A Study of Wave Processes in Elastic Topographic Waveguides

The characteristic features of acoustic wave propagation in orthotropic elastic topographic waveguides are investigated for waveguides in the form of extended cylindrical structures with symmetric cross sections of different shapes (rectangular or trapezoidal). A method for an approximate study of problems using variable-rigidity plate models on the basis of the Hamilton–Ostrogradskii principle is proposed. Based on a field structure hypothesis that is similar to the Timoshenko model in the theory of plates, a functional depending on three functions of a single variable has been constructed. The stationary value of the functional is determined by the Ritz method. Its convergence has been investigated depending on the number of coordinate functions. An algebraic system has been formed whose determinant, being set equal to zero, allows one to construct the dispersion equation of the problem. Dispersion dependences were obtained for cross sections of different geometries. A comparison has been carried out between the dispersion curves formed on the basis of the Timoshenko-type model and the previously studied Kirchhoff model. The cut-off frequencies are determined for elastic waveguides with triangular, rectangular, and trapezoidal cross sections, and a comparative analysis has been performed.