Exact Analysis of Wave Motions in Rods and Hollow Cylinders

摘要: In a deformable isotropic infinitely long cylinder discrete number of propagating guided modes regularly exists in limited interval frequency (f) and wavenumber (ξ). The calculation the is best done via Helmholtz’s method, where Bessel functions are used to scale scalar wave potentials. Solving three-dimensional equations, leads displacement stress componenets terms potential be found. By imposing free boundary conditions for inner outer surface cylinder, dispersion equation can obtained. shows how phase velocity, c p = 2πf/ξ, change with frequency. group i.e. speed along obtained as g ∂(2πf)/∂ξ.