任意边界条件下功能梯度阶梯圆柱壳的振动特性研究

Research on Vibration Characteristics of Functionally Graded Stepped Cylindrical Shells with Arbitrary Boundary Conditions

对金属-陶瓷功能梯度材料阶梯圆柱壳在任意边界条件下的振动特性展开了研究.首先,采用Voigt模型和幂函数体积分数得到金属-陶瓷功能梯度材料属性.其次,引入人工弹簧技术,模拟各壳段间的连续耦合及壳体两端的边界条件,并基于一阶剪切变形理论推导出壳体的能量表达式.最后,选取Chebyshev多项式构造容许函数,基于Rayleigh-Ritz法对任意边界条件下壳体的动力学微分方程进行求解计算,通过与现有文献对比,验证了本文方法的有效性与收敛性.结果表明:体积分数指数增长,壳体固有频率也随之增长;而长径比和厚径比对壳体的振动特性影响均不同,随着长径比的增加壳体的固有频率减小,随着厚径比的增加壳体的固有频率增大;且相较于旋转弹簧,平动弹簧的刚度值对壳体振动特性的影响显著.

Research on vibration characteristics of functionally graded materials(FGMs)in the aero-space field is a hot topic of current research.In this paper,the vibration characteristics of metal-ceramic functionally graded(FG)stepped cylindrical shells under arbitrary boundary conditions are studied.To conduct this research,a mechanical model of a metal-ceramic FG stepped cylindrical shell based on the axi-al segmentation concept is developed.First,the properties of metal-ceramic FGMs are obtained using the Voigt model and power function volume fraction.Second,the artificial spring technique is introduced to simulate continuous coupling conditions of shell segments and arbitrary boundary conditions at the ends of the shell.The energy expression for the cylindrical shell is then derived based on the first-order shear de-formation theory.Finally,the admissible function is constructed via the Chebyshev polynomial,and the dynamic differential equations of the metal-ceramic FG stepped cylindrical shell under arbitrary boundary conditions are calculated using the Rayleigh-Ritz method.The validity and convergence of the method are verified through comparison with existing literature,and the effects of boundary conditions,volume frac-tion,geometric parameters,and spring stiffness on modal frequencies are analyzed.It is found that the natural frequency of the FG stepped cylindrical shell initially decreases and then increases with increased number of circumferential waves under classical boundary conditions,and it increases with the number of circumferential waves under both elastic boundary conditions.The natural frequency of the shell increases exponentially with volume fraction.The effects of length-to-radius ratio and thickness-to-radius ratio on the vibration characteristics of the shell differ,with the natural frequency of the shell decreasing with in-creased length-to-radius ratio and increasing with thickness-to-radius ratio.Additionally,the stiffness of translational springs significantly influences the vibration characteristics of the shell compared to rotational springs.