Secondly,the influences of viscoelastic layer thickness on the free vibration are study.The results show that:with the increase of thickness of damping layer, the natural frequency decreases gradually, and the loss factor value increases gradually; but when total thickness of beam is unchanged, the first four order natural frequency showed a trend of sharp decline.The value of loss factor is less than half the total thickness of damping layer thickness, change is gentle, but when the thickness is more than half of the total thickness,loss factor of integral component increases sharply.
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