Structural-acoustic Problems Research Articles

Sensitivity Analysis of Underwater Structural-Acoustic Problems Based on Coupled Finite Element Method/Fast Multipole Boundary Element Method with Non-Uniform Rational B-Splines

For the direct differentiation technique-based modeling of acoustic fluid–structure interaction and structural-acoustic sensitivity analysis, a coupling algorithm based on the finite element method (FEM) and the fast multipole boundary element method (FMBEM) is suggested. By bypassing the challenging volume parameterization process in isogeometric finite element techniques and the laborious meshing process in traditional FEM/BEM, non-uniform rational B-splines (NURBS) isogeometric analysis (IGA) is utilized to immediately perform numerical analysis on CAD models. The matrix-vector products in the boundary element analysis are accelerated using the fast multipole method (FMM). To hasten the solution of the linear system of equations, the iterative solver GMRES is used. The numerical prediction of the effects of arbitrarily shaped vibrating structures on the sound field is made feasible by the FEM/FMBEM technique. A number of numerical examples are provided to show the applicability and effectiveness of the suggested approach.

Parallelized optimization for substructured finite element structural acoustic problems

This work explores the use of parallelized optimization techniques for structural acoustics problems. In particular, the underlying problems studied here utilize finite element substructuring in order to solve the objective function, though the substructuring aspect is not the primary focus of this work. Instead, several different optimization strategies were employed on a selection of problems to better understand the tradeoffs between the different algorithms. Throughout this effort, the Python library PyGMO is used due to its capabilities to wrap around many different optimization algorithms and distribute optimization tasks over multiple CPUs. The candidate algorithms studied in this work include both heuristic global optimizers and gradient based local optimizers such as the following: Extended Ant Colony (GACO), Conjugate Gradient (CG), Sequential Quadratic Programing (SLSQP), and Method of Moving Asymptotes (MMA). Each method is evaluated individually as well as in combination with some or all of the others to evaluate if a mixed algorithm approach is advantageous. A range of computational resources are employed to understand the scalability and other aspects of the parallelized calculations.

Multi-fidelity surrogate modeling for structural acoustics applications

Recently, surrogate modeling methods have been explored for structural acoustics applications. These often involve evaluation of an “expensive” high-fidelity computational model to obtain training data. However, in many applications, models of varying fidelity and computational cost are available. In such situations, one can leverage multi-fidelity surrogate modeling, where the training data from models of varying fidelity are combined and simultaneously used to produce a surrogate model. A particularly popular class of multi-fidelity surrogate modeling techniques is known as co-Kriging, where simulation output from both “expensive” and “cheap” computational models are correlated and a correction process is obtained that maps between the results of these models of varying fidelity. This talk will review co-Kriging and demonstrate its utility on a canonical structural acoustics problem. [Work supported by the Office of Naval Research.]

Acoustic insulation characteristics improvement of a thick CNT-reinforced doubly-curved shell by using GPLRC and MEE composite layers

Noise reduction in structures and human living environments is one of the most important issues in engineering that is always given special attention. Sound insulation has always been improved using different methods, one of which is to use the properties of materials. Herewith, the aim of this paper is to take advantage of graphene-platelet reinforced composites and magneto-electro-elastic (MEE) material properties for sound attenuation. The present paper deals with the analysis of sound transmission loss (STL) through a three-layer sandwich doubly-curved shell where an MEE sheet is integrated with two nanocomposite sheets. In addition, these two nanocomposite sheets are reinforced by functionally graded (FG) distributions of CNT and graphene platelet (GPL)-reinforced composites, respectively. Firstly, the three-dimensional elasticity theory is employed to derive the governing equations of motion. Then, the vibroacoustic analysis for the resultant equations is completed according to the state space and transfer matrix method. Comparing the obtained results with the available literature discloses that the offered procedure has a high precision for structural acoustic problems. In the next step, in addition to inspecting two kinds of MEE composites, the effective parameters, such as layup configuration, FG distribution, volume fraction, weight fraction, radii of curvature, electromagnetic boundary conditions, and interphase thickness, are assessed on the STL. This assessment shows that the parameters involved in this paper are highly interdependent. Accordingly, the analysis of these parameters is done simultaneously with the aid of three- and four-dimensional plots in order that the optimal value for each parameter can be realized. As seen clearly in the outcomes, the electromagnetic boundary conditions parameters, compared to the other parameters, can much more alter the STL trend, so that a slight change in electric potential results in great change in the STL.

Modified Elliptic Integral Approach for the Forced Vibration and Sound Transmission Analysis of a Nonlinear Panel Backed by a Partitioned Cavity

This article is the further work of previous papers and also the first study to adopt the elliptic integral approach to solve the forced nonlinear structural acoustic problem. A previous elliptic integral approach, which was only used for the free vibration analyses of various nonlinear structural acoustic problems, is modified and custom designed for conducting this forced vibration analysis. The main advantage of the proposed approach is that one elliptic cosine contains various harmonic components, while one simple cosine term only carries one particular harmonic component. That is why the proposed solution form can be more concise than those in the harmonic balance procedures. This is the first study to employ the proposed elliptic cosine solution form for the forced vibration and sound transmission of a nonlinear panel backed by a partitioned cavity. This study has two focuses: (1) the development of elliptic integral approach for solving the nonlinear structural acoustic governing equations, and (2) the effect of partitioned cavities on the forced vibration response and sound transmission loss. Moreover, a set of elliptic cosine solutions is verified by that from the modified residue harmonic balance method. A mode convergence study and a harmonic contribution analysis are also conducted.

High performance computing and inverse problems in acoustics and structural acoustics

Engineering applications in acoustics and structural acoustics commonly require finite element models with large numbers of degrees of freedom. Examples include applications with infinite and semi-infinite domains, as well as problems at high frequency (e.g., ultrasound) where the number of wavelengths in the domain becomes large. The finite element solution of such problems, and their inclusion inside an optimization loop for inverse problems, inevitably involves large numbers of degrees of freedom and systems of equations. Modern high-performance computing is enabling numerical solutions of acoustics applications that were previously intractable. In this talk, we will present an overview of massively parallel acoustic and structural acoustic solution capabilities in Sandia’s Sierra-SD (Structural-Dynamics) software. Sierra-SD is a massively parallel finite element application for structural dynamics and acoustics, having recently demonstrated the implicit solution of models with over 2 × 109 degrees of freedom and running on up to one hundred thousand distributed memory cores. Domain decomposition and MPI parallelism are used to split a large domain into many small domains that can be solved in parallel. Large-scale applications in ship shock loading and vibration of reentry bodies will be shown as demonstrations. [SNL is managed and operated by NTESS under DOE NNSA Contract DE-NA0003525.]

Efficient multi-frequency solutions of FE–BE coupled structural–acoustic problems using Arnoldi-based dimension reduction approach

The frequency sweep analysis is indispensable for the performance prediction and optimization design of structural–acoustic interaction problems. The coupled finite element and boundary element (FE–BE) method has been widely used to perform such simulations. However, the straightforward solution of the resulting hybrid model for a large number of frequencies is computationally prohibitive due to the unfavorable properties of involved matrices, e.g. large-scale, non-symmetric and especially frequency-dependent. In order to ease this challenge, a three-step structure-preserving model order reduction method is presented, which is based on an offline-online computing framework. As a first step, the second-order Arnoldi process is used to speed up calculations of the sparse structural part of the strongly coupled system. In a second step, the low-dimensional approximations of the FE unknown variables are eliminated from the global system of equations and after that the remaining dense BE degrees of freedom are reduced by application of the standard Arnoldi-based Krylov subspace algorithm. A transformation technique based on Taylor’s theorem is incorporated to decouple the frequency from the Green’s function and a column-by-column low-memory projection is further sought to favor the overall storage requirements. In the last step, a robust reduced order model can be quickly retrieved by simple algebraic manipulations, which allows a direct solver without any costly matrix operation to be used for the online sweeps, requiring only a very small fraction of the total CPU runtime. Two numerical cases are investigated to highlight the potential of the proposed approach in multi-frequency applications.

Comparison of quadrature and regression based generalized polynomial chaos expansions for structural acoustics

This work performs a direct comparison between generalized polynomial chaos (GPC) expansion techniques applied to structural acoustic problems. Broadly, the GPC techniques are grouped in two categories: , where the stochastic sampling is predetermined according to a quadrature rule; and , where an arbitrary selection of points is used as long as they are a representative sample of the random input. As a baseline comparison, Monte Carlo type simulations are also performed although they take many more sampling points. The test problems considered include both canonical and more applied cases that exemplify the features and types of calculations commonly arising in vibrations and acoustics. A range of different numbers of random input variables are considered. The primary point of comparison between the methods is the number of sampling points they require to generate an accurate GPC expansion. This is due to the general consideration that the most expensive part of a GPC analysis is evaluating the deterministic problem of interest; thus the method with the fewest sampling points will often be the fastest. Accuracy of each GPC expansion is judged using several metrics including basic statistical moments as well as features of the actual reconstructed probability density function.

Frequency–Amplitude Relationship of a Nonlinear Symmetric Panel Absorber Mounted on a Flexible Wall

This study addresses the frequency–amplitude relationship of a nonlinear symmetric panel absorber mounted on a flexible wall. In many structural–acoustic works, only one flexible panel is considered in their models with symmetric configuration. There are very limited research investigations that focus on two flexible panels coupled with a cavity, particularly for nonlinear structural–acoustic problems. In practice, panel absorbers with symmetric configurations are common and usually mounted on a flexible wall. Thus, it should not be assumed that the wall is rigid. This study is the first work employing the weighted residual elliptic integral method for solving this problem, which involves the nonlinear multi-mode governing equations of two flexible panels coupled with a cavity. The reason for adopting the proposed solution method is that fewer nonlinear algebraic equations are generated. The results obtained from the proposed method and finite element method agree reasonably well with each other. The effects of some parameters such as vibration amplitude, cavity depth and thickness ratio, etc. are also investigated.

Structural acoustic problem and dynamic nonlinear plate equations

ABSTRACT The purpose of this paper is to investigate a structural interaction model coupled with dynamic von Karman equations, without neither rotational inertia nor clamped boundary conditions. Our fundamental goal is to establish the existence and the uniqueness of the weak solution for the so-called global functional energy. The stability is also discussed. At the end, a numerical study based on the finite difference method is presented as well.

Power flow analysis for quantifying structural modifications

Structural modification is the process of changing the physical properties of a structure to achieve a desired objective. For structural-acoustic problems, the objective is usually to minimize structure-borne and air-borne sound, which are generally quantified in terms of power. Mathematically, additions made to the mass, damping, and stiffness matrices, which form the structure's impedance matrix, will change the amount of power that can be input to, dissipated by, flow through, and radiated by the structure. After making structural modifications, the impedance matrix can be expressed as the sum of the impedances of the original structure and the modifications made to the structure. An analytical means of determining how structural modifications affect the aforementioned power metrics with respect to the original structure is examined by utilizing the properties of the inverse of sums of matrices, with emphasis on using spring, dashpot, point mass, and generalized impedances as the structural modifications. Several examples are developed in order to validate the method for numerically generated data, and parametrically show how the modifications affect the power metrics in physical and modal space.

Material parameter optimization for interior and exterior fluid‐structure acoustic problems

SummaryWe present an efficient adjoint‐based framework for computing sensitivities of quantities of interest with respect to material parameters for coupled fluid‐structural acoustic systems with explicit interface coupling. The fluid is modeled using the Helmholtz equation and the structure is modeled using the Navier‐Cauchy equations. Sensitivities are used to drive a gradient based optimization algorithm to solve important problems in structural acoustics, viz noise minimization and vibration isolation. For each problem, we consider two different priors: one where the optimal solution has a smooth variation and another with a bimaterial distribution. These priors are imposed with the help of suitable regularization terms. The effectiveness of this approach is demonstrated on both interior and exterior structural acoustic problems.

Application of a Krylov subspace method for an efficient solution of acoustic transfer functions

Solving acoustic radiation problems, arising from systems including fluid–structure interaction, is of interest in many engineering applications. Computing frequency response functions over a large frequency range is a concern in such applications. A method which solves the Helmholtz equation for multiple frequencies in one step is the matrix-Padé-via-Lanczos connection for unsymmetric systems, as presented by Wagner et al. [1]. The present work is based on Ref. [1] and presents a method for efficiently computing frequency responses over a frequency range for coupled structural-acoustic problems, where the structure and the acoustic near field are discretized with finite elements and an analytical Dirichlet-to-Neumann map approximates the far field. The method is based on a Krylov-subspace projection technique which derives a matrix-valued Padé approximation for a restricted area in the near field and the pressure field on a spherical boundary. On the spherical boundary, where the finite domain is truncated, the non-local modified Dirichlet-to-Neumann operator is applied as a low-rank update matrix. The present contribution extends this method and incorporates new techniques for a more stable model reduction through the Lanczos algorithm and a novel weighted adaptive windowing technique. Further, structural damping is incorporated, for computing the acoustic radiation of a harmonically excited plate. These computed results are compared with acoustic measurements in an anechoic chamber and verified with computational results obtained with a commercial code that uses the perfectly matched layer method.

Subdivision Surfaces — Boundary Element Accelerated by Fast Multipole for the Structural Acoustic Problem

A novel boundary element method based on subdivision surfaces is applied to simulate wave scattering problems governed by the Helmholtz equation. The Loop subdivision scheme widely used in the CAD (computer aided design) field is applied to represent the geometric model and approximate physical field variables. The novelty of this work is that it is the first time to apply the fast multipole method for subdivision surface boundary element method to accelerate the solution of the system of equations. It is demonstrated that the subdivision surfaces boundary element method based on the Loop subdivision scheme performs well in terms of accuracy, and automatically provides multiresolution subdivision hierarchy models to meet the requirements of different precision. This approach is then applied to several real-world applications to illustrate the potential for integrated engineering analysis.

A Multidomain Spectral Method for Analysis of Interior Vibroacoustic Systems with Segmented Boundaries

Spectral methods have previously been applied to analyze a multitude of vibration and acoustic problems due to their high computational efficiency. However, their application to interior structural acoustics systems has been limited to the analysis of a single plate coupled to a fluid-filled cavity. In this work, a general multidomain spectral approach is proposed for the eigenvalue and steady-state vibroacoustic analyses of interior structural-acoustic problems with discontinuous boundaries. The unified formulation is derived by means of a generalized variational principle in conjunction with the spectral discretization procedure. The established framework enables one to easily accommodate complex systems consisting of both a structure assembly and a built-up cavity with moderate geometric complexities and to effectively analyze vibroacoustic behaviors with sufficient accuracy at relatively high frequencies. Two practical examples are chosen to demonstrate the flexibility and efficiency of the proposed formulation: a built-up cavity backed by an assembly of multiple connected plates with arbitrary orientations and a thick irregular elastic solid coupled with a heavy acoustic medium. Comparison to finite element simulations and convergence studies for these two examples illustrate the considerable computational advantage of the method as compared to finite element procedures.

A greedy reduced basis scheme for multifrequency solution of structural acoustic systems

SummaryThe solution of frequency dependent linear systems arising from the discretization of vibro‐acoustic problems requires a significant computational effort in the case of rapidly varying responses. In this paper, we review the use of a greedy reduced basis scheme for the efficient solution in a frequency range. The reduced basis is spanned by responses of the system at certain frequencies that are chosen iteratively based on the response that is currently worst approximated in each step. The approximations at intermediate frequencies as well as the a posteriori estimations of associated errors are computed using a least squares solver. The proposed scheme is applied to the solution of an interior acoustic problem with boundary element method (BEM) and to the solution of coupled structural acoustic problems with finite element method and BEM. The computational times are compared to those of a conventional frequencywise strategy. The results illustrate the efficiency of the method.

Efficient, wide-band coupled structural-acoustic computations combining time and frequency domain finite elements/equivalent sources

Time and frequency domain computations are complementary, and here, the overall goal is to combine them to generate wide-band solutions of coupled structural-acoustic problems. Modal frequency response computations are efficient for low frequencies but become inefficient as the number of basis functions required to represent the response grows large. Modal formulations are required for large problems because the coupled equation system becomes densely populated when acoustic pressure forces are included. In contrast, the equation system remains sparsely populated in time domain formulations when the time step size is chosen appropriately, allowing large problems to be solved efficiently in terms of nodal degrees-of-freedom. However, the analysis times depend linearly on the number of time steps and a large number are generally required to represent the ringing response of low frequency modes. Here, the number of time steps is limited by applying an exponential taper to the time domain solution and truncating the computations. This reduces leakage effects, but does not affect components of response that have damped out before it is applied. Examples are given to illustrate the computations and the tradeoff between number of basis functions in the modal frequency response computations and number of time steps in the transient analyses.Time and frequency domain computations are complementary, and here, the overall goal is to combine them to generate wide-band solutions of coupled structural-acoustic problems. Modal frequency response computations are efficient for low frequencies but become inefficient as the number of basis functions required to represent the response grows large. Modal formulations are required for large problems because the coupled equation system becomes densely populated when acoustic pressure forces are included. In contrast, the equation system remains sparsely populated in time domain formulations when the time step size is chosen appropriately, allowing large problems to be solved efficiently in terms of nodal degrees-of-freedom. However, the analysis times depend linearly on the number of time steps and a large number are generally required to represent the ringing response of low frequency modes. Here, the number of time steps is limited by applying an exponential taper to the time domain solution and truncat...

Efficient, wide-band rigid-body and elastic scattering computations using transient equivalent sources.

A previous paper by the author has shown that transient structural-acoustic problems can be solved using time stepping procedures with the structure and fluid modeled using finite elements and equivalent sources, respectively. Here, the analysis is extended to included scattering problems. Although scattering problems have been discussed extensively in the literature, the current formulation is unique because the acoustic coupling matrix is treated as sparse. Also, most of the previous analyses have assumed the problem is time harmonic, and there is an advantage to performing the computations in the time domain because only a limited number of time steps are required to obtain wideband frequency resolution. This is especially true if the main emphasis is on the mid- to high-frequencies since the ringing response is typically dominated by the lowest frequency modes. Several examples are solved to validate the computations and to document the computation times and solution accuracy.

The effect of large amplitude vibration on the pressure-dependent absorption of a structure multiple cavity system.

This study addresses the effects of large-amplitude vibration on the pressure-dependent absorption of a structure multiple-cavity system. It is the first study to consider the effects of large-amplitude vibration and pressure-dependent absorption. Previous studies considered only one of these two factors in the absorption calculation of a perforated panel absorber. Nonlinear differential equations, which represent the structural vibration of a perforated panel absorber, are coupled with the wave equation, which represents the acoustic pressures induced within the cavities. The coupled nonlinear differential equations are solved with the proposed harmonic balance method, which has recently been adopted to solve nonlinear beam problems and other nonlinear structural-acoustic problems. Its main advantage is that when compared with the classical harmonic balance method, the proposed method generates fewer nonlinear algebraic equations during the solution process. In addition, the solution form of the nonlinear differential equations from this classical method can be expressed in terms of a set of symbolic parameters with various physical meanings. If a numerical method is used, there is no analytic solution form, and the final solution is a set of numerical values. The effects of the excitation magnitude, cavity depth, perforation ratio, and hole diameter on the sound absorption of a panel absorber are investigated, and mode and solution convergence studies are also performed. The solutions from the proposed harmonic balance method and a numerical integration method are compared. The numerical results show that the present harmonic balance solutions agree reasonably well with those obtained with the numerical integration method. Several important observations can be made. First, perforation nonlinearity is a very important factor in the absorption of a panel absorber at the off structural resonant frequency range. The settings of the hole diameter, perforation ratio, and cavity depth for optimal absorption differ greatly with consideration of perforation nonlinearity. Second, the “jump up phenomenon,” which does not occur in the case of linear perforation, is observed when perforation nonlinearity is considered. Third, one or more absorption troughs, which worsen the average absorption performance, may exist in cases with multiple cavities.

A homogenization-based Chebyshev interval finite element method for periodical composite structural-acoustic systems with multi-scale interval parameters

For the periodical composite structural-acoustic system with multi-scale interval uncertainties, a new interval analysis approach is presented in this study. In periodical composites structural-acoustic systems with multi-scale interval parameters, the variation ranges of the sound pressure response can be calculated using the homogenization-based interval finite element method. However, the homogenization-based interval finite element method that is based on Taylor series can only suit periodical composites structural-acoustic problems with small uncertainty degree. To consider larger uncertainty degree, by combining the Chebyshev polynomial series and the homogenization-based finite element, a homogenization-based Chebyshev interval finite element method is presented to predict the sound pressure responses of the structural-acoustic system involving periodical composite and multi-scale interval parameters. Compared with homogenization-based interval finite element method, homogenization-based Chebyshev interval finite element method can obtain higher accurate numerical solutions in the approximate process. Besides, homogenization-based Chebyshev interval finite element method can be implemented without conducting the complex derivation process. Numerical results verify the validity and practicability of the presented homogenization-based Chebyshev interval finite element method for the periodical composite structural-acoustic problem.