Vibro-acoustics analysis of uid-filled shells using the transfer matrix method

Kamani, Ravikumar V and B, Venkatesham (2018) Vibro-acoustics analysis of uid-filled shells using the transfer matrix method. Masters thesis, Indian Institute of Technology Hyderabad.

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Abstract

Cylindrical and conical shell structures are commonly used in Heating Ventillation and Air-Conditioning (HVAC) ducts, aircraft fuel tank, submarine, for conveying petroleum products, etc. The presence of uid inside the structure changes the dy- namical behavior of the shell structure. So, it motivates us to perform vibro-acoustic analysis of uid-�lled structures and understand the in uence of uid on natural fre- quencies, especially when the uid in consideration is much denser than the air. A vibro-acoustic analysis is the prediction of structural vibration caused by the uid inside the structure. Here, the uid essentially acts as a lumped mass without chang- ing the sti�ness of the structure. Hence, the analysis deals only with the e�ect of uid on the structure, and the consequence of structural vibration on the uid properties such as uid pressure, particle velocity, uid density, is not considered. In the current thesis, the vibro-acoustic modal analysis is performed on a uid-�lled structure, using the transfer matrix approach. The transfer matrix connects the up- stream 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 uid pressure force term is introduced into the equation of motion in radial direction and also assuming the inside pressure distribution in circumferential and axial direction is same as shell wall radial displacement pattern. At the uid-structure interface, the shell-structure nor- mal vibration velocity is equated to uid particle velocity to ensure the continuity. The governing equations are written in state-space form, which is integrated to get the transfer matrix in terms of eight state variables. The continuity condition leads to a uid-loading term. The same transfer matrix formulation is applicable for uncoupled structural problem by making uid 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. Numerical model of cylindrical shell �lled with water is developed using Finite and Boundary Element Method (FEM-BEM). The shell-structure is modeled with six de- grees of freedom shell elements in �nite element model and uid boundary is taken as mesh model in Boundary Element Model (BEM). These two model meshes are mapped in the circumferential direction. The transfer matrix method results are val- idated with FEM-BEM model and with available literature data.

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