Random excitations can result from various types of non-deterministic loads such as wind loads, terrain loads, and other types of white noise loads. In this paper, an overview is presented of the modal method to obtain the random response of a coupled structural-acoustic system subjected to random excitations. When the structural system is coupled with an enclosed cavity, the structural-acoustic frequency response functions (FRFs) can be obtained using the uncoupled structural modes and the uncoupled acoustic modes, with structural-acoustic coupling as well as modal damping included in the formulation. The random response of the coupled structural-acoustic system is then obtained by summation of the structural-acoustic FRFs with the applied auto- and cross-spectral random loadings at the excitation locations. The theoretical formulation of the coupled structural-acoustic system is described. An example of a rectangular cavity coupled with flexible panels exposed to external random white noise load is presented. The methodology is then applied to an automotive vehicle travelling over a randomly rough road to predict the interior sound pressure response in the vehicle.

In the past decade, plate-like structures embedded with one or more acoustic black hole (ABH) features have been developed as a promising passive approach for structural sound and vibration control. In this study, the concept of combining dynamic vibration absorbers (DVAs) and the ABH effect is proposed to further improve the vibration control effectiveness of a variable thickness plate. A finite element (FE) model is developed to analyze the vibration response of a plate embedded with both ABHs and DVAs under point force excitations. To demonstrate the effectiveness of different vibration control approaches, the vibration responses of plates of uniform thickness, variable thickness embedded with ABH features, variable thickness embedded with both ABH features and damping layers, and variable thickness embedded with both ABH features and DVAs are compared experimentally. It is shown that, in the frequency range considered in the current study which is up to 6.4 kHz, the uniform plate presents high average velocity response level. On the other hand, although 11.5% lighter, the variable thickness plate integrated with both ABH and DVA features results in the lowest response level. Results in this study demonstrate the potential of combing DVAs and ABHs together as an effective lightweight noise and vibration control approach.

The Acoustic Black Hole (ABH) has been developed in recent years as an effective, passive, and lightweight method for attenuating bending wave vibrations in beams and plates. The acoustic black hole effect utilizes a local change in the plate or beam thickness to reduce the bending wave speed and increase the transverse vibration amplitude. Attaching a viscoelastic damping layer to the ABH results in effective energy dissipation and vibration reduction. Surface averaged mobility and radiated sound power measurements were performed on an aluminum plate containing an array of 20 two-dimensional ABHs with damping layers and compared to a similar uniform plate. Detailed laser vibrometer scans of an ABH cell were also performed to analyze the vibratory characteristics of the individual ABHs and compared with mode shapes calculated using Finite Elements. The diameter of the damping layer was reduced in successive steps to experimentally demonstrate the effect of damping layer distribution on the ABH performance. The experimental analysis demonstrated the importance of low order ABH modes in reducing the vibration and radiated sound power of plates with embedded ABHs. The results will be useful for designing the low frequency performance of future ABH systems and describing ABH performance in terms of design parameters.

Inside micro cavities, specific dissipative mechanisms influencing acoustic wave propagation occur due to viscous and heat-conducting nature of the fluid. This work focuses on a possible extension of the so called “Low Reduced Frequency” model for acoustic wave propagation in a thermoviscous fluid. This extension is built starting from geometrical and physical assumptions (boundary layer theory, straight waveguides) and consists in the incorporation of a stationary laminar and subsonic mean flow. The resulting equivalent fluid model provides a new damping coefficient which depends on the Mach number, the shear and thermal wave numbers and the cross-sectional profiles of axial velocity and temperature. The main application area is the study of acoustic attenuation within automotive catalytic converters or also thin fluid layers like cooling systems in small electronic devices. This formulation has been implemented for a simple one dimensional thin tube. Convergence to the original model in the absence of mean flow has been reached and comparisons with variational solutions given by Peat show good agreements.

This paper describes the design of a thin plate whose thickness is tailored in order to focus bending waves to a desired location on the plate. Focusing is achieved by smoothly varying the thickness of the plate to create a type of lens, which focuses structure-borne energy. Damping treatment can then be positioned at the focal point to efficiently dissipate energy with a minimum amount of treatment. Numerical simulations of both bounded and unbounded plates show that the design is effective over a broad frequency range, focusing traveling waves to the same region of the plate regardless of frequency. This paper also quantifies the additional energy dissipated by local damping treatment installed on a variable thickness plate relative to a uniform plate.

Tire noise is one of the major causes of road traffic noise. The high-frequency component dominates tire radiation noise, which is caused by tire tread bending vibration excited by rough road surface textures. As a result of such complicated phenomena, including very complicated tread vibration modes in the high-frequency range, heavy damping, and non-periodic patterns of the road surface texture, the modal analysis approach may appear to have a low potential for analyzing this problem. Based on the above considerations, we attempted to model the tread vibration phenomenon as a group of traveling bending waves excited at an array of pavement chippings. By setting the tread shoulders as reflecting lines, the interference effect of diagonally propagating direct and reflected waves is clarified. The vibration propagation speed and decay rate were estimated through shaker tests. The shape of the probability distribution function of the chippings intervals affects the traveling wave patterns. These observations will help engineers to develop less noisy tires.

For experimental determination of structural loss factor with mechanical excitation, the excitation location — i.e. “where to excite?” — and sensor placement — i.e. “where to measure?” — are quintessential considerations. For a highly-damped panel a significant portion is not experiencing reverberant field conditions, especially in higher frequency bands. That is, localized disturbances “die-out” before they can reflect off boundaries. As energy flows away from the excitation point, the energy the level in the direct field is higher than elsewhere, thereby resulting in higher response levels. Since the level of response is inversely proportional to damping, the loss factor predicted inside the direct field is underestimated. The size of direct field is proportional to frequency and loss factor. Therefore, for a highly damped and/or small plate, loss factor estimation based on randomly positioned accelerometers—which have a higher probability of being inside the direct field—will tend to underestimate damping.

The present work seeks to optimize the spatial distribution of damping in structures with boundary damping. This work is motivated by design considerations, such as weight and cost, that often limit the amount of damping that can be used. In such cases, the designer must choose the spatial distribution of damping in order to reduce the structural vibration. One intuitively expects that the presence of boundary damping affects the optimal distribution of damping in the structure. In particular, one expects that the optimal design places damping treatments away from such boundaries in order to achieve an even distribution of power flow from the structure. To investigate this effect, finite element models of vibrating structures are developed in which the spatial distribution of damping is parameterized. These parameters are regarded as optimization parameters that are searched to minimize a cost function related to vibration or noise, such as the average response of the structure over a frequency band. Examples are presented that illustrate the effect of boundary damping on the optimal distribution of damping.

The ubiquity of porous materials in engineering applications has driven a large body of work in the development of predictive and analytical models for their behavior, as well as the numerical implementation of these models. Here, the implementation of a specific class of models is described: materials for which an equivalent-fluid adequately captures the dynamic behavior. These materials include limiting cases where the solid matrix is either so stiff that it is relatively immobile, or so compliant that its motion has only a damping effect on the fluid motion. A wide class of automotive trim materials, acoustic insulation, fabrics, and aerospace materials fit this description. Several material models have been implemented recently in the commercial finite element code, Abaqus. These include the models of Craggs, Delany-Bazley, Miki, and the generalized model of Kang & Bolton. All of the models share an implementation using frequency-dependent material properties. In Abaqus, these properties are assigned to standard acoustic finite elements. Frequency-domain solution is significantly more efficient through the use of a distributed-memory parallel sparse solver, and through projection onto the space of real-valued modes. Results from the new implementation are compared to established benchmarks, and performance is discussed.

Flow-induced vibration tests were performed on a beam with a square cross section. The test article was induced into a plunge mode self-excited vibration by forcing air across the beam while it was suspended by leaf springs. The natural frequency and the damping were varied during these tests to alter the variables that contribute the onset of flow-induced vibration. Additionally, cantilevered beams were tested in the same wind tunnel and results proved to be consistent with results from the leaf spring supported beam. The slope of the vertical force coefficient was determined from this testing; this coefficient was determined to be approximately unity, which was roughly 1/3 of the value found in other published data.

Lock-in occurs between many different types of flow instabilities and structural-acoustic resonators. Factors that describe the coupling between the fluid and structure have been defined for low flow Mach numbers. This paper discusses how different flow instabilities influence lock-in experimentally and analytically. A key concept to the lock-in process is the relative source generation versus dissipation. The type of fluid instability source dominates the generation component of the process, so a comparison between a cavity shear layer instability with a relatively stronger source, for example wake vortex shedding from a bluff body, will be described as a coupling factor. In the fluid-elastic cavity lock-in case, the shear layer instability produced by flow over a cavity couples to the elastic structure containing the cavity. In this study, this type of lock-in was not achieved experimentally. A stronger source, vortex shedding from a bluff body however, is shown experimentally to locks into the same resonator. This study shows that fluid-elastic cavity lock-in is unlikely to occur given the critical level of damping that exists for a submerged structure and the relatively weak source strength that a cavity produces. Also in this paper, a unified theory is presented based on describing functions, a nonlinear control theory used to predict limit cycles of oscillation, where a self-sustaining oscillation or lock-in is possible. The describing function models capture the primary characteristics of the instability mechanisms, are consistent with Strouhal frequency concepts, capture damping, and are consistent with mass-damping concepts from wake oscillator theory. This study shows a strong consistency between the analytical models and experimental results.

In the high frequency limit, a vibrating panel subject to spatially-random temporally-broadband forcing is shown to have broadband power and directivity properties that can be expressed in simple analytical terms by a limited set of parameters. A lightly-loaded fixed-fixed membrane with a distribution of broadband uncorrelated drive points is analyzed. The theory is developed using classical modal methods and asymptotic modal analysis, assuming small damping. The power and directivity of the radiated pressure field are characterized in terms of structural wave Mach number, damping ratio, and dimensionless frequency. The relatively simple directivity pattern that emerges can be shown to arise from edge radiation. From the point of view of edge radiation, assuming a lightly damped reverberant structure, the same radiation formula and directivity pattern can be derived in a much simpler manner. Broadband radiation from structures with subsonic and supersonic flexural wave speeds is discussed and characterized in terms of a simple interpretation of the surface wavenumber spatial transform. The results show that the physical idea of interpreting edge radiation in terms of uncancelled volumetric sources is not correct, and the effect of higher order edge singularities is in fact very significant. The approach implies a relationship between radiation and structural power flow that is potentially useful in energy-intensity based prediction methods, and can be generalized to more complex structures with application to vehicle interior noise prediction.

A new algorithm for mode-based frequency response analysis, which takes into account frequency-dependent material properties, is proposed. First, the projection subspace is determined by computing the eigenmodes of the system. If the AMLS-type eigensolver is used and the frequency-dependent material is confined to a limited area (often less than 1% of the whole model), eigenmodes are computed only in the region with the frequency-dependent material. Next, during the frequency response analysis portions (corresponding to the frequency-dependent material) of the stiffness, viscous damping, and structural damping operators are computed and projected onto the modal subspace. The original contribution of this paper is the algorithm, which augments the projected operators (stiffness, viscous damping, or structural damping) by the contributions from the area with the frequency-dependent material properties without the need to recompute the operator over the whole domain. This algorithm was successfully implemented in a commercial finite element code, Abaqus 6.8. The results for a vehicle body-in-prime model show good agreement with a direct-solution frequency response analysis. In the addition, the cost of the proposed algorithm is a fraction of the directsolution analysis.

Sound transmission through multi-element flexible barriers is studied. Configurations analyzed include panels with different thickness and elastic modulus in different regions and layered structures connected by an elastic suspension. The purpose of the research is to see if flexibility and controlled resonant behavior can be used to block sound transmission even when structural damping is very low. Strategies are considered to alter vibrating surface wavenumber spectra to reduce coupling between the structure and the acoustic field. Another approach that can be employed is the utilization of structural wave cut-off with multi-element materials. Finally, multiple differentially tuned subsidiary elements acting as resonators can be used to greatly reduce the structural response. Examples of acoustic transmission loss through panel barriers using different strategies are presented, and the potential advantages and possible shortcomings of various approaches are evaluated.

This paper examines numerical techniques to compute the resonant frequencies and coupled mode-shapes of general structural-acoustic systems using the finite element method. This information is useful in quantifying the key frequencies and vibration patterns of elastic structures coupled to bounded or unbounded acoustic fluid volumes. This paper reviews and evaluates three finite element solution techniques that deal with the computational difficulties encountered in structural-acoustic eigen-analysis. One of the difficulties stems from the fluid-structure coupling in the finite element equations, which depending on the variable used to discretize the acoustic fluid, either introduces non-symmetric area coupling terms in the mass and stiffness matrices or adds symmetric area coupling terms in the damping matrix. The other difficulty is related to the application of a radiation boundary condition in those structural-acoustic problems involving unbounded acoustic domains. The radiation boundary condition introduces damping terms in the finite element equations that lead to a complex eigen-analysis to determine the resonant frequencies and coupled mode-shapes. The finite element techniques evaluated in this paper consist of subspace projection employing an augmented-symmetric form of the fluid-structure equations as well as new extensions of component mode synthesis (CMS). Basic examples of simplified structural-acoustic systems are used to compare the solution accuracy between the three finite element techniques. Examples consist of simplified one-dimensional (1-D) and two-dimensional (2-D) elastic structures coupled to closed and open acoustic spaces.