A hybrid method for the vibration analysis of complex structural-acoustic systems
02 Mar 1999-Journal of the Acoustical Society of America (Acoustical Society of America)-Vol. 105, Iss: 3, pp 1657-1671
TL;DR: In this paper, 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.
Abstract: 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.
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TL;DR: The theory behind the hybrid method combining FE and SEA for predicting the steady-state response of vibro-acoustic systems with uncertain properties is summarized and a number of detailed numerical and experimental validation examples for structure-borne noise transmission are presented.
Abstract: 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.
143 citations
TL;DR: In this paper, a number of frequency-domain dynamic analysis procedures of randomly disordered structural systems in the medium frequency range are integrated into the stochastic finite element method to minimize the computational effort in the mid-frequency range.
122 citations
TL;DR: In this article, the authors proposed a new approach for determining the distribution of mechanical and acoustic wave energy in complex built-up structures by interpolating between standard statistical energy analysis (SEA) and full ray tracing.
97 citations
Cites background or methods from "A hybrid method for the vibration a..."
...SEA has been used as a starting point for penetrating the mid-frequency regime by employing hybrid methods based on combining FEM and SEA treatments [18,41,42,44]....
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...Wave effects often become important in mechanical structures containing elements with short and long wavelengths (at the same basic frequency) and hybrid SEA—finite element methods have been developed in this case [18,41,42]....
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TL;DR: In this paper, the authors provide an overview over basic concepts in this emerging field of wave chaos, which ranges from ray approximations of the Green function to periodic orbit trace formulae and random matrix theory and summarizes the state of the art in applying these ideas in acoustics.
Abstract: Interpreting wave phenomena in terms of an underlying ray dynamics adds a new dimension to the analysis of linear wave equations. Forming explicit connections between spectra and wavefunctions on the one hand and the properties of a related ray dynamics on the other hand is a comparatively new research area, especially in elasticity and acoustics. The theory has indeed been developed primarily in a quantum context; it is increasingly becoming clear, however, that important applications lie in the field of mechanical vibrations and acoustics. We provide an overview over basic concepts in this emerging field of wave chaos. This ranges from ray approximations of the Green function to periodic orbit trace formulae and random matrix theory and summarizes the state of the art in applying these ideas in acoustics—both experimentally and from a theoretical/numerical point of view.
96 citations
TL;DR: In this article, a wave-based model for the acoustic cavity and a direct or modally reduced Finite Element Method for the structural part are combined for coupled structural-acoustic analysis.
67 citations
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TL;DR: In this article, first-order reliability and finite element methods are used to develop a methodology for reliability analysis of structures with stochastically varying properties and subjected to random loads, and the influence of the correlation length of random property or load fields on the reliability of example structures are investigated.
515 citations
234 citations
TL;DR: In this paper, the authors present a discussion of the rationale for the use of probabilistic energetic models for high-frequency vibration prediction, and introduce the postulate upon which conventional SEA is based.
Abstract: For the benefit of the ‘enquirer within’, who may not be familiar with the background and concepts of SEA, this overview opens with a discussion of the rationale for the use of probabilistic energetic models for high-frequency vibration prediction, and introduces the postulate upon which conventional SEA is based. It compares and relates the modal and travelling wave approaches, discusses the strengths and weaknesses of SEA as currently practised and points out needs and directions for future research. Critical discussions of individual contributions to the development of the subject are presented only in as much as they treat specific matters of concept, principle or reliability. The roles of SEA in providing a framework for experimental investigations of the high-frequency dynamic behaviour of systems and in interpreting observations on operating systems, although equally important, are not substantially addressed. Nor are specific experimental techniques which involve considerations of transducers, spatial sampling, signal processing, error analysis and data interpretation, which require a critical review in their own right.
193 citations
TL;DR: In this article, the average and variance of power injected by point sources are calculated and the statistics of response near and away from the driving point are also found, and two kinds of estimation intervals are derived and applied to some simple examples.
Abstract: The calculation of input power and response of simple models of rooms and structures is described. The approach is essentially statistical. Random variations in time are not considered; these fluctuations are averaged out. Randomness is introduced into the system models by considering basic parameters such as resonance frequencies and observation position to be selected statistically. Simplifying assumptions on the damping and mode shapes are made. The average and variance of power injected by point sources are calculated. The statistics of response near and away from the driving point are also found. It has not been possible to calculate the exact forms for the response distributions. Accordingly, in order to find confidence coefficients for estimation intervals, a distribution is chosen ad hoc. The selected one, the gamma distribution, has several desirable features. It is, in fact, exact for some important cases. Two kinds of estimation intervals are derived and applied to some simple examples. Finally, an interesting alteration of the frequency‐spacing statistics, inspired by nuclear spectroscopy, is explored. It is found that a “level‐repulsion” phenomenon causes small separations in resonance frequency to be less probable. This can smooth the multimodal response of systems in some important, practical instances.
164 citations
TL;DR: In this paper, a probabilistic model of the structural fuzzy is proposed to improve the calculated estimates of the vibrations into the master structure and of the far field radiated by itself in or out of context of the acoustic scattering.
Abstract: In linear dynamical analysis of complex mechanical systems, the structural fuzzy is defined as the set of minor subsystems that are connected to the master structure but are not accessible by classical modeling. The notion of master structure is presently extended to others elements such as an external dense compressible fluid strongly coupled with the primary structure. For the low‐frequency (LF) dynamical analysis, the modeling of the structural fuzzy is commonly made with a system of masses. If the LF modeling of the structural fuzzy is applied in the medium‐frequency (MF) domain, there are some large differences between calculations and experiment. It is therefore necessary to take into account internal degrees of freedom of the structural fuzzy. A global probabilistic modeling of the structural fuzzy is proposed to improve the calculated estimates of the MF vibrations into the master structure and of the far field radiated by itself in or out of context of the acoustic scattering. This paper reviews the author’s previous work and introduces the type II probabilistic constitutive law. In this paper: (1) a probabilistic modeling of the structural fuzzy is presented, (2) two probabilistic constitutive laws of the structural fuzzy are constructed, (3) the modeling in the MF range for vibroacoustic predictions using theory of structural fuzzy is developed, (4) the fuzzy solution in the MF range is studied, and (5) numerical simulations on standard structures and on a submerged complex industrial structure are shown.
158 citations