Vibro-acoustic analysis of complex systems

The law of reciprocity in acoustics and elastodynamics codifies a relation of symmetry between action and reaction in fluids and solids. In its simplest form, it states that the frequency-response functions between any two material points remain the same after swapping source and receiver, regardless of the presence of inhomogeneities and losses. As such, reciprocity has enabled numerous applications that make use of acoustic and elastic wave propagation. A recent change in paradigm has prompted us to see reciprocity under a new light: as an obstruction to the realization of wave-bearing media in which the source and receiver are not interchangeable. Such materials may enable the creation of devices such as acoustic one-way mirrors, isolators and topological insulators. Here, we review how reciprocity breaks down in materials with momentum bias, structured space-dependent and time-dependent constitutive properties, and constitutive nonlinearity, and report on recent advances in the modelling and fabrication of these materials, as well as on experiments demonstrating nonreciprocal acoustic and elastic wave propagation therein. The success of these efforts holds promise to enable robust, unidirectional acoustic and elastic wave-steering capabilities that exceed what is currently possible in conventional materials, metamaterials or phononic crystals. Nonreciprocal acoustic and elastic wave propagation may enable the creation of devices such as acoustic one-way mirrors, isolators and topological insulators. This Review presents advances in the creation of materials that break reciprocity and realize robust, unidirectional acoustic and elastic wave steering.

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Nonreciprocity in acoustic and elastic materials

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).

On the reciprocity relationship between direct field radiation and diffuse reverberant loading.

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.

Numerical and experimental validation of a hybrid finite element-statistical energy analysis method

Mid-frequency structural dynamics with parameter uncertainty

A number of methods have been proposed for predicting the vibro-acoustic response of an automobile in the mid-frequency range. This paper provides a review of a number of these methods and contrasts their strengths and weaknesses. In the past, the term 'mid-frequency' has sometimes been applied rather loosely to differing classes of problem. This paper provides a qualitative definition of the term 'mid-frequency' and identifies the physical behavior that is unique to 'mid-frequency' problems.

A Review of Mid-Frequency Methods for Automotive Structure-Borne Noise

Modeling structure-borne noise with the hybrid FE-SEA method

This paper discusses the development of a computationally efficient numerical method for predicting the acoustics of rattle events upfront in the design cycle The method combines Finite Elements, Boundary Elements and SEA and enables the loudness of a large number of rattle events to be efficiently predicted across a broad frequency range A low frequency random vibro-acoustic model is used in conjunction with various closed form analytical expressions in order to quickly predict impact probabilities and locations An existing method has been extended to estimate the statistics of the contact forces across a broad frequency range Finally, broadband acoustic radiation is predicted using standard low, mid and high frequency vibro-acoustic methods and used to estimate impact loudness The approach is discussed and a number of validation examples are presented

Predicting the Acoustics of Squeak and Rattle

When used correctly, Statistical Energy Analysis (SEA) can provide good predictions of high frequency vibration levels in built-up structures. Unfortunately, the assumptions that underlie SEA break down as the frequency of excitation is reduced, and the method does not yield accurate predictions at "medium" frequencies (and neither does the Finite Element Method, which is limited to low frequencies). A basic problem is that parts of the system have a short wavelength of deformation and meet the requirements of SEA, while other parts of the system do not - this is often referred to as the "mid-frequency" problem, and there is a broad class of mid-frequency vibration problems that are of great concern to industry. In this paper, a coupled deterministic-statistical approach referred to as the Hybrid Method (Shorter & Langley, 2004) is briefly described, and some results that demonstrate how the method overcomes the aforementioned difficulties are presented.

PJ Shorter

Papers

A Review of Mid-Frequency Methods for Automotive Structure-Borne Noise

Modeling structure-borne noise with the hybrid FE-SEA method

Predicting the Acoustics of Squeak and Rattle

Hybrid deterministic-statistical modelling of built-up structures

The spatial correlation of vibrational wavefields and their application to mid-frequency structural-acoustics