Dynamic Response of a Lined Rigid Inclusion

A theoretical analysis is made to predict the dynamic response of an elastically lined cylindrical rigid inclusion subjected to plane compressional sinusoidal stress waves. Solutions in the form of infinite series involving Hankel functions of the first and second kinds for the wave equations are determined from the prescribed boundary conditions. The nondimensional parameters are then identified and typical material properties are used in numerical calculations. It is found that the angular distribution of the maximum dynamic stresses follows a certain pattern depending on the wave number. In addition, the lining-inclusion density ratio and the lining thickness also have strong influence on the critical stresses. The translation of the rigid inclusion, although having similar response characteristics against wave number as the stresses, always reaches its critical value at a lower wave number than do the stresses.