HIGH FREQUENCY RESPONSE OF A FLUID-FILLED CYLINDRICAL SHELL WITH AN INTERNAL COLUMN OF GAS BUBBLES: APPLICATION TO ACTIVE ACOUSTIC GAS LEAK DETECTION

Abstract

The high frequency response to a point force excitation of an infinite elastic cylindrical shell, filled with a liquid including a column of gas bubbles, is investigated. A state vector approach is used for the shell theory to include the effects of shear deformation and rotary inertia. The far field mobility of the shell for each propagating circumferential mode nis calculated using a residue method. Each of these residues are evaluated at the poles k ns of the infinite coupled system. The waves associated with axial wavenumbers of the same type (order s) reveal similar characteristics in the fluid field, such as the number of radial nodal lines, and the corresponding residues are thus grouped together. The resulting wave type decomposition of the system response carries important information. At the non-dimensional Ω = 10 for the shell studied, the response of the system is dominated by s= 1 waves and a column of gas bubbles in the fluid field is difficult to detect by its effects on the vibrations of the shell. As the frequency is increased (to Ω = 50, for example), the system response is dominated by waves of increasing type order ( s= 15, 16, ...,) and a column of gas bubbles has the effect of bringing a large attenuation to the shell response. Various experiments were performed to verify these results.