功能梯度粘弹性板中的Lamb波  

Lamb waves in a functionally graded Kelvin viscoelastic plate

作　　者：蒋海宁 曹小杉[1] 

机构地区：[1]西安理工大学土木建筑工程学院工程力学系,西安710048

出　　处：《应用力学学报》2018年第4期715-721,共7页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11572244);陕西省自然科学基金(2015JQ1001)

摘　　要：研究功能梯度Kelvin模型粘弹性板中Lamb波传播的频散和衰减特性,基于弹性力学理论,建立了以位移函数表示的功能梯度粘弹性板中Lamb波传播问题的控制方程;采用幂级数方法求得其渐近解,得到波速-波数方程的解析形式;采用最小模值逼近法求解复数域超越方程。通过对比均质粘弹性板和特殊梯度粘弹性板中Lamb波传播的精确解析解和幂级数渐近解,由此验证幂级数解的可靠性。研究结果表明:当梯度参数同时变化时,梯度板中的Lamb波波速的实部、虚部、减幅系数较均匀板中均无显著变化;仅密度梯度参数增大时波速实部和虚部绝对值都减小,减幅系数增大;仅弹性模量梯度参数增大时,波速实部和虚部绝对值都增大,减幅系数减小。准S0模态和准A0模态的减幅系数基本相同,而与准A1模态相差较大。在同模态下频率越高减幅系数越大,同频率下高模态对应的减幅系数较小。这些结论可为非均质粘弹性板结构无损检测提供理论依据。The dispersion and attenuation characteristics of Lamb wave propagation in a functionally graded Kelvin visco-elastic plate are investigated. The governing equations of Lamb wave propagation in a functionally graded visco-elastic plate are deduced by displacement functions based on the theory of elasticity. The asymptotic solution is obtained by using the power series method and the analytical form of wave velocity-wave number equation is deduced, transcendental equation with the complex coefficient of the Lamb wave in the functionally graded viscoelastic plate via the minimum modulus approximation method is solved. The reliability of the power series solution is verified by comparing the exact analytical solution and the power series asymptotic solution of the Lamb wave propagation in homogeneous viscoelastic plates and special gradient regular visco-elastic plates. When the gradient parameters vary with the same exponential law, the real part, the imaginary part of the Lamb wave velocity and the damping coefficient in the gradient plate have no significant change compare with the uniform plate. Only the density gradient parameter increases, both the real part and the absolute value of the imaginary part decrease and the damping coefficient increases. On the other hand, the elastic modulus gradient parameters increase, the real part and the absolute value of the imaginary part increase, and the damping coefficient decreases. The damping coefficients of quasi S0 mode and quasi A0 mode are nearly the same, while they differ from the damping coefficient of quasi A1 mode. In the same mode, the higher the frequency is, the greater the damping coefficient is. The damping coefficient is small in the high mode with the similar frequency. The validity of this conclusion can provide the theoretical basis for nondestructive testing of heterogeneous visco-elastic structures.

关 键 词：功能梯度材料 粘弹性 LAMB波 幂级数法 频散特性 

分 类 号：O34[理学—固体力学]