Nonlinear structural and acoustic responses of three-dimensional elastic cylindrical shells with internal mass-spring systems

Abstract

Abstract Prediction of the vibration and sound radiation of an elastic cylindrical shell with nonlinear internal structures is of significant interest to marine and aerospace industries. This paper investigates the structural and acoustic behaviors of a finite cylindrical shell attached with a nonlinear spring-mass-damper system and embedded in an infinite acoustic medium. The restoring forces of the springs are expressed as general polynomial functions of the spring deformation, from which the nonlinear quadratic, cubic and quartic springs can be directly recovered. The exact three-dimensional theory of elasticity is employed for the structural modeling of the cylindrical shell. The discretized equations of motion of the coupled nonlinear structural system are established using an efficient modified variational method, and the fluid surrounding the shell is computed by a time-domain Kirchhoff boundary integral formulation. The two sets of structural and acoustic equations are coupled together through the compatibility conditions on the fluid-structure interface. The present results are validated by comparing the solutions obtained from the finite element method and those available in the literature. The vibration and sound pressure responses of the coupled structural system with nonlinear quadratic, cubic and quartic springs are investigated. The contributions of the circumferential wave modes of the shell to the nonlinear vibro-acoustic responses and sound directivity patterns of the nonlinear coupled structural system are discussed.