... methods that are based on the dynamic stiffness matrix, symplectic transfer matrix, and mixed energy matrix are developed to compute the dispersion relations. The dispersion relations in layered media can be reduced to a standard eigenvalue problem of ordinary differential equations (ODEs...

... extensibility, rotary inertia, and shear deformation. The assessment is carried out by comparing the dynamic behavior predicted by each curved beam model in terms of the dispersion relations, frequency spectra, cutoff frequencies, natural frequencies and mode shapes, and frequency responses. In order to ensure...

... ) Mu 0 , j ( k ) The resulting scalar equation can be solved in terms of ω 1 , j , which defines the frequency correction for the j -th branch of the dispersion relation. The corresponding nonlinear dispersion branch is estimated as follows 51 ω j = ω...

...Yu Cheng Liu; Yun Fan Hwang; Jin Huang Huang This paper reinvestigates the classic problem of the dispersion relations of a cylindrical shell by obtaining a complete set of analytical solutions, based on Flügge’s theory, for all orders of circular harmonics, n = 0,1,2 , … , ∞ . The traditional...

...Nikolay A. Losin The Rayleigh-Lamb frequency equations for the free vibrations of an infinite isotropic elastic plate are expanded into the infinite power series and reduced to the polynomial frequency and velocity dispersion relations. The latter are compared to those of the operator plate model...