Vibro-acoustic Systems Research Articles

The Radiation Efficiency Measurements of Real System of a Thin Circular Plate Embedded Into a Thick Square Baffle

Most of sound sources are complex vibroacoustic objects consist of numerous elements. Some coupled vibrating plates of different shapes and sizes can be easily found in urban environments. The main aim of this study is to determine the sound radiation of coupled plates system of practical importance. The investigated vibroacoustic system consist of a thin circular plate coupled with a thick flat baffle with a circular hole. The circular plate has been mounted to the baffle’s hole using screws and two steel rings. The measurement setup was located inside a semi-anechoic chamber to assure the free field conditions. It was necessary to take into account the whole system surface to obtain the radiation efficiency based on the Hashimoto’s method. Such an approach can be troublesome and time-consuming. Therefore, the criterion has been proposed which allows the vibration velocity measurements and calculations to be performed only for the thin plate’s area. An alternative approach has been proposed based on the classical Rayleigh integral formula. Its advantage is a simpler implementation in a computer code. The obtained results have been compared with the theoretical results obtained for the elastically supported circular plate. A good agreement has been obtained at low frequencies.

Vibroacoustic analysis of multi-layered micro-perforated plates coupled to an acoustic enclosure

A vibroacoustic study of multi-layered micro-perforated plates (MPP) coupled to an enclosure cavity excited by internal and external acoustic excitations is presented. Most previous research centered on the multi-layered MPPs structure itself, the absorption and transmission performances were often calculated or tested in a simple acoustic environment. In a more realistic setting, the surrounding systems may affect the efficiency of MPPs. The proper modeling of the MPPs within acoustic enclosures requires careful study. The break-out sound from an enclosure via multi-layered MPP and the energy transmission of the structure into an acoustic enclosure undergoing exterior excitation are studied with an emphasis on the use of MPP in acoustic enclosures to suppress specific resonances of the enclosure. Therefore, an analytical formulation is proposed to model the behavior of the coupled system to address this issue. Using a modified Fourier series for the acoustic pressure, the continuity of the normal velocities at the interfaces of the plate or the MPP and the acoustic medium is assured accurately. A modified variational form for the acoustic and structure medium yields a completely coupled vibroacoustic system. Comparison with the finite element method (FEM) and available literature findings prove the efficacy and precision of the current approach. The effect of important parameters on the vibroacoustic behavior of multi-layered MPPs structure connected to an acoustic enclosure is examined. These parameters include micro-perforation of the plate, hole diameter, air gap thickness, acoustic enclosure dimensions, and the insertion of absorbent material in the gap.

Evaluation of Resonance Frequency and Micromotion to Achieve Implant Stability Using Vibroacoustic Resonance Frequency Analysis: A Mathematical Model

AbstractDental implants are surgically implanted into the patient's jaw to replace a missing tooth. The implant should have adequate time to integrate with bone before being subjected to masticatory force to avoid early failure. Resonance frequency analysis (RFA) is one of the approaches for determining an implant system's primary stability in terms of micromotion. This research aims to create a two degrees-of-freedom (DOF) mathematical model for dental prostheses based on the vibroacoustic RFA approach. In vibroacoustic system, a loudspeaker or buzzer is used as an input and the displacement of implant is measured using RFA. A sinusoidal force is used which produces a combination of translational and rotational motion of the implant system. While adjusting the input frequency from 4000 to 12,000 Hz, is used with the help of matlab which later computes the implant system's subsequent micromotion and resonance frequency. matlab is used to visualize the resonance frequency, which is 6658.38 Hz in case of rotational motion and 8138 Hz in translational motion. The micromotion was 1.2692 × 10−11 m in case of translational motion and 6.91088 × 10−9 radians in case of rotational motion. When there is less micromotion, a higher resonance frequency suggests more excellent osseointegration. For the evaluation of implant stability, a mathematical model is a primary approach that can be implemented to design a stability device using vibroacoustic RFA.

Development of experimental Vibro-acoustic transfer function for a system with impact

Systems with combined sliding-rolling contacts such as cam-follower, clutches, and gearbox are prone to have clearance(s) as per the design and/or due to manufacturing imperfections or wearing as a result of sliding between components. This clearance non-linearity results in an impact between components, which in turn generates a significant rattle during operation. The noise generation mechanism in rattle is a strong function of impact-velocity and contact forces. The objective of this study is to develop an experimental transfer function to quantify the vibro-acoustics of a cam-follower system with clearance non-linearity. Contact between the cam and the follower is lubricated to minimize the sound generated due to friction. Follower acceleration, reaction forces, and acoustic pressure are measured on a cam-follower setup with combined rolling-sliding contact during impacts under various conditions. Velocity and contact forces are back-calculated using measured signals and the analytical model dynamics. Transfer functions relating the acoustic pressure to velocity and contact forces are estimated in the frequency domain. These transfer functions provide insights into the vibro-acoustic system and can be directly used in conjunction with dynamics models. The output of the study can be used in designing quieter systems with impact.

Statistical Energy Analysis (SEA) based approaches for the mid- and high-frequency vibro-acoustic analysis of complex systems

This paper will present methods for predicting the statistics of the frequency response functions of complex random vibro-acoustic systems. The statistical properties include the ensemble mean, the ensemble variance, level crossing rates, extreme values, and quefrencies. The approach is based on a combination of statistical energy analysis (SEA), the finite element method, random point process theory, and random matrix theory. In the mid frequency range the finite element method is used to model components that have a low modal density, while other components are modelled as SEA subsystems. The coupling between the finite element components and the SEA subsystems is effected using the diffuse field reciprocity principle, which was developed some years ago. The blocked modes of the SEA subsystems are assumed to have natural frequency statistics that are governed by the Gaussian Orthogonal Ensemble, and this enables the statistical properties of the response to be found without any need for Monte Carlo simulations. The use of SEA leads to a relatively low number of degrees of freedom used in the model, and thus the approach is numerically efficient well suited to the design stage, where many design options may be explored.

Use of the vibroacoustic system for determining the range of a ski jump for training athletes

The principle of vibroacoustic systems operation for determining the distance of a ski jump from a springboard, the possible location of sensors on the springboard and sensor signals that occur when athlete lands are considered. The problems of calculating the jump distance and methods for solving these problems are described. The interrelation of the technique of performing a jump (the spatial position of the skis at the time of landing and the normal component of the landing speed relative to the surface of the springboard) with the form of sensor signals is considered. Real waveforms of signals obtained both during the summer artificial covering of the springboard and in winter, as well as generalized results of experimental operation of the system on springboards with different heights of the acceleration mountain are presented. It is shown that the use of vibroacoustic systems allows achieving the required accuracy of determining the ski jump distance – 0.5 m, and the integration of the system with the general jump monitoring system opens up new opportunities for independent training of athletes and training of a group of athletes under the guidance of a coach.

Robust error assessment for reduced order vibro-acoustic problems

Robust and efficient automatic model order reduction is important in the design process of vibro-acoustic structures. For correct assessment of the reduction error without requiring the solution of the full order model, reliable error estimation techniques are required. Such error estimators can be used in iterative algorithms to automatically determine a reasonable order and expansion point distribution for reduced-order models. An accurate estimation of the approximation error is important in order to design an efficient adaptive model order reduction process requiring as little a priori knowledge of the system response as possible. In this contribution, different techniques for estimating the approximation error of reduced-order models are compared and employed in adaptive algorithms aiming at generating reduced-order models of vibro-acoustic systems. For many applications, vibro-acoustic systems need to be evaluated in a specific frequency range, as certain system characteristics are only observed in this region. Therefore, the employed error estimation methods are assessed regarding their effectiveness estimating the error in a particular frequency region.

A hybrid method for creating auralizations of vibroacoustic systems

A hybrid method for creating a unified broadband acoustic response from separate low-frequency and high-frequency simulation responses is proposed. This hybrid method is ideal for creating simple auralizable approximations of complex acoustic systems. The process consists of four steps: 1) creating separate low- frequency and high-frequency responses of the system of interest, 2) interpolating between the two responses to get a single broadband magnitude response, 3) introducing amplitude modulation to the high-frequency portion of the response, and 4) calculating approximate phase information. Once the appropriate frequency response is obtained, an inverse fast Fourier transform is applied to obtain an impulse response. An experimental setup of an acoustic cavity with one flexible wall is used to validate the hybrid method. The simulated and measured impulse responses are both convolved with various excitation signals, so the validity of the approach could be assessed by listening. Listening tests confirm that the method is able to produce realistic auralizations. The degree of realism is subject to a few limitations, such as pitch differences and dependence on the presence of transients in the excitation signal, but these limitations are incidental and only indirectly related to the proposed method.

A hybrid modal/statistical formulation for predicting the energy response of vibroacoustic systems in the mid frequency range

The Statistical modal Energy distribution Analysis (SmEdA) method predicts the power flow between coupled subsystems excited by random excitations from a deterministic modal description of the uncoupled subsystems. As the modes can be computed by Finite Element Method (FEM) for complex subsystems, it can be seen as an extension of FEM to the mid frequency range where the modal densities of subsystems are not too high. Conversely, the Statistical Energy Analysis (SEA) method is a statistical approach predicting the mean power flow of a population of similar structures presenting manufacturing uncertainties. Assuming a diffuse field within each subsystem, it is dedicated to the high frequency range where modal densities of subsystems are high. However, in many applications, subsystems with low and high modal densities can coexist in the mid frequency range and in that case neither SmEdA nor SEA is well adapted. The purpose of this article is then to propose a hybrid SmEdA/SEA formulation allowing some subsystems with low modal densities to be described by SmEdA and other ones by SEA. For the SEA-described subsystems, the vibratory field of the statistical population is supposed to be diffuse. These subsystems are then characterized by sets of natural frequencies and mode shapes constructed from the Gaussian Orthogonal Ensemble matrix and the cross-spectrum density of a diffuse field, respectively. In another hand, the SmEdA-described subsystems are represented by their modes that can be extracted by usual computer codes. In order to couple the two models, Monte Carlo simulations are used for generating samples of the stochastic modes of the SEA-described subsystems. From the distribution of the estimated energy response of the coupled subsystems, the ensemble average and the confidence interval can finally be estimated. For validation purpose, the results of the proposed hybrid SmEdA/SEA approach are compared to the numerical results computed with the finite element method (FEM) on a population of plate-cavity systems having similar properties. A good agreement is observed whereas the computation time of the proposed approach is much less important than the one of the FEM which can be up to several days for each element of the population.

A hybrid CSRPIM/SEA method for the analysis of vibro-acoustic problems in mid-frequency range

Hybrid methods are commonly methods to solve the response of mid-frequency vibro-acoustic system. In this study, a novel hybrid CSRPIM/SEA method is proposed to calculate the coupling problem between enclosed cavity and flexible plate. Deterministic subsystem with low modal density is modeled by the Cell-based Smoothed Radial Point Interpolation Method (CSRPIM) and statistical subsystem with the high modal density is modeled by the Statistical Energy Analysis (SEA). Owing to the generalized gradient smoothing technique and the condensed shape function technique used, the stiffness of discrete model is softened and the dispersion error can be reduced obviously, which makes the hybrid CSRPIM/SEA method give satisfactory numerical results considering the examples studied. The proposed method has provided an effective way for analyzing mid-frequency virbo-acoustic problems.

Structured model order reduction for vibro-acoustic problems using interpolation and balancing methods

Vibration and dissipation in vibro-acoustic systems can be assessed using frequency response analysis. Evaluating a frequency sweep on a full-order model can be very costly, so model order reduction methods are employed to compute cheap-to-evaluate surrogates. This work compares structure-preserving model reduction methods based on rational interpolation and balanced truncation with a specific focus on their applicability to vibro-acoustic systems. Such models typically exhibit a second-order structure and their material properties as well as their excitation may be depending on the driving frequency. We demonstrate the effectiveness of all considered methods in terms of their accuracy and computational cost by applying them to numerical models of vibro-acoustic systems depicting structural vibration, sound transmission, acoustic scattering, and poroelastic problems. The results of the experiments are extensively discussed to derive guidelines for the choice of model reduction methods based on the problem setting.

Comparing the effectiveness of structure-preserving model order reduction methods for vibro-acoustic problems

For the analysis of the vibration and dissipation behavior of structures, the evaluation of the systems' frequency response is essential. However, evaluating a frequency sweep on a high-fidelity model can be computationally very expensive. A remedy to this are model order reduction methods, which allow the computation of cheap-to-evaluate surrogate models. Additionally to the reduction of the internal system dimensions, model order reduction methods that preserve the matrix structure of the transfer function are preferred as the results may allow for physical reinterpretation and the use of similar analysis tools as for the original systems. In this work, we compare system-theoretic, structure-preserving model order reduction methods with a specific focus on their applicability to vibro-acoustic systems. We demonstrate their effectiveness in terms of accuracy and computational costs by applying them to numerical models of vibro-acoustic systems depicting structural vibration, sound transmission, acoustic scattering, and poroelastic-acoustic coupling. As a result, this comparative study allows us to derive some general recommendations for the choice of suitable model order reduction methods depending on the specific problem statement.

Size optimization of mid-frequency vibro-acoustic systems in the framework of modal energy analysis

Size optimization of mid-frequency vibro-acoustic systems in the framework of modal energy analysis

Accelerated dispersion curve calculations for periodic vibro-acoustic structures

Over the years, metamaterials have shown their potential in a wide range of different disciplines, e.g. optics, electromagnetics, dynamics etc. Metamaterials are, often periodic, engineered structures made of conventional materials but which exhibit properties not encountered in nature. In the field of noise and vibration, metamaterials have received increasing interest since they can obtain frequency ranges of high noise and vibration attenuation, called stop bands. Their performance is often investigated by means of dispersion curves, which are calculated based on a single unit cell and assuming a structure of infinite periodic extent. Nowadays, the attenuation of acoustic and structural waves is commonly tackled as two separate problems, whereby either acoustic or structural dispersion curves are used. Recently, vibro-acoustic unit cell designs have come to the fore which can exhibit appealing characteristics, such as simultaneous structural and acoustic stop bands. To consider the vibro-acoustic coupling in these unit cell designs during the performance predictions, vibro-acoustic dispersion curve calculations are thus required. However, these computations are typically cumbersome to perform due to the associated high computational cost and therefore, often, uncoupled dispersion curves are used during the performance assessment. Although several unit cell model order reduction approaches have recently been proposed to accelerate the dispersion curve computations, such as the Bloch mode synthesis (BMS) and Generalized Bloch mode synthesis (GBMS), they are not readily applicable to vibro-acoustic unit cells. To accelerate vibro-acoustic dispersion curve calculations, this work extends the BMS and GBMS techniques towards 2D and 3D periodic vibro-acoustic systems. To balance accuracy versus speed, the extended BMS reduction basis is constructed using a split set of vibro-acoustic coupled modes, while the extended GBMS reduction basis uses the uncoupled modes. Several verification cases demonstrate that strongly accelerated vibro-acoustic dispersion curve computations are achieved whereby the vibro-acoustic coupling inside the unit cell is accurately accounted for.

Performances of coupled the partition of unity finite element method and the discrete shear gap method for the analysis of 3D vibro-acoustic problems

In 3D vibro-acoustic analysis, the accuracy of the vibro-acoustic FE model degrades with increasing excitation frequency due to the “dispersion error”. In this paper, an efficient hybrid method, namely the PUFEM/DSG, is proposed for improving the computational performance of vibro-acoustic analysis, which uses the partition of unity finite element method for the acoustic cavity and the discrete shear gap method for the flexible shell. The acoustic cavity is discretized into tetrahedral elements of large size, and a plane wave function is introduced in the interpolation space to construct the PUFEM. Triangular elements are adopted for the shell, and the DSG eliminates the “shear locking”. At the interface with non-matching meshes, this paper realizes the coupling of two field variables by dividing virtual elements and implementing coordinate transformation and applies the exact integration method for the PUFEM system matrix and coupling matrix to improve the efficiency of the proposed method. The proposed method not only retains the FEM’s ability to model complex vibro-acoustic systems but also effectively reduces the “dispersion error” and the computational effort. It also can improve the accuracy by adding plane waves at the nodes of the acoustic cavity without remeshing.

On the experimental vibroacoustic modal analysis of a plate-cavity system

This paper proposes a methodology to the experimental vibroacoustic modal analysis on a coupled plate-cavity system. The method is based on the nonlinear curve fitting to the Frequency Response Functions (FRFs) obtained through a roving hammer test. These FRFs are divided into two groups: one is for the acceleration of the plate; the other is for the sound pressure inside the cavity. The modal parameters are estimated independently in each group using both the single/multi-mode all-curve and the all-mode single-curve fitting techniques. Such a way overcomes the identification difficulties when the natural frequencies of the coupled system slightly change over the roving hammer process. Meanwhile, the mode shapes extraction is eased from the different scales between structural and acoustic responses. The two groups of FRFs are fitted by two different types of FRF models, respectively. The results are in agreement with respect to the natural frequencies and modal damping ratios. Particularly, the FRF models are in alternative forms instead of the conventional ones, and they fit the measured FRFs very well with the estimation outcomes applied. Furthermore, the identified modal parameters are verified by the counterpart estimation based on the conventional FRF models formulated by partial fraction expansions. It is shown that the proposed FRF models contain fewer unknown parameters but do not downgrade the estimation accuracy, making the curve fitting process more practical and efficient. Hence, the two-group strategy with the proposed FRF models provides a practical and efficient way for the experimental modal analysis of vibroacoustic systems.

Coupling strength evaluation in vibro-acoustic systems

Statistical energy analysis (SEA) and related approaches to the high-frequency analysis of vibro-acoustic systems rely on a conceptual division of the system into subsystems that are assumed to carry a diffuse field and to be weakly coupled. Weak coupling in this context means that the exchange of energy between any two subsystems can be described in terms of their uncoupled free vibration modes. In this paper, a criterion is derived for assessing the coupling strength in the general case where the subsystems are rigidly coupled and/or via a deterministic linear dynamic component. First, the subsystems are taken to be deterministic and in a subsequent analysis they are taken to be diffuse subsystems in an SEA setting. The criterion is then elaborated such that it can be directly evaluated from quantities that appear in the SEA power balance. In this process, the hybrid deterministic-SEA approach is employed such that subsystems and connections of arbitrary complexity can be tackled in a rigorous way. In one of its approximate forms, the proposed general coupling strength criterion is shown to be identical to the γ criterion that has appeared in the literature for the coupling strength assessment of some special cases. The use of the criterion is illustrated with instructive validation examples involving two diffuse plate subsystems rigidly connected and/or via a deterministic beam, whose dynamic behaviour influences the coupling strength.

The use of locally resonant metamaterials to reduce flow-induced noise and vibration

Locally resonant metamaterials (LRMs) have recently emerged and shown potential in the field of noise control engineering, given their superior noise and vibration reduction performance in tunable frequency ranges, referred to as stop bands. This paper aims to experimentally assess the potential of LRMs to suppress flow-induced noise and vibration of coupled vibro-acoustic systems such as a cavity-backed plate. At first, the vibrations of a flat plate under a turbulent flow excitation are measured and analyzed. Subsequently, different LRM solutions are designed to tackle the vibrations of the plate. In a second stage, a hard-walled backing-cavity is coupled to the system and the noise radiation due to the vibrations of the plate into the backing cavity is evaluated. The plate is then treated with the designed LRM configurations. The results show that the designed LRM solutions are able to reduce the vibrations and noise radiation of the system due to a turbulent flow excitation.

An approach for modal coupling based on experimental and computed modes using non-conforming grids

The combination of experimental and numerical data is a typical challenge in complex vibro-acoustic problems. Rather than employing model-updating techniques, we combine the modal substructuring technique with non-conforming grids in order to be able to directly employ experimental and numerical modes for the description of weakly coupled vibro-acoustic systems. By incorporating Delaunay triangulation in the process, mechanical modes of any origin and discretized in terms of point clouds can be coupled with computational acoustic modes. The method is validated using a two-sided vibro-acoustic box. It is demonstrated that, by employing suitable interpolation techniques, systems based on coarsely discretized experimental modes can be used analogously to computational modes. The approach makes it straightforward to take into account modal damping and to fit numerical modes via experimental modal parameters, such as eigenfrequency, modal mass and damping.

Automatic model order reduction for systems with frequency-dependent material properties

The frequency response of vibro-acoustic systems can be improved by using various forms of damping materials. Their material properties are typically varying with the excitation frequency and are introduced by one or multiple complex-valued functions. Numerical models of such systems are typically large and require efficient solving strategies. In this contribution, a workflow to reduce the numerical complexity of systems containing frequency-dependent damping materials is presented. The functions modeling the material’s frequency-dependent behavior are approximated in rational form and the resulting transfer function is used in a Krylov based moment matching method. The approximation is performed automatically using the adaptive Antoulas–Anderson algorithm. As robust and efficient automatic reduction algorithms are vital for an efficient design process of vibro-acoustic structures, we also show an adaptive procedure to automatically find a reasonably sized reduced model for a given system under a certain tolerance. The algorithms are tested for two forms of damping materials common in vibro-acoustic systems: poroelastic materials following the Biot theory and a constrained layer damping material.