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Abstract :
Cylindrical shell structures are commonly used in HVAC ducts, aircraft fuel tank, submarine, for conveying petroleum products, etc. The presence of fluid inside the structure changes the dynamical behavior of the shell structure. So, it motivates to do vibro-acoustic analysis of fluid-filled structures and understand the influence of fluid on natural frequencies, especially when the fluid in consideration is much denser than the air. A vibro-acoustic analysis is the prediction of structural vibration caused by the fluid inside the structure. Here, the fluid essentially acts as a lumped mass without changing the stiffness of the structure. Hence, the analysis deals only with the effect of fluid on the structure, and the consequence of structural vibration on the fluid properties such as fluid pressure, particle velocity, fluid density, is not considered. In the current paper, the vibro-acoustic modal analysis is performed on a fluid-filled cylindrical shell, using the transfer matrix approach. The transfer matrix connects the upstream state variables to the downstream state variables, and it is computationally less expensive. In this method, the governing equations of shell vibration are expressed in terms of eight state variables. These parameters are three displacements, one slope, two membrane forces, one moment and one shear force. The fluid pressure force term is introduced into the equation of motion in the radial direction and also assuming the inside pressure distribution in circumferential and axial direction is same as shell wall radial displacement pattern. At the fluid-structure interface, the shell-structure normal vibration velocity is equated to fluid particle velocity to ensure the continuity. The governing equations are written in the state-space form, which is integrated to get the transfer matrix in terms of eight state variables. The continuity condition leads to a fluid-loading term. The same transfer matrix formulation is applicable for the uncoupled structural problem by making fluid loading term zero. Symmetric and asymmetric boundary conditions are used to reduce the transfer matrix size. Natural frequencies are calculated by making the determinant of the reduced transfer matrix as zero. A numerical model of cylindrical shell filled with water is developed using Finite and Boundary Element Method (FEM_BEM). The shell-structure is modeled with six degrees of freedom shell elements in finite element model and the fluid boundary is taken as mesh model in Direct Boundary Element Model (DBEM). These two model meshes are mapped in the circumferential direction. The fluid loading is incorporated as an extra mass in the structural equations. In this analysis, vibro-acoustic natural frequencies of the cylindrical shell are presented for the clamped-clamped boundary condition. The transfer matrix method results for cylindrical shell structure with and without fluid are validated with FEM-BEM model and with available literature data.