Damping of structural vibrations by acoustic radiation.
Damping of real structures, such as panels, can be caused by different mechanisms of energy dissipation. Sound radiation from a vibrating, elastic body is a loss of energy and represents damping of the motion of the body. Damping due to acoustic radiation is significant for thin plates and lightweight sandwich structures. Knowledge of damping is important in the estimation of the vibratory stress response of a resonant mode in structures subjected to random excitation. Equivalent viscous modal damping ratios are required in the estimation of stress at the fundamental or low order modes in panels which are liable to acoustic fatigue. In this Item modal damping, due to acoustic radiation, is defined in terms of the specific damping capacity, which is related to the sound radiation efficiency, a measure of how well a panel radiates sound. The resonant modes of a simply-supported, isotropic, rectangular panel in an infinite baffle are considered in the context of specific damping capacity, which can also be related to the loss factor and the equivalent viscous damping ratio.
Values of specific damping capacity (as well as equivalent viscous damping ratio) are given for sixteen modes (up to m = 4, n = 4) for rectangular panels with different geometry. Design curves from which the specific damping capacity for a particular mode can be estimated are presented for rectangular, simply-supported panels and can be used for any material of the panel. Each design curve, dependent only on aspect ratio of the panel, is presented as a relation between a non-dimensional parameter, Δmn, for the (m,n) mode and a scaling factor, H. The non-dimensional parameter, Δmn, is proportional to the specific damping capacity multiplied by the product of the ratio of the sound velocity in the plate material to the velocity of sound in the fluid and the ratio of the fluid density to the density of the panel material. The scaling factor, H, is essentially the non-dimensional thickness of the panel (thickness/ square root of panel area) multiplied by the ratio of the sound velocity in the plate to the sound velocity in the fluid. Hence, the specific damping capacity for a panel of the required geometry can be estimated from the design curves, if the material properties of the panel, such as Young's modulus, density and Poisson's ratio, as well as the density of the surrounding fluid and the velocity of sound in the fluid, are known. Additionally, for the special case of rectangular panels made from a typical aluminium alloy design curves are presented, representing a direct relationship between the equivalent viscous damping ratio and the dimensionless thickness for 16 modes (up to m = 4, n = 4).
The most significant damping occurs at the fundamental mode (1, 1) for a wide range of the dimensionless panel thickness and aspect ratios. In the case of mode (1, 1) the equivalent viscous damping ratio maintains a constant value within a wide range of the dimensionless plate thickness for a particular aspect ratio. This constant value of the damping ratio increases with the aspect ratio. The equivalent viscous damping ratio can reach for the majority of modes maximum values comparable to those of the fundamental mode, but only within a limited range of the dimensionless panel thickness. Besides the mode (1, 1), only the modes (3, 1) and (1, 3) exhibit constant damping ratios within a relatively wide range of panel thickness.
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