Modes and resonances of finite elastic structures under heavy fluid loading

1981 ◽  
Vol 70 (S1) ◽  
pp. S9-S9
Author(s):  
D. G. Crighton ◽  
D. Innes
Keyword(s):  
Fluid Loading ◽  
Heavy Fluid ◽  
Elastic Structures

The modes, resonances and forced response of elastic structures under heavy fluid loading

1984 ◽  
Vol 312 (1521) ◽  
pp. 295-341 ◽  
Keyword(s):  
Order Approximation ◽  
Low Frequency ◽  
Forced Response ◽  
Mode Shapes ◽  
Thin Elastic Plate ◽  
Fluid Loading ◽  
Heavy Fluid ◽  
Elastic Structures ◽  
Strip Plate ◽  
First Time

This paper reports analytical studies of problems that involve the motion of plane elastic structures under conditions of heavy fluid loading. The main aspect concerns the description of the vibration response of a thin elastic plate (or membrane), of finite extent in at least one dimension, when the structure is excited by concentrated mechanical drive along a line or at a point; and as part of this the possibility of resonant response is discussed, and the resonance conditions and free modes of oscillation are obtained. There is also some discussion of the acoustic fields radiated by the structures under localized mechanical excitation. The analysis makes extensive use of results for the reflection of a structural wave (subject to heavy fluid loading) at an edge, and the paper gives results for that reflection process covering waves incident normally on eight different edge configurations and waves incident obliquely on two edge configurations. These results include the reflection coefficient (whose magnitude is unity in the leading-order approximation of low-frequency heavy fluid loading), and the amplitude and directivity of the edge-scattered sound. By using the argument that edge reflection is a local process, the response is then calculated for a strip plate, under both line and point forcing, and the response is, for the first time, obtained for structures finite in both dimensions and subject to heavy fluid loading. Specifically, solutions are given here for a circular plate with eccentric drive, and for a membrane model of a rectangular panel, with central point drive. For some conditions and geometries expressions in simple form are found for the natural frequencies and mode shapes, and for the off-resonance forced response. Expressions for the drive admittances are found which display a variety of interesting features.

A hybrid method for predicting heavy fluid loading of structures

2015 ◽  
Vol 137 (4) ◽  
pp. 2324-2324
Author(s):  
Micah R. Shepherd ◽  
John B. Fahnline
Keyword(s):  
Hybrid Method ◽  
Fluid Loading ◽  
Heavy Fluid

Transmission of energy down periodically ribbed elastic structures under fluid loading

1984 ◽  
Vol 394 (1807) ◽  
pp. 405-436 ◽  
Keyword(s):  
Surface Wave ◽  
Long Range ◽  
Formal Solution ◽  
Stop Band ◽  
Elastic Membrane ◽  
Wave Component ◽  
Fluid Loading ◽  
Heavy Fluid ◽  
Resonance Frequencies ◽  
Acoustic Component

The paper studies a model configuration in which an elastic membrane is immersed in static compressible fluid, excited by a time-harmonic line force and supported by a periodic array of line supports (ribs) of infinite mechanical impedance. At the driven rib the velocity has a prescribed value V 0 , while the velocities vanish at the locations, x = nh ( n = ± 1, ± 2,. . .), of the supporting ribs. Fluid loading provides the only coupling between adjacent bays, and the aim is to expose the dual role of that coupling (local and long range) in the transmission of energy from the excitation to infinity along the structure and to the acoustic radiation field. This transmission is characterized by the variation with n of the force F n exerted on the structure by the n th rib. An exact formal solution is obtained for F n in terms of the Green function G(x) of the unribbed fluid-loaded structure, and explicit expressions are obtained for F n when only the subsonic surface wave component, G s ( x ), is included in G(x) (though with full account of fluid loading in G s ( x ) itself). These expressions show that under ‘significant’ and ‘heavy’ fluid loading (terms made precise in the text), fluid loading in the form of subsonic surface waves provides a local bay-to-bay coupling very much like that of an imperfect mechanical isolation, and induces a pass and stop band structure of the kind familiar from other studies of wave propagation in mechanically-coupled periodic structures in the absence of fluid loading. Under ‘light’ fluid loading it is shown that there can be no strict pass bands, but frequency bands around the vacuum bay resonance frequencies are identified within which the energy decay rate along the structure is very slow. In all these calculations the fate of the power injected by the excitation is followed in all detail, whether to infinity in the structure or to infinity in the acoustic field. The acoustic component G a ( x ) is then included, and specific asymptotic expressions for G a ( x ) are used to deal with the light and heavy fluidloading cases. These expressions for G a ( x ) involve slow algebraic decay with x , and induce a generally similar decay of the F n with n . In this sense, the acoustic component G a ( x ) provides a long-range coupling between the driven rib and distant ribs which, in the stop bands, is much stronger than the exponentially weak coupling provided by the surface wave component G s ( x ). Numerical estimates are given which indicate that in both light and heavy fluid loading the acoustic component of the force F n exceeds the surface wave component once n exceeds a very modest value. The paper ends with a discussion of the possible implications for structure-borne noise control in periodic fluid-loaded structures, for the application of Statistical Energy Analysis to structures under fluid loading, and for the relevance of the ideas of Anderson localization in an irregular structure under fluid loading.

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