Last modified: 2018-04-16

#### Abstract

An acoustic-velocity based finite element procedure is presented in this paper to investigate the propagation of pressure transients in a two-dimensional fluid-structure acoustic system. The nine-node Lagrangian finite elements are employed to formulate the dynamic equations of fluid and solid media. The strong interactions between the fluid and the structure are modelled by enforcing no-separation condition in the direction normal to the fluid-structure interface. In the tangential direction, the slip and stiction of the fluid particles relative to the fluid-structure interface for varying dynamic pressure are modelled using the classical law of friction. The so-obtained wave equations are discretized in the time domain using the implicit Newmark integration scheme. For fluid-structure interactions in the tangential direction, the discontinuous frictional force problem involving both equality and inequality frictional constraints is successfully reduced to a quadratic mathematical problem or the linear complementary problem (LCP) with the introduction of non-negative and complementary variable pairs (supremum velocities and slack forces). The so-obtained complementary equations in the complementary pairs can be solved efficiently using the Lemke algorithm.

Motion of different media in the acoustic system is induced exclusively by a local sound source away from the structure. The fluid is considered stationary with no bulk flow. For small scale acoustic motion, the initial cold and conformal finite mesh is used effectively to address the key fluid-structure interaction phenomena. If needed, the initial mesh can be updated at the end of each time step to more accurately account for the fluid-structure interactions. The objectives of this research are to present a generic model for the tangential fluid-structure interactions, understand the transient properties of acoustic pressure in the multi-media acoustic system, and reveal the sound reflection/absorption characteristics. From the numerical results, obtained using the proposed scheme, and comparisons with ANSYS for various scenarios, the proposed scheme is found to be efficient and accurate in solving strong fluid-structure interaction problems.