Transverse Vibrations of Composite, Circular Annular Membranes: Exact Solution

Vibration analysis of composite circular and annular membranes

“…The solution to the vibration problem of a nonhomogenous membrane in a closed form can be derived only for the cases of some functions describing the change in the material density and thickness of this membrane. Free vibration problems of circular and annular membranes when the density varies with the radial co-ordinate are the subject of papers [1][2][3][4][5]. The solution to the vibration problem of a membrane comprising two concentric annular membranes has been derived in an exact form by Laura et al in paper [1].…”

“…Free vibration problems of circular and annular membranes when the density varies with the radial co-ordinate are the subject of papers [1][2][3][4][5]. The solution to the vibration problem of a membrane comprising two concentric annular membranes has been derived in an exact form by Laura et al in paper [1]. Gottlieb [2] gives the explicit values of the radial spectrum of an annular membrane with a stepped density which contains inverse fourth power logarithmic terms in the density function.…”

Free vibration of composite circular membranes

“…In particular, the eigenfrequencies of membranes have great significance to the design of aeronautical, naval and civil structures as well as musical instruments. The free vibration of composite, circular annular membranes are the subject of papers [1][2][3].…”

“…The solution to the vibration problem of a composite membrane consisting of two concentric membrane segments (each with constant density), can be derived in an exact form [1,2]. In this case the membrane segments create the nonhomogenous membrane for which the frequency equation by determinant of a 4x4 matrix is expressed.…”

“…In this case the membrane segments create the nonhomogenous membrane for which the frequency equation by determinant of a 4x4 matrix is expressed. Using this equation in paper [1] the eigenfrequencies of the membrane for various ratio of membrane densities and various ratio of radii of the distinguished membrane segments were numerically determined. The general formulation of the eigenproblem for membrane of arbitrary discontinuous variations of the density in the radial direction is given in paper [2].…”