Acoustic characteristics of annular cavities with locally non-uniform media

A theoretical approach is developed to obtain the natural frequencies and the mode shapes of annular cavities that have locally non-uniform media. The equation of motion is derived based on a special form of the wave equation that is capable of representing the variation of material properties with position, and the unit step function is used in the equation to express the local non-uniformity of the media. The Laplace transform is adopted in eigenvalue analysis to calculate the natural frequencies and the normal mode shapes of the annular cavities. The validity of the presented method is verified through finite element analysis and experiments. Parametric studies are performed to find out the relation between the acoustic characteristics of the cavity and the local deviation of the media, and the acoustic characteristics are explained in terms of the mass and stiffness effect of the local deviation in an annular cavity upon the natural vibration characteristics.