Evaluation of complex spectrum of the symmetrical Lamb waves for three-layered plates at low frequency. Part II: Asymptotics/numerical results

Abstract

Developing the approach outlined in Part I, the wavenumber spectrum is evaluated. Firstly, for the nth complex dispersion curve the asymptotics of the wavenumber’s static value is considered as n→+∞. Two approaches to obtain this asymptotics are compared. Then, for any n the exact value in statics is calculated using iterations, starting with the asymptotic value as the initial approximation. The parametric analysis revealed a specific (critical) value of the geometrical parameter at which the wavenumbers are redistributed. Secondly, the low frequency asymptotics of the dispersion curves are obtained. They exibit the flat initial segment of each complex dispersion curve which is the longer, the larger is the index n of the curve. Thus, this part of spectrum can be described by simple analytical formulas. The exact dispersion curves are evaluated using another iterative algorithm for improving the approximations. For both steps the numerical results are in a good agreement with the asymptotics. Finally, the perspectives of the method for other composite structural members are discussed.