Dynamic Stability of a Cylindrical Shell in an Acoustic Medium

A plane-strain investigation of the dynamic stability of an infinitely long cylindrical shell undergoing breathing oscillations in an infinite inviscid fluid medium is presented. Kinematic nonlinearities of the shell are retained while the fluid is regarded as a linear acoustic medium. A stability criterion which depends strongly upon the acoustic reactance is developed. When the shell is immersed in a fluid, the added mass of the fluid reduces the frequency for parametric resonance. The damping provided by the acoustic resistance proves to be negligible at parametric resonance. The validity of the neglect of kinematic nonlinearities of the fluid is demonstrated by means of an example.