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Imperfections during the manufacturing process can cause significant variations in the noise and vibration levels exhibited by nominally identical structures. Any response calculations employed during the design process should ideally take account of these uncertainties and predict the expected range in performance. Recently a hybrid method has been developed to predict the ensemble average response of a built-up system by combining a deterministic model of parts of the system with a statistical model of other components [Shorter, P. J., and Langley, R. S. (2005) J. Sound. Vib., 288, 669–700]. In this paper the method is extended to predict the ensemble variance of the response. Expressions are derived for the variance of the vibrational energies in the statistical components, and for the variance of the cross spectrum of the response of the deterministic components, which augment the mean values of these quantities predicted by the original theory. The method employs a nonparametric model of uncertainty, in the sense that the statistical components are taken to carry diffuse wave fields, and this obviates the requirement for a detailed description of the system uncertainties. The method is validated by application to a range of coupled plate structures, and good agreement with detailed Monte Carlo simulations is found. [ABSTRACT FROM AUTHOR]

A method is presented for computing the acoustic radiation from baffled, unbaffled, or partially baffled planar structures. The surface displacement and the surface pressure are expressed in terms of wavelets, and the acoustic dynamic stiffness (baffled case) or the acoustic receptance (unbaffled case) between any two wavelets is derived in closed form. The wavelets are employed with translation only (i.e., no dilation), and the jinc function is used; the Hankel transform of this function is the Heavyside step function, and this feature greatly simplifies the analysis. There is a trivial mapping between the wavelet amplitudes and the physical motion of the structure, and hence the dynamic stiffness and receptance results can readily be used to derive the acoustic dynamic stiffness matrix (by inverting the receptance matrix in the unbaffled case) in any set of generalized coordinates. Partially baffled systems can then be studied by substructuring the dynamic stiffness matrix. A set of example problems is considered in which the method is used to compute the resistive and reactive radiation efficiency of a range of benchmark systems. [ABSTRACT FROM AUTHOR]

A recent paper has shown that under certain conditions the cross-spectral matrix of the forces exerted by a vibrational or acoustic wave field on its surrounding boundaries can be expressed in terms of (i) the energy of the wave field, and (ii) the direct field dynamic stiffness matrix of the boundary. This “diffuse field reciprocity relation” was derived using wave mechanics, and it is not immediately clear how the required wave field properties translate to conditions on the vibrational modes of the system or the applied forcing. This issue is addressed here by deriving an extended version of the reciprocity relation using modal methods, and the conditions required for the extended version to reduce to the existing relation are delineated. It is shown that the existing diffuse field reciprocity relation leads to an anomalous result when used to predict the energy variance of a subsystem, and that this anomaly is resolved by using the present extended version of the relation. A supplementary result arising from the analysis is that for systems with a sufficient degree of randomness the ensemble average of the dynamic stiffness matrix of a random subsystem is equal to the inverse of the ensemble average of the receptance matrix. [ABSTRACT FROM AUTHOR]

This paper is concerned with the ensemble statistics of the energy density of a random system subjected to a harmonic point load. Both the mean and variance of the reverberant energy density (i.e., the total response minus the direct field) are investigated. It is shown that the ensemble average of the reverberant energy density is not spatially homogeneous, but rather the value at the drive point is between two and three times the spatially averaged value, depending on the modal overlap factor. This result is closely analogous to established results regarding the case of transient excitation. Expressions are also derived for the relative variance of the reverberant energy density both remote from the drive point and at the drive point, and a number of anomalies are found in existing results. A comparison is made with simulation results for a randomized plate, and this comparison highlights the importance of the ensemble size considered in the simulations. The present analysis is based on a random point process model of the system natural frequencies, and both Gaussian orthogonal ensemble (GOE) statistics and Poisson statistics are considered. [ABSTRACT FROM AUTHOR]

This analysis is concerned with the derivation of a “diffuse field” reciprocity relationship between the diffuse field excitation of a connection to a structural or acoustic subsystem and the radiation impedance of the connection. Such a relationship has been derived previously for connections described by a single degree of freedom. In the present work it is shown that the diffuse–field reciprocity relationship also arises when describing the ensemble average response of connections to structural or acoustic subsystems with uncertain boundaries. Furthermore, it is shown that the existing diffuse–field reciprocity relationship can be extended to encompass connections that possess an arbitrary number of degrees of freedom. The present work has application to (i) the calculation of the diffuse field response of structural–acoustic systems modeled by Finite Elements, Boundary Elements, and Infinite Elements; (ii) the general calculation of the Coupling Loss Factors employed in Statistical Energy Analysis (SEA); and (iii) the derivation of an alternative analysis method for describing the dynamic interactions of coupled subsystems with uncertain boundaries (a generalized “boundary” approach to SEA). © 2005 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

A diffuse wavefield is normally defined in terms of plane waves-to quote one textbook definition 'plane waves are incident from all directions with equal probability and random phase.' In some vibro-acoustic problems the response of a two-dimensional component such as a plate is more conveniently expressed in terms of cylindrical waves, and it is not immediately obvious what properties should be assigned to the cylindrical waves to constitute a diffuse field. It is shown here that a diffuse wavefield can be modeled as a summation of statistically independent cylindrical waves, apart from the fact that each outgoing wave of a particular order is fully correlated to an incoming wave of the same order. A simple relationship is derived between the energy flow P in each wave component and the energy density e of the wavefield: P=ecg/k, where cg is the group velocity and k is the wavenumber. This result is shown to hold true for both bending waves and in-plane waves (longitudinal and shear) in a plate. The work has application to the calculation of coupling loss factors in statistical energy analysis. © 2002 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

An effective investigation of alternative control strategies for the reduction of vibration levels in satellite structures requires realistic, yet efficient, structural models to simulate the dynamics of the system. These models should include the effects of the sources, receivers, supporting structure, sensors, and actuators. In this paper, a modeling technique which meets these requirements is developed and some active control strategies are briefly investigated. The particular subject of investigation is an equipment-loaded panel and the equations of motion are derived using the Lagrange-Rayleigh-Ritz (LRR) approach. The various pieces of equipment on the panel are mounted on active or passive suspensions, and resonators are used to represent the internal dynamics of the mounted equipment. Control of the panel, which transmits vibrations from sources to receivers, is by means of piezoelectric patches and the excitation consists of dynamic loads acting on the equipment enclosures and/or directly on the panel. The control objective is to minimize the displacement at an arbitrary output location. The LRR model developed is verified against one produced by using the finite-element method. Finally, some initial controller design studies are undertaken to investigate and compare the effectiveness of different control strategies (e.g., minimization at the source, along the vibration path, or at the receiver). © 2000 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

A new method is presented for the analysis of complex dynamic systems which is based on partitioning the system degrees of freedom into a 'global' set and a 'local' set. The global equations of motion are formulated and solved in a standard deterministic manner, although due account is taken of the presence of the local degrees of freedom via an approach which is analogous to fuzzy structure theory. The local equations of motion are formulated and solved by using statistical energy analysis (SEA) with due account being taken of power input from the global degrees of freedom. The method can be considered to encompass a number of existing analysis techniques and to form a flexible framework within which a number of detailed modeling strategies can be devised. A simple rod system provides an initial application, and it is shown that the method yields very good results from low to high frequency excitation. © 1999 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

Microvibrations, at frequencies between 1 and 1000 Hz, generated by on board equipment, can propagate throughout a spacecraft structure and affect the performance of sensitive payloads. To investigate strategies to reduce these dynamic disturbances by means of active control systems, realistic yet simple structural models are necessary to represent the dynamics of the electromechanical system. In this paper a modeling technique which meets this requirement is presented, and the resulting mathematical model is used to develop some initial results on active control strategies. Attention is focused on a mass loaded panel subjected to point excitation sources, the objective being to minimize the displacement at an arbitrary output location. Piezoelectric patches acting as sensors and actuators are employed. The equations of motion are derived by using Lagrange's equation with vibration mode shapes as the Ritz functions. The number of sensors/actuators and their location is variable. The set of equations obtained is then transformed into state variables and some initial controller design studies are undertaken. These are based on standard linear systems optimal control theory where the resulting controller is implemented by a state observer. It is demonstrated that the proposed modeling technique is a feasible realistic basis for in-depth controller design/evaluation studies. © 1997 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

It is well known that an undamped periodic structure displays passbands and stop bands, which are frequency bands over which wave motion, respectively, can and cannot propagate. For narrow-band excitation the response of the structure will be minimized by a design which places the excitation band within a stop band. For wideband excitation the effect of the structural periodicity is not obvious, as the response will be enhanced within a passband and suppressed within a stop band. The wideband performance of a periodic structure is investigated here by considering the wave transmission coefficient of an N-bay embedded periodic system. Simple closed-form expressions are derived for the passband and wideband-averaged transmission coefficient in the absence of damping; these expressions depend only upon the amplitude of the transmission coefficient of a single joint within the system. Damping is then considered and it is shown that the wideband efficacy of a damping treatment can be significantly enhanced by structural periodicity, and a simple approximate formula for the effect of damping is derived. The analytical results are illustrated by application to an example system which represents a beam on multiple rotational spring supports. © 1996 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

The modal density of a structural component is a key parameter in high-frequency vibration prediction techniques such as statistical energy analysis (SEA). A study of the literature reveals that the standard method of computing the modal density of a two-dimensional component, such as a plate or shell, is restricted to orthotropic components. This method (which is usually referred to as Courant's method) is extended here to a generally anisotropic component by considering initially the case of periodic (or Born-von Kármán) boundary conditions. It is then shown that the resulting modal density is independent of the nature of the actual boundary conditions which act on the component. On a related issue, doubts have been expressed in the literature as to whether the results yielded by Courant's method are applicable to general boundary conditions if the component exhibits degeneracy of the dynamic edge effect; the present analysis demonstrates that the method is in fact valid in such cases. The developed technique is applied to the bending vibrations of an anisotropic plate, and good agreement is found with empirical results for the modal density derived from natural frequency computations. © 1996 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

The finite element (FE) and statistical energy analysis (SEA) methods have, respectively, high and low frequency limitations and there is therefore a broad class of "mid-frequency" vibro-acoustic problems that are not suited to either FE or SEA. A hybrid method combining FE and SEA was recently presented for predicting the steady-state response of vibro-acoustic systems with uncertain properties. The subsystems with long wavelength behavior are modeled deterministically with FE, while the subsystems with short wavelength behavior are modeled statistically with SEA. The method yields the ensemble average response of the system where the uncertainty is confined in the SEA subsystems. This paper briefly summarizes the theory behind the method and presents a number of detailed numerical and experimental validation examples for structure-borne noise transmission.

This analysis is concerned with the calculation of the elastic wave transmission coefficients and coupling loss factors between an arbitrary number of structural components that are coupled at a point. A general approach to the problem is presented and it is demonstrated that the resulting coupling loss factors satisfy reciprocity. A key aspect of the method is the consideration of cylindrical waves in two-dimensional components, and this builds upon recent results regarding the energetics of diffuse wavefields when expressed in cylindrical coordinates. Specific details of the method are given for beam and thin plate components, and a number of examples are presented.