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May 1988

Volume 83, Issue S1, pp. S1-S122

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back to top Session C. Structural Acoustics and Vibration I: Special Session on Response of Coupled Dynamic Systems
Invited Papers
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Modeling structural acoustics for active control (A)

A. H. von Flotow, D. W. Miller, and D. J. Pines

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S6-S7 (1988); (2 pages)

Online Publication Date: 13 Aug 2005

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Active techniques are beginning to be considered for the control of structure‐borne sound. Expertise from many fields is being brought to bear upon this problem, including experience in active control of the acoustic response of ducts and air volumes, and the active control of flexible spacecraft. High‐fidelity modeling is a necessary prerequisite to high‐performance active control. This paper briefly reviews the past approaches to the modeling of structure‐borne sound and approaches taken for their verification. The main body of the paper explains a recently developed approach to such modeling, applicable to a restricted class of structures. The paper closes with the description of two techniques developed for the design of active control systems for structure‐borne sound, and describes preliminary laboratory experimental efforts.
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Response of coupled one‐dimensional dynamic systems (A)

J. Dickey, L. J. Maga, and G. Maidanik

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S7-S7 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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Attention is focused on a complex of one‐dimensional dynamic systems. The extent of a dynamic system is defined in terms of two terminal positions, one at each of two junctions. A terminal vector per junction can thus be constructed. The propagation in a dynamic system is defined in terms of two propagation functions each describing the propagation toward one or the other junction. A diagonal propagation matrix per junction can thus be constructed. The coupling among the dynamic systems is defined in terms of two junction matrices. The external drive at a position on a given dynamic system is defined in terms of the responses that it initiates toward one junction and toward the other junction. With this model and definitions of a complex of coupled one‐dimensional dynamic systems one may appropriately derive the various component matrices of the impulse response matrix. The matrix yields the response of the complex to the appropriately defined external drive vector. The derivation is explained and discussed. The basic (exponential‐type) propagation forms and the nonbasic (e.g., Bessel functional‐type) propagation forms are contrasted. The utility of the formalism is briefly cited and discussed.
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Structural power flow analysis of coupled structures (A)

J. M. Cuschieri

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S7-S7 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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Structural power flow techniques are an effective tool for the dynamic analysis of complex coupled structures, especially those types of coupled structures that are somewhat repetitive. Using the structural power flow method, the response of a structure is analyzed by tracking the flow of the vibrational power through the coupled structures, from the location of the excitation. An advantage of the power flow technique is that, if one component of the structure is modified, the analysis need only be repeated for the modified structural component, and the reevaluation of the coupling expressions. The use of the structural power flow method is demonstrated for beamlike and platelike structures including an analysis of the influence of structural and excitation parameters on the response of the coupled structures. Power flow methods can also be used to analyze more than one type of wave motion, which is useful in cases where incident wave power is scattered into other wave types near structural discontinuities. Additionally, experimental results for structural power flow are discussed. [Work supported by NASA.]
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Coupled systems of anisotropic layers: A group formulation (A)

Michael Schoenberg and Francis Muir

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S7-S7 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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A matrix formalism allows for the simple calculation of the anisotropic, homogeneous medium equivalent to a stationary distribution of thin layers in welded contact. Each layer itself may be an elastic anisotropic medium. The calculated medium is equivalent to the layered medium in the long wavelength limit. The physical properties of any constituent of the heterogeneous system can be shown to be transformable to an element of a commutative group. Adding group elements GA and GB (corresponding to thin layers of constituents A and B, respectively) gives the group element for the homogeneous medium equivalent to the interleaved layers of A and B. The group formulation, which is essentially a statement of conservation laws applicable to layered media, enables us to “decompose” an anisotropic medium into several constituent sets of layers by successive additions of inverse elements, i.e., subtractions. If, after each subtraction, the remaining group element corresponds to a stable anisotropic medium, a valid decomposition is obtained. Within the group of all anisotropic constituents there are nests of subgroups, each subgroup corresponding to a symmetry system more restrictive than the most general triclinic anisotropy. Given the symmetry systems to which the constituents belong, the subgroup structure reveals, a priori, the symmetry of the equivalent medium.
Contributed Papers
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Dominant parameters of weakly coupled systems (A)

Takeru Igusa

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S7-S7 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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A modal analysis framework was developed to identify the dominant characteristics of weakly coupled systems using perturbation analysis and mode synthesis techniques. Modal parameters were obtained to quantify four types of characteristics—tuning, coupling, nonclassical damping, and spatial interaction. These parameters were subsequently used to determine the response of the system to broadband excitation. It was found that the parameters could be used to isolate certain modes of the system with dominant effects on the response. The response characteristics were also examined in the high‐frequency range by extending asymptotic modal analysis [E. H. Dowell and Y. Kubota, J. Appl. Mech. 52, 949–957 (1985)] to include the asymptotic properties of the coupled system parameters. The results were used to illustrate applications in design of isolation mounts in the low‐frequency range, and in providing insight into statistical energy analysis in the high‐frequency range. The work is an extension of the dynamic analysis of lumped mass secondary systems subjected to low‐frequency excitation [T. Igusa and A. Der Kiureghian, J. Eng. Mech. 101, 20–41 (1985)].
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Effect of foundation design and resilient mount positions on structure‐borne noise transmission (A)

Peter K. Kasper and Russel D. Miller

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S8-S8 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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A typical structure‐borne noise control configuration consists of a vibrating machine, a set of resilient isolation mounts, a foundation supporting structure, and a building floor or deck. If the floor is represented by an infinite flat plate and the foundation is comprised of structural beam elements, the acoustic power transmitted to the floor can be calculated in exact fashion using the dynamic direct stiffness technique. This analysis approach involves the representation of beam segment properties in terms of dynamic frequency‐dependent stiffness coefficients. The solution of dynamic displacement response to a harmonic input force parallels the solution of static deflections to an applied constant load. Calculations of transmitted acoustic power were made for a range of foundation structural parameters and resilient mounting configurations. The results indicate the sensitivity to such design parameters on structure‐borne noise transmission.
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Fluid‐loaded constrained‐layer analysis by exact elasticity theory (A)

Laurene V. Fausett and Pieter S. Dubbelday

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S8-S8 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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The constrained‐layer damping technique is based on the attachment of an absorbing viscoelastic layer and a stiff constraining layer to the surface of a metal structure to be damped. Starting from the model by F. M. Kerwin [J. Acoust. Soc. Am. 31, 952–962 (1959)], based on thinplate theory for the base plate, a hybrid model of a fluid‐loaded plate was developed whereby only the base plate is described by exact elasticity theory [P.S. Dubbelday, J. Acoust. Soc. Am. Suppl. 1 80, S121 (1986)]. A description based on exact elasticity theory for all three layers, without fluid loading, was also formulated [D. W. Fausett, L. V. Fausett, and P.S. Dubbelday, J. Acoust. Soc. Am. Suppl. 1 80, S121 (1986)]. The present study further explores the interaction of viscoelastic damping and fluid loading by a description according to exact elasticity theory of all three layers, combined with fluid loading. For flexural waves, the model shows reasonable agreement with the earlier hybrid model at intermediate frequencies, but discrepancies occur at lower and higher frequencies. These are discussed, and possible mechanisms for the behavior are brought forward. [Work supported by ONR.]
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General relationships between acoustic impedance and modal density (A)

Jerome E. Manning

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S8-S8 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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A general formulation of the acoustic impedance is set out using modal analysis. It is shown that the average acoustic resistance can be generally expressed in terms of the modal density of the acoustic space, the bulk compliance of the space, and the average joint acceptance. Examples are given for both simple and complex sources. Although the work presented offers no previously unknown solutions to acoustic radiation problems, it provides a very convenient engineering result that can be used in statistical energy analysis and other related acoustic analysis techniques.
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An analytic model of shear and moment interaction of reinforcing ribs with cylindrical shells for acoustic radiation (A)

Courtney B. Burroughs and Kenneth J. Becker

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S8-S8 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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In response to vibratory motion of a cylindrical shell, reactive forces and moments are generated by reinforcing ribs attached to the interior surface of the shell. These reactive forces and moments modify the shell motion and thereby the farfield acoustic radiation from the shell. Equations governing the motion of a rib, modeled as a circular ring, are derived that include normal and circumferential shear forces, and moments applied to the outer edge of the ring where the ring is attached to the inner surface of the shell. Approximate solutions for the impedances of the ring at the outer edge are obtained and used in equations of motion for a point‐excited, fluid‐loaded, circular cylindrical shell reinforced by periodically spaced ribs.
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