含焊接残余应力薄圆板结构自由振动近似解

研究焊接残余应力对薄圆板结构振动特性的影响,解决薄圆板结构振动中存在非均匀分布预应力问题。根据含预应力结构的应变-应力方程,建立含预应力薄圆板结构的运动控制方程。基于Rayleigh-Ritz法构造Lagrange能量泛函方程。将预应力和位移试函数展开成三角级数形式,对含预应力薄圆板结构的自由振动问题进行求解。以周边简支边界薄圆板结构为例,对比焊接残余应力的不同分布形式对薄圆板结构固有频率及振型的影响。数值计算结果验证了所提方法的有效性,可应用于解决任意分布预应力问题。

Approximate solutionto free vibration of thin circular plate structure with welding residual stress

Effects of welding residual stress on vibration characteristics of a thin circular plate structure were investigated here to solve the problem of non-uniform prestress distribution existing in the plate structure vibration.According to strain-stress equations of a plate structure with prestress,the governing dynamic equation of the thin circular plate structure with prestress distribution was derived.Lagrange energy functional equation was constructed,in which prestress distribution function and vibration displacement trial function were expanded into trigonometric series.The free vibration problem of the thin circular plate structure with prestress distribution was approximately solved based on Rayleigh-Ritz method.Taking the thin circular plate structure with simply supported boundary as an example,effects of different distribution forms of welding residual stress on natural frequencies and modal shapes of the plate structure were compared.The numerical results showed that the effectiveness and convergence of the proposed method are verified;the proposed method can be applied to solve free vibration problems of thin circular plate structures with arbitrary prestress distribution.