Received RevisedWhen a structure vibrates immersed in a fluid it is known that the dynamic properties of the system are modified. The surrounding fluid will, in general, contributes to the inertia, the rigidity and the damping coefficient of the coupled fluid-structure system. For light structures, like spacecraft antennas, even when the fluid is air the contribution to the dynamic properties can be important. For not so light structures the ratio of the equivalent fluid/structure mass and rigidity can be very small and the fluid contribution could be neglected. For the ratio of equivalent fluid/structure damping both terms are of the same order and therefore the fluid contribution must be studied. The working life of the spacecraft structure would be on space and so without any surrounding fluid. The response of a spacecraft structure on its operational life would be attenuated by the structural damping alone but when the structure is dynamically tested on the earth the dynamic modal test is performed with the fluid surrounding it. The results thus are contaminated by the effects of the fluid. If the damping added by the fluid is of the same order as the structural damping the response of the structure in space can be quite different to the response predicted on earth. It is therefore desirable to have a method able to determine the amount of damping induced by the fluid and that should be subtracted of the total damping measured on the modal vibration test. In this work a method for the determination of the effect of the surrounding fluid on the dynamic characteristics of a circular plate has been developed. The plate is assumed to vibrate harmonically with the vacuum modes and the generalized forces matrix due to the fluid is thus computed. For a compressible fluid this matrix is formed by complex numbers indicating that include terms of inertia, rigidity and damping. The matrix due to the fluid loading is determined by a boundary element method (BEM). The BEM used is of circular rings on the plate surface so the number of elements to obtain an accurate result is very low. The natural frequencies of the system are computed by an iteration procedure one by one and also the damping fluid contribution. Comparisons of the present method with various experimental data and other theories show the efficiency and accuracy of the method for any support condition of the plate.
Interaction of an oscillating membrane with a fluid is important because the wide variety of technological applications. A boundary element method has been employed for the analysis of a vibrating rectangular membrane in contact with a compressible fluid at rest. The deformation modes of the membrane correspond to the vacuum case. For the calculation of the pressure jump over the membrane, the Helmholtz’s integral equation for the fluid pressure is employed taking into account the fluid-membrane interface boundary condition. Considering the membrane equation and applying a collocation method, the natural frequencies of the interacting system are obtained. The influence of various parameters such as aspect ratio, fluid density and membrane dimension on these frequencies is evaluated. Furthermore, the influence of the wave number on the fluid mass coefficient and the acoustic damping ratio are evaluated. The validity of the method is deduced when comparing the results obtained by other authors and theories.
Received RevisedT he study of the dynamic behaviour of a membrane in contact with a fluid is interesting due to the numerous applications in technology. The vibro-acoustic behaviour of a circular membrane in a cylindrical container or a membrane drum filled with a non-viscous fluid is analyzed . A boundary element method is used and the acoustic pressure over the boundary is calculated employing the Kirchhoff`s integral equation and that with the equation of motion of the membrane, the natural frequencies of vibration are obtained. Furthermore the effect of the drum height, drum radius, membrane material density, tension parameter and fluid density on the frequencies are evaluated, as well as the variation of the fluid mass coefficient with the wave number. Validation of the method is made comparing the results with those obtained by other authors and theories.
In this paper, the thermo-acoustic behavior of a rectangular panel fully immersed in a compressible fluid at rest is investigated. A boundary element method (BEM) has been employed taking into account the Kirchhoff–Helmholtz (K-H) integral equation for the acoustic pressure and with the fluid-plate interface boundary condition the acoustic pressure jump over the panel is calculated. The thermal effects are considered regarding in the form of a uniform increment of temperature of the panel and are analyzed in order to prevent the buckling phenomena. The deformation modes of the panel correspond to the vacuum case. Applying a collocation method for the panel equation, the natural frequencies are obtained. The effects of several geometric parameters regarding different thermal loads on these frequencies are evaluated. Furthermore, the influence of the wave number for different temperatures of the panel on the acoustic damping ratio is evaluated, as well as the acoustic radiation efficiency for the different modes. The verification of the method is proven with other works.
In this work, the influence of the surrounding fluid on the dynamic characteristics of almost circular plates is investigated. First the natural frequencies and normal modes for the plates in vacuum are calculated by a perturbation procedure. The method is applied for the case of elliptical plates with a low value of eccentricity. The results are compared with other available methods for this type of plates with good agreement. Next, the effect of the fluid is considered. The normal modes of the plate in vacuum are used as a base to express the vibration mode of the coupled plate-fluid system. By applying the Hankel transformation the nondimensional added virtual mass 2 increment (NAVMI) are calculated for elliptical plates. Results of the NAVMI factors and the effect of the fluid on the natural frequencies are given and it is shown that when the eccentricity of the plate is reduced to zero (circular plate) the known results of the natural frequencies for circular plates surrounded by liquid are recovered.
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