Vibration analysis of composite circular and annular membranes

Abstract

Abstract. In this paper a solution to the free vibration problem of composite circular and annular membranes is presented. The vibrations of membranes whose material densities and/or thicknesses varied step-wise with the radial co-ordinate are considered. This approach is applied to approximate the solution to the vibration problem of a membrane with continuously varying density and/or thickness with the radial co-ordinate. The obtained analytical solutions are used in numerical investigations into the effect of parameters characterizing the composite membranes on their eigenfrequencies.

Advanced non-dimensional dynamic influence function method considering the singularity of the system matrix for accurate eigenvalue analysis of membranes

“…Siedlecka et al obtained eigenfrequencies of composite circular and annular membranes with nonuniform material property. 16 Yakhno and Ozdek 17 solved the free vibration problem of a composite circular membrane whose density and tension change piecewisely by approximately commutating the Green's function. Lastly, Wang and Chien 18 Ming derived exact solutions for eigenvalue analysis of circular, annular and sector membranes and investigated the effect of shape variables of the membranes on natural frequencies.…”

Circular membrane with a centrally‐located opening ‐ analytical model using parameterisation of the non‐empty torus

“…They can describe all kinds of electrical, thermal, thermo‐acoustic and acoustic phenomena, flow‐related phenomena, and many others. In this paper, however, the modelled phenomena are mechanical vibrations . Vibrations belong to the most interesting category of phenomena because they can be used in many different ways, for example for energy recovery but most frequently, they are employed to test the technical state of constructions.…”