Acoustics of Fluid-Structure Interactions (Cambridge by M. S. Howe

By M. S. Howe

Acoustics of Fluid-Structure Interactions addresses an more and more vital department of fluid mechanics--the absorption of noise and vibration via fluid circulation. This topic, which bargains a number of demanding situations to traditional parts of acoustics, is of transforming into hindrance in areas the place the surroundings is adversely plagued by sound. Howe offers valuable historical past fabric on fluid mechanics and the simple innovations of classical acoustics and structural vibrations. utilizing examples, lots of which come with whole labored options, he vividly illustrates the theoretical thoughts concerned. He presents the foundation for all calculations beneficial for the choice of sound iteration through airplane, ships, normal air flow and combustion structures, in addition to musical tools. either a graduate textbook and a reference for researchers, Acoustics of Fluid-Structure Interactions is a vital synthesis of knowledge during this box. it's going to additionally relief engineers within the concept and perform of noise regulate.

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Example text

However, it is simpler to derive the general acoustic reciprocal theorem directly from the continuum differential equations of motion. 5). 2 Reciprocal Theorem for Fluid-Structure Interactions Consider a stationary (viscous) fluid of uniform mean pressure po, but with variable mean density po(x) and sound speed co(x). ). 1. The reciprocal theorem. 4a, b) where vt = i;/ (x, co) denotes the complex amplitude of the velocity v(x, a))t~l(O\ and so forth. The simplifying approximation (l/p)Dp/Dt = (l/pc2)Dp/Dt— (PT/Cp)Ds/Dt & —(ico/pocl)p has been made in the continuity equation.

1, involving a small deformation from a planar interface, the undisturbed values of r/y and ptj may be assumed to vanish. 5) is applied at the undisturbed position x2 = 0 of the interface. 8) this becomes x22 ( = —p + 2rj I dv2/ax2 l x2a = 2r](dv2/dxa + dva/dx2), \ div v I , a = 1, 3. 6) At high Reynolds number viscous stresses are often negligible compared to the normal pressure forces. 6) are then r22 = —p, z2a = 0, a = 1,3. If the surface is highly compliant, however, it may be necessary to retain the contribution from the tangential component of the viscous stress.

14)). The velocity v associated with the sound is called the acoustic particle velocity. 3 Plane Waves A plane acoustic wave propagates one dimensionally, say in the x\ -direction, and satisfies (d2/c2odt2 - d2/dx2)cp = 0. 16) where

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