This paper presents an study and analysis of acoustic wave scattered and radiated from a truncated conical shell excited by an time-harmonic constant amplitude acoustic wave arriving from infinity by specified angle of incidence. The shell immersed in unbounded air and inner face has in-vacuo condition. Donnel-mushtari theory of shell displacement field proposed to investigate the kinetic and potential energy of shell and Hamilton principal is employed to extract the shell dynamic equation. Incident sound wave is considered as plane wave which is an incoming wave solution of reduced homogenous wave equation. The Helmholtz integral equation is use to model the scattered and radiated sound by shell. Boundary element method (BEM) is employed to relate the surface nodal pressure to nodal displacement. Then by combination of BEM and Rayleigh-Ritz method, the coupled structural-acoustic problem is solved and the sound pressure in any point of medium and shell surface is obtained. The final result has been compared with Finite Element – Boundary Element (FE-BE) method and result shows that the analytical result is in good agreement with the numerical FE-BE method. Also the bahaivor of medium fluid is studied by considering air and water as two case of fluid medium

Keywords: Conical shell vibration, Acoustic Helmholtz integral eqation, Boundary element method, Rayleigh-Ritz method

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