Structural-acoustic Model Research Articles

Exponential stability for a classical structural acoustic model with thermoelastic boundary control

The uniform stabilization of a coupled system arising in the active control of noise in a cavity with a flexible boundary (strings under thermal effects) is considered. Unlike most articles on this subject, which employ the scalar wave equation when analyzing the asymptotic behavior of structural acoustic models, in this paper, we consider classical equations in terms of flow velocity and pressure to describe the acoustic vibrations of the fluid which fills the cavity. This allows to consider, for example, more realistic boundary conditions to model the coupling on the interface between the acoustic chamber and the wall. The main result of this paper, concerning the exponential stability of the model, is established by means of the frequency domain method and the semigroup theory. This method can be adapted to other first‐order hyperbolic dissipative systems as well.

Exponential stabilization of a structural acoustic model arising in the control of noise

Exponential stabilization of a structural acoustic model arising in the control of noise

The assignment of zero sound pressure frequencies using measured sound pressure receptances and structural receptances

In structural receptances, the zeros (antiresonances) define those frequencies at which vibrations disappear. In this paper, the zero sound pressure frequency is defined as the frequency at which the sound pressure is zero at certain locations. A method for the assignment of zero sound pressure frequencies using measured sound pressure receptances and structural receptances is proposed through two forms of structural modifications: rank-one modification and higher-rank modification. In rank-one modification, the sound pressure receptances of the modified structure are obtained by using the structural receptances with the Sherman-Morrison formula. In higher-rank modification, the modifications are determined by an analysis of the null space of a matrix consisting of structural receptances and sound pressure receptances. This method requires only a few structural receptances and sound pressure receptances, and no structural models or acoustic models are needed. Numerical examples involving a baffled plate vibrating in air and a fluid-loaded finite cylindrical shell are used to demonstrate the methods. Numerical results show that the zero sound pressure frequencies can be assigned to specific frequencies by structural modification.

On the asymptotic behavior of solutions to a structural acoustics model

This article is concerned with the long term behavior of solutions to a structural acoustics model consisting of a semilinear wave equation defined on a bounded domain Ω⊂R3 which is coupled with a Berger plate equation acting on a flat portion of the boundary of Ω. The system is influenced by several competing forces, in particular a source term acting on the wave equation which is allowed to have a supercritical exponent.Our results build upon those obtained by Becklin and Rammaha [8]. With some restrictions on the parameters in the system and with careful analysis involving the Nehari manifold we obtain global existence of potential well solutions and establish either exponential or algebraic decay rates of energy, dependent upon the behavior of the damping terms. The main novelty in this work lies in our stabilization estimate, which notably does not generate lower-order terms. Consequently, the proof of the main result is shorter and more concise.

Blow-up theorems for a structural acoustics model

This article studies the finite time blow-up of weak solutions to a structural acoustics model consisting of a semilinear wave equation defined on a bounded domain Ω⊂R3 which is strongly coupled with a Berger plate equation acting on the elastic wall, namely, a flat portion of the boundary. The system is influenced by several competing forces, including boundary and interior source and damping terms. We stress that the power-type source term acting on the wave equation is allowed to have a supercritical exponent, in the sense that its associated Nemytskii operator is not locally Lipschitz from H1 into L2. In this paper, we prove the blow-up results for weak solutions when the source terms are stronger than damping terms, by considering two scenarios of the initial data: (i) the initial total energy is negative; (ii) the initial total energy is positive but small, while the initial quadratic energy is sufficiently large. The most significant challenge in this work arises from the coupling of the wave and plate equations on the elastic wall.

Uniform Decay Rates for a Variable-Coefficient Structural Acoustic Model with Curved Interface on a Shallow Shell

Uniform Decay Rates for a Variable-Coefficient Structural Acoustic Model with Curved Interface on a Shallow Shell

Trends in the 40 + -year development of advanced structural acoustic and vibration computational modeling

Over the course of the past 40-45 years of computational modeling in the fields of structures, structural acoustics, and vibrations, there have been extreme advancements made in numerous areas that have greatly increased and improved the size, accuracy, efficiency, and complexity of numerical solutions possible. Most of this progress has been made through a combination of improvements in the distinct areas of computer processing approaches/speed and available memory, primarily evolutionary enhancements in detailed numerical material and continuum mechanics models, development of entirely new physics-based numerical vibroacoustic modeling approaches, etc. This paper presents a historical review of the detailed progress made in computational structural acoustics and vibration from the “early days” in the 1980s through current state-of-the-art advanced numerical approaches, much of which would not have been dreamed possible back four decades ago! While most of the examples utilized in this talk are pulled from the speaker’s specific technical area of undersea vehicle/ system structural acoustics, the overall trends presented are certainly represented across the broad spectrum of vibro-acoustics modeling applications.

Exact boundary controllability of the structural acoustic model with variable coefficients

We consider the boundary controllability of the structural acoustic model with variable coefficients. The structural acoustic model is a coupled partial differential equation, which comprises an acoustic wave equation in the interior domain, a Kirchoff plate equation on the boundary portion, with the coupling being accomplished across a boundary interface. In this model, the wave propagation medium and the plate material are all inhomogeneous. By the Riemannian geometry theory and the multiplier technique, our paper derives the exact controllability with two boundary controls under some checkable conditions and the exact–approximate boundary reachability with only one control for the boundary Kirchoff plate equation.

PRINCIPLES OF FORMATION OF STRUCTURAL GEOLOGICAL MODELS OF HETEROGENEOUS LAYERED BOTTOM

The article describes the developed and implemented analytical and numerical methods for modeling layered geological structures with cavities of simple and complex shape. The developed author’s analytical and numerical methods of mathematical modeling of the structure and spatial distribution of acoustic properties of marine sediments, presented as a layered inhomogeneous medium, which allow to create discrete, continuous or mixed structural-acoustic models of inhomogeneous seabed taking into account stratification, the presence of cavities and inclusions of various shapes and properties. Models of geological layered environment implemented according to these algorithms are necessary for modeling panoramic survey (SSS), SSS with interferometric channel, multibeam sounder, three-dimensional profiling, construction of isobathic maps based on sounder measurements.

Hadamard well-posedness for a structure acoustic model with a supercritical source and damping terms

<p style='text-indent:20px;'>This article is concerned with Hadamard's well posedness of a structural acoustic model consisting of a semilinear wave equation defined on a smooth bounded domain <inline-formula><tex-math id="M1">\begin{document}$ \Omega\subset\mathbb{R}^3 $\end{document}</tex-math></inline-formula> which is strongly coupled with a Berger plate equation acting only on a flat part of the boundary of <inline-formula><tex-math id="M2">\begin{document}$ \Omega $\end{document}</tex-math></inline-formula>. The system is influenced by several competing forces. In particular, the source term acting on the wave equation is allowed to have a <i>supercritical</i> exponent, in the sense that its associated Nemytskii operators is not locally Lipschitz from <inline-formula><tex-math id="M3">\begin{document}$ H^1_{\Gamma_0}(\Omega) $\end{document}</tex-math></inline-formula> into <inline-formula><tex-math id="M4">\begin{document}$ L^2(\Omega) $\end{document}</tex-math></inline-formula>. By employing nonlinear semigroups and the theory of monotone operators, we obtain several results on the existence of local and global weak solutions. Moreover, we prove that such solutions depend continuously on the initial data, and uniqueness is obtained in two different scenarios.</p>

Structural-Acoustic Modeling and Analysis of Carbon/Glass Fiber Hybrid Composite Laminates

The vibration and acoustic behaviors of both glass fiber laminated plates and carbon/glass fiber hybrid laminated plates are investigated by numerical simulation. The free vibration, forced vibration and acoustic radiation of laminated plates including glass fiber laminates and carbon/glass fiber hybrid laminates in air and water are calculated by the coupled finite element and boundary element method and compared with the corresponding test results. It was demonstrated that results obtained by the coupled finite element and boundary element method are in good agreement with the experimental ones. The effects of dispersion, outer fiber types and fiber hybrid ratio on the vibration and sound radiation of the laminates plates are also discussed.

Vibroacoustic responses of a heavy fluid loaded cylindrical shell excited by a turbulent boundary layer

A fully coupled structural–acoustic model of a cylindrical shell under external turbulent boundary layer excitation is herein developed. The numerical process requires computation of the wall pressure cross spectral density function as well as sensitivity functions for the fluid-loaded cylindrical shell. A semi-empirical model from literature is used to describe the wall pressure field induced by the turbulent boundary layer in the wavenumber–frequency domain. An analytical expression of the wall pressure field for a flat surface is adapted to describe the wall pressure field for a cylindrical surface. Circumferential sensitivity functions are derived using a wavenumber-point reciprocity principle. Results for the near-field and far-field acoustic pressure spectra are presented. Contributions of individual circumferential modes to the acoustic pressure spectra are examined, showing distinct trends below and above the ring frequency. The proposed method is computationally efficient and provides an effective approach to investigate vibroacoustic responses for maritime platforms.

Structural-acoustic modeling and analysis of an engineering machinery cab in the mid-frequency range

The hybrid finite element method and statistical energy method was used to study the vibro-acoustic coupling characteristics of an engineering vehicle cab. The parameters of the statistical energy method, such as modal densities, damping loss factors and coupling loss factors of substructures, were acquired by numerical and analytical methods. The acoustic-structure coupling of the cab was established based on the modal densities of substructures. The vibration and noise excitations of the cab were measured by test and the sound pressure level response of the driver’s ear was predicted. It was shown that the prediction results based on the hybrid method are in agreement with the experiments and the proposed method can be applied to predict the mid-frequency response of complex vibro-acoustic coupling systems with a moderate computational cost and accuracy.

Experimental characterization of basic violin structural acoustics

Considering its simple construction the complex material-shape traditional violin, fashioned from nominally orthotropic materials to form a ported, compliant-wall cavity, enjoys a notable scientific complexity, e.g., four separate radiation mechanisms, coupling between the two lowest cavity modes A0 (Helmholtz resonance, ∼275 Hz) and A1 (1st longitudinal “slosh” mode, ∼470 Hz), and between A0 and two 1st corpus bending (B1) modes near 500 Hz. Comprehensive EMA (velocity/force), radiativity (pressure/force) and near-field acoustical holography ( f -hole volume flows/force) measurements plus bridge tuning systematics were combined to establish a dual-region structural acoustics model of the violin. In the “deterministic” region the large-volume-change B1 modes drive large, in-phase f-hole volume flows accounting for >50% of B1 radiation and excite A0; oppositely directed upper-bout/lower-bout cavity volume flows excite A1. A wall-driven, dual-Helmholtz resonator network successfully modeled A0 and B1 radiation. In the “statistical” region where the major bridge and plate tuning effects occur, radiation efficiency (averaged-over-sphere radiativity divided by averaged-over-corpus mobility) led to radiation damping and critical frequency. With total damping from mobility fits the radiation/total damping ratio (fraction of vibrational energy radiated) was combined with a parametric model of mobility. Splicing the regions created the “dynamic filter” model of violin radiation.Considering its simple construction the complex material-shape traditional violin, fashioned from nominally orthotropic materials to form a ported, compliant-wall cavity, enjoys a notable scientific complexity, e.g., four separate radiation mechanisms, coupling between the two lowest cavity modes A0 (Helmholtz resonance, ∼275 Hz) and A1 (1st longitudinal “slosh” mode, ∼470 Hz), and between A0 and two 1st corpus bending (B1) modes near 500 Hz. Comprehensive EMA (velocity/force), radiativity (pressure/force) and near-field acoustical holography ( f -hole volume flows/force) measurements plus bridge tuning systematics were combined to establish a dual-region structural acoustics model of the violin. In the “deterministic” region the large-volume-change B1 modes drive large, in-phase f-hole volume flows accounting for >50% of B1 radiation and excite A0; oppositely directed upper-bout/lower-bout cavity volume flows excite A1. A wall-driven, dual-Helmholtz resonator network successfully modeled A0 and B1 radiat...

Structural-Acoustic Modeling and Optimization of a Submarine Pressure Hull

<div class="section abstract"><div class="htmlview paragraph">The Energy Finite Element Analysis (EFEA) has been validated in the past through comparison with test data for computing the structural vibration and the radiated noise for Naval systems in the mid to high frequency range. A main benefit of the method is that it enables fast computations for full scale models. This capability is exploited by using the EFEA for a submarine pressure hull design optimization study. A generic but representative pressure hull is considered. Design variables associated with the dimensions of the king frames, the thickness of the pressure hull in the vicinity of the excitation (the latter is considered to be applied on the king frames of the machinery room), the dimensions of the frames, and the damping applied on the hull are adjusted during the optimization process in order to minimize the radiated noise in the frequency range from 1,000Hz to 16,000Hz. Constraints on the total amount of damping that can be used are considered (resource driven constraints) and structural collapse constraints are also taken into account in order to avoid degrading the structural integrity of the pressure hull. Two different optimization strategies are exercised. First a concurrent multidisciplinary analysis is performed; optimal configurations for structural performance and for acoustic radiation are identified and the results are used for producing a single design with optimized performance in both disciplines. Then, an analysis based on set-based design principles is performed. The latter identifies several alternative and diverse hull configurations that provide similar levels of performance with respect to the radiated noise. Having several alternative solutions of nearly equal performance provides insight into the design trade-offs when configuring the pressure hull. The results from both optimization strategies are analyzed and discussed.</div></div>

Structural–Acoustic Modeling and Analysis for a Flexible Partition Panel in Three-Dimensional Acoustic Cavity

Structural–acoustic coupling problem can be commonly seen in sound field analysis and noise reduction areas. It is of great significance for the further research of the structural–acoustic coupling between flexible panel and enclosure cavity. For the purpose of this paper, a three-dimensional acoustic cavity with flexible partition is modeled. The field functions of structural–acoustic coupling solution domain are described by employing improved Fourier series method. Various different boundary conditions of the panel partition are presented by means of continuous distribution of restrained springs along each edge of the panel partition. The general formula considering the structural–acoustic coupling between the panel and the cavities is obtained by the Rayleigh–Ritz method based on the energy principle. A series of numerical examples are given to demonstrate the performance of the present method by comparison with FEM, as well as experimental works. Meanwhile, the results are provided to examine the effect of the translational and rotational stiffness of structural boundaries on the structural–acoustic coupling characteristics of the model. The effectiveness of the present model is validated by a good agreement obtained in the comparison works. This study also shows that how the structural boundary condition affects the coupling system in detail. These results provide a theoretical basis for structural–acoustic coupling analysis and low-noise design of enclosures with panel partition.

A Methodology Based on Structural Finite Element Method-Boundary Element Method and Acoustic Boundary Element Method Models in 2.5D for the Prediction of Reradiated Noise in Railway-Induced Ground-Borne Vibration Problems

This work is focused on the analysis of noise and vibration generated in underground railway tunnels due to train traffic. Specifically, an analysis of noise and vibration generated by train passage in an underground simple tunnel in a homogeneous full-space is presented. In this methodology, a two-and-a-half-dimensional coupled finite element and boundary element method (2.5D FEM-BEM) is used to model soil–structure interaction problems. The noise analysis inside the tunnel is performed using a 2.5D acoustic BEM considering a weak coupling. The method of fundamental solutions (MFS) is used to validate the acoustic BEM methodology. The influence of fastener stiffness on vibration and noise characteristic inside a simple tunnel is investigated.

Rail defect inspection based on coupled structural–acoustic analysis

The inspection of rail defects is of importance in high-speed railway operation and maintenance. As a highly efficient method for both nondestructive testing and structural health monitoring of the rail, ultrasonic guided waves (UGWs) inspection provide increased sensitivity to smaller defects. These advantages can be fully exploited only if the complexities of UGWs propagation between the medium of air and rail are unveiled and managed for the given inspection method. The development and validation of modeling procedure for the rail based on coupled structural–acoustic model is presented in this paper. Acoustic–structure interaction between air and rail is simulated based on COMSOL Multiphysics software. The transient response and natural characteristics of UGWs in the rail was computed and predicted. Moreover, the displacement distribution of UGWs in the defective rail and nondefective rail are analyzed both in time and frequency domain. A feasible method for detecting small defects in the rail is proposed in the paper. The results indicated that a defect of 8 mm in rail head can be inspected effectively using UGWs with frequencies of 40 kHz and above. And for small defects in rail web, the X-crystallographic direction ultrasonic transducer should be chosen for inspection.

Adaptive Sliding Mode Fault-Tolerant Control for a Class of Uncertain Systems With Probabilistic Random Delays

This paper investigates the robust control problem of uncertain nonlinear systems subject to actuator faults via the integral sliding mode control (ISMC) scheme. The actuator failures contain the cases of an outage, loss of effectiveness, and stuck fault, which are frequently encountered in practical applications. Furthermore, in this paper, the time-varying delay considered obeys the probability distribution within certain intervals. By fully considering the information of the probabilistic random delay, new sufficient conditions are given to ensure the asymptotical stability of the controlled system with prescribed $H_\infty $ performance. Moreover, a new control law is proposed to compensate for the effects induced by the actuator faults, and an adaptive mechanism is adapted to estimate the unknown terms. In a word, the proposed ISMC scheme ensures the asymptotical stability with guaranteed $H_\infty $ performance of the closed-loop system and forces that the state trajectories are attracted to the pre-designed sliding surface. Finally, a practical example of the rocket fairing structural acoustic model is used to clarify the validly of the presented control method.

Analytical modelling of structure-borne sound transmission through I-junction using Chebyshev-Ritz method on cascaded rectangular plate–cavity system

A Chebyshev-Ritz based analytical model is proposed to investigate I-junction within the structural–acoustic model of a cascaded rectangular plate–cavity system. By considering of the structural interconnection force and the moment at edges and structural-acoustic interaction on the interface, the structural and acoustic systems are coupled. Two-dimensional and three-dimensional Chebyshev Polynomial series are used to present the unknown panel displacements and the sound pressure field variable inside the cavities, respectively. The effectiveness and correctness of the proposed model on an I-junction in a typical marine offshore platform are verified with those calculated from Finite Element Analysis. The influence of boundary conditions, structural coupling, plate properties, and size of the source-to-receiver cavities on the offshore platform on structure-borne sound transmission are analyzed and addressed. Numerical examples are simulated for several different configurations. It is shown that the boundary conditions, structural coupling manner, plate properties, and the volume ratio of the source-to-receiver cavity will change the structure-borne sound transmission characteristics of the cascaded rectangular plate–cavity system. With the proposed approach, a better prediction can be obtained for structure-borne sound transmission via proper tuning of the cascaded rectangular plate–cavity system on the offshore platform.