Peddeti Kranthi, Santhanam Sridhar
Mechanical Engineering Department, Villanova University, Villanova, Pennsylvania 19085, USA.
J Acoust Soc Am. 2018 Feb;143(2):829. doi: 10.1121/1.5023335.
Acoustoelastic techniques have been recently used to characterize the state of prestress in structures such as plates. The velocity of guided wave modes propagating through plates is sensitive to the magnitude and orientation of the initial state of stress. Dispersion curves for phase velocities of plate guided waves can be computed using the superposition of partial bulk waves (SPBW) method. Here, a semi-analytical finite element (SAFE) method is formulated for the acoustoelastic problem of guided waves in weakly nonlinear elastic plates. The SAFE formulation is shown to provide phase velocity dispersion curve results identical with those provided by the SPBW method for the problem of a plate under a uniaxial and uniform tensile stress. Analytical phase and group velocity dispersion curves are also obtained for a plate with an initial prestress gradient through its thickness using the SAFE method. The magnitude of the prestress gradient is shown to have a significant effect on phase and group velocities of the fundamental and first order Lamb modes, only in certain frequency-thickness regimes.
最近，声弹性技术已被用于表征诸如板等结构中的预应力状态。在板中传播的导波模式的速度对初始应力状态的大小和方向敏感。板导波相速度的频散曲线可以使用部分体波叠加（SPBW）方法来计算。在此，针对弱非线性弹性板中导波的声弹性问题，制定了一种半解析有限元（SAFE）方法。对于单轴均匀拉伸应力作用下的板问题，SAFE公式给出的相速度频散曲线结果与SPBW方法给出的结果相同。使用SAFE方法，还获得了具有沿厚度方向初始预应力梯度的板的解析相速度和群速度频散曲线。结果表明，仅在某些频率 - 厚度范围内，预应力梯度的大小对基阶和一阶兰姆波模式的相速度和群速度有显著影响。
