Mathematical modeling of two-ply ribbed cylinder vibrations

Abstract

In mechanical systems, the elastic properties and mass of the elements characterize the natural frequencies. The damping properties of longitudinal vibrations are expressed in terms of the characteristic mechanical impedance within the range of the natural frequencies. The natural frequency of transverse vibrations is obtained from the stiffness and mass of the longitudinal mechanical elements. These parameters can be used to optimize the system frequency response amplitudes (transfer functions) with the objective to reduce mechanical vibrations and vibro-acoustic intensity. A mathematical model for vibration of longitudinal mechanical elements (cylinders, pipes) is developed using the stiffness of the rib (ring). The governing equations of motion of cylinder vibrations stiffened with a ring are developed by the variational principal of potential and kinetic energy. A Kirchhoff-Lam method is used. The equations for displacement at the cylinder surface are obtained. These solutions provided a procedure to calculate the natural frequencies for various limited conditions and were validated by experiments.