Induced Damping on Vibrating Circular Plates Submerged in Still Fluid

Abstract

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.

Interactions of an Oscillating Rectangular Membrane with a Compressible Fluid

“…It must be said that the case studied by Kwak is not exactly the same as the one considered here because the rectangular plate is situated in an aperture of an infinite rigid plane wall in contact with water and not fully filled submerged in water as in the present case. Furthermore, one can observe a great reduction in frequency in the wet case (with water) with respect to the vacuum case, and this reduction is higher, the lower the value of the mode considered, see Gascón-Pérez et al [2015]. presents an oscillating variation with the wave number k , reaching a maximum for a certain value of k and decreasing to a zero value for high values of k , so this fluid mass coefficient is analogous to a transfer function relating the fluid pressure jump and the deformation of the membrane.…”

Free Vibration Investigation of Submerged Thin Circular Plate

“…Due to the dynamic nature of the system, the boundaries and the fluid-structure interaction forces between the plate and the fluid do not remain constant. Therefore, the need for fluid-structure interaction modelling seems inevitable for the structure and fluid [Gascon-Pérez, 2015;Mnassri and El Baroudi, 2017;Bahaadini and Saidi, 2018;Bahaadini et al, 2018a,b;Saidi et al, 2019].…”

Dynamic Analysis of Circular Plates in Contact with Fluid and Resting on Two-Parameter Foundations

“…Eztensive literatures had studied the characteristic of immersed and submerged plate in fluid Lamb [11] carried out an analytical approach into the investigation of fluidplate coupled system. They determined the natural frequency of clamped circular plate in contact with water using Rayleigh's method, the results were validated later with experimental results of Gascón-Pérez and García-Fogeda [12]. The reviewed of the past studies showed that the analysis of the dynamic behaviour of circular plates resting on Winkler and Pasternak foundations with the aid of differential transformation method has not been investigated.…”