The present investigation is devoted to an acoustic radiation induced by steady-state low-frequency vibration of an arbitrary shell of revolution with mass and stiffness inhomogeneities along the x axis (Fig.1). Assuming the axial symmetry of thesource, we shall consider the desired solution in terms of circumferential coordinate,Φ), according to every vibrating mode, m, regardless of the over circumferential vibrating modes. Hereafter all transformations will be related to the amplitude values, corresponding to the mth vibrating mode. The general equation of the linear theory of thin axisymmetrical shell in terms of the mid-surface translation [1], {U} ={sup}T under external pressure load, {P}={sup}T assumed to beZ ({(U)- λ{sup}2ρh{U} + Iλγ{U}={P} + {0.0,p0}(vertical array)where Z is the linear differential operator, λ the circular frequency, p the mass density, h the shell thickness, γ the damping coefficient, P{sub}0 the hydrodynamic pressure load.
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