Structural-acoustic Optimization Research Articles

Impedance Sensitivity Analysis Based on Discontinuous Isogeometric Boundary Element Method in Automotive Acoustics

Abstract Acoustic sensitivity analysis is an essential technique to determine the direction of structural-acoustic optimization by evaluating the gradient of the objective functions with respect to the design variables. However, acoustic sensitivity analysis with respect to acoustic impedance, which is an important parameter representing the interior absorbent material in automotive acoustics, is lacking in the study. Moreover, acoustic sensitivity analysis implemented with conventional numerical methods is time and effort-consuming in automotive acoustics, due to the large-scale mesh generation. In this work, the impedance sensitivity analysis for automotive acoustics based on the discontinuous isogeometric boundary element method is presented. The regularized boundary integral equation with impedance boundary conditions is established, then the sensitivity is derived by differentiating the boundary integral equation. The efficiency of the proposed method is improved by employing the parallel technique and generalized minimal residual solver. A long duct example with an analytical solution validates the accuracy of the proposed method, and an automotive passenger compartment subjecting to impedance boundary conditions illustrates that the computing time of the proposed method is one order of magnitude less than the conventional method. This work presents an easily implementable and efficient tool to investigate acoustic sensitivity with respect to impedance, showing great potential in the application of automotive acoustics.

A parallel computing framework for performing structural-acoustic optimization with stochastic forcing

Structural-acoustic optimization procedures can be used to find the optimal design for reduced noise or vibration in many real-world scenarios. However, the time required to compute the structural-acoustic quantity of interest often limits the size of the model. Additionally, structural-acoustic optimization using state-of-the-art evolutionary algorithms may require tens of thousands of system solutions, which add to the limitations for large full-scale systems. To reduce the time required for each function evaluation, parallel processing techniques are used to solve the system in a highly scalable fashion. The approach reduces the analysis time by solving the system using a frequency-domain formulation and distributing solution frequencies amongst processors to solve in parallel. To demonstrate, the sound radiated from a curved panel under the influence of a turbulent boundary layer is minimized in the presence of added point masses, which are varied during the optimization procedure. The total mass is also minimized and the Pareto front relating the trade-off between added mass and reduced noise is determined. Solver scaling information is provided that demonstrates the utility of the parallel processing approach.

Vibration and Sound Transmission Performance of Sandwich Panels with Uniform and Gradient Auxetic Double Arrowhead Honeycomb Cores

Auxetic mechanical metamaterials that exhibit a negative Poisson’s ratio (NPR) can be artificially designed to exhibit a unique range of physical and mechanical properties. Novel sandwich structures composed of uniform and gradient auxetic double arrowhead honeycomb (DAH) cores were investigated in terms of their vibration and sound transmission performance stimulated by nonhomogeneous metamaterials with nonperiodic cell geometries. The spectral element method (SEM) was employed to accurately evaluate the natural frequencies and dynamic responses with a limited number of elements at high frequencies. The results indicated that the vibrating mode shapes and deformations of the DAH sandwich models were strongly affected by the patterned gradient metamaterials. In addition, the sound insulation performance of the considered DAH sandwich models was investigated regarding the sound transmission loss (STL) from 1 Hz to 1500 Hz under a normal incident planar wave, and this performance was compared with that for hexagonal honeycomb sandwich panels. A programmable structural-acoustic optimization was implemented to maximize the STL while maintaining a constant weight and high strength. The results showed that the uniform DAH sandwich models with larger NPRs generally exhibited better vibration and acoustic attenuation behaviors and that the optimized gradient increasing NPR models yielded higher STL values than the optimized gradient decreasing NPR models for two specified frequency cases, with improvements of 6.52 dB and 2.52 dB and a higher bending stiffness but a lower overall STL. Thus, sandwich panels consisting of auxetic DAHs can achieve desirable vibroacoustic performance with a higher bending stiffness than conventional hexagonal honeycomb sandwich structures, and the design of gradient DAHs can be extended to obtain optimized vibration and noise-control capabilities.

Multi-objective structural-acoustic optimization of beams made of functionally graded materials

This paper presents a study of multi-objective structural-acoustic optimization of elastic beams made of functionally graded materials. The goal of this research is to discover the potentials to design multi-objective optimal volume fraction for better acoustic performance. The transfer matrix method is applied to obtain the structural-acoustic response of functionally graded beams. The hybrid of particle swarm optimization and cell mapping method is used to search for the Pareto optimal solutions. Two well-known distribution laws of material distribution are considered and compared with the spline interpolation of material distribution when spatially sampled material properties are used as design variables. Several cases are studied to demonstrate the multi-objective optimal design of functionally graded beams.

From Berlin to Atlanta, with a sojurn in Oz

Having been lured away from Exxon to pursue a Ph.D. by Gary Koopmann, I had no idea during a 1989 visit to the TU in Berlin, with the Berlin Wall still a looming presence, that he was laying the ground work with Herr Dr. Prof. Manfred Heckl of the Institute of Technical Acoustics to host me should I receive the Hunt. When I arrived in July 1990, the wall had fallen, and great changes were underway. The year passed all too quickly, with Pink Floyd at “The Wall,” technical visits to Dresden, Gottingen, and ISVR, and more. The work I did in that year remains some of my highest cited work. Having already accepted a faculty position at Georgia Tech made the year much less stressful. The connections and colleagues I made at the TU remained throughout my career. At GT I explored a number of areas triggered by my Hunt year, including structural acoustic optimization, acoustic mode representation for exterior fields, and active structural acoustic control which led to a sabbatical year, with results akin to my Hunt year, at the University of Adelaide in Australia. I am also a founding member of a successful acoustic consultancy (Arpeggio).

Structural-acoustic optimization based on Fast Multipole Boundary Element Method sensitivity analysis of a coupled acoustic fluid-structure system

For the light structures immersed in water, a full fluid-structure interaction (FSI) has to be considered when structural acoustics is analyzed. However, the computation costs for the FSI prediction and optimization is always huge. The Fast Multipole Boundary Element Method (FMBEM) is one of the most widely used methods to accelerate the computations. Meanwhile, sensitivity analysis for FSI problems is the most time-consuming part of gradient-based optimization strategies. In this research, a FMBEM-based sensitivity analysis is applied to a practical underwater model’s structural-acoustic optimization. Object function that represents the overall radiated sound power are investigated, where the damping material thickness in some specific areas were chosen as design parameters. An improvement of the object functions are found within a limited number of function evaluations. The FEM/FMBEM based sensitivity analysis is used to calculate the sensitivity of the object function to the design parameters. The method of moving asymptotes (MMA) is chosen as the optimization algorithm. The efficiency of this optimization strategy applied on FSI practical model is investigated in detail.

Structural-acoustic optimization using cluster computing

Structural-acoustic optimization using state-of-the-art evolutionary algorithms may require tens of thousands of system solutions, which can be time-limiting for full-scale systems. To reduce the time required for each function evaluation, parallel processing techniques are used to solve the system in a highly-scalable fashion. The system acoustic radiation is modeled as a stochastic problem using finite elements for the structural vibration and boundary elements for the fluid loading and acoustic analysis. The approach is demonstrated by minimizing the sound radiated from curved panel under the influence of a turbulent boundary layer in the presence of added point masses. Details of the point mass magnitudes and distribution are outcomes of the optimization. Solver scaling information is provided that demonstrates the utility of the parallel processing approach.

An Adjoint Operator Approach for Sensitivity Analysis of Radiated Sound Power in Fully Coupled Structural-Acoustic Systems

Full interaction between structural and fluid domains must be considered for light structures immersed in heavy fluid (e.g. thin steel shells in water). The structural-acoustic design sensitivity analysis provides information on the effect of the design variable on acoustic performance, which makes it a key step for noise control and structural-acoustic optimization. This study uses the finite element method (FEM) to model the structure domain, while the fast multipole boundary element method (BEM) is applied to the exterior acoustic domain. An adjoint operator approach is developed to calculate the sensitivity of the radiated sound power with respect to the design variables, which can be any structural or fluid parameter (e.g. fluid or structural density, Poisson’s ratio, Young’s modulus, and geometric measures). Numerical examples are presented to demonstrate the validity and efficiency of the proposed algorithm.

A structural-acoustic optimization of two-dimensional sandwich plates with corrugated cores

This paper presents an optimization study of sandwich plates with corrugated cores for minimizing the transmitted sound power, considering the manufacturability of the structure and constraints on the structural weight and fundamental frequency. A two-dimensional plate model is developed based on the spectral element method (SEM) for the calculation of the frequency-domain vibration response of the whole sandwich structure subject to airborne excitation, and the Rayleigh integral formula is used to calculate the transmitted sound power via its structure-born path. A genetic algorithm-based multi-parameter optimization method is employed to search for the optimal structural parameters with the objective to minimize the sound power transmitted. It is indicated that the optimization results depend highly on the properties of resonant modes in the targeted frequency band. Because of the local modes of the sandwich structure in the high frequency band, the transmitted sound power can be significantly reduced with neither increasing the structural weight nor deteriorating the bending stiffness.

Minimizing the acoustic power radiated by a fluid-loaded curved panel excited by turbulent boundary layer flow.

In order to address noise control problems in the design stage, structural-acoustic optimization procedures can be used to find the optimal design for reduced noise or vibration. However, most structural-acoustic optimization procedures are not general enough to include both heavy fluid loading and complex forcing functions. Additionally, it can be difficult to determine and assess trade-offs between weight and sound radiation. A structural-acoustic optimization approach is presented for minimizing the radiated power of structures with heavy fluid loading excited by complex forcing functions. The procedure is demonstrated on a curved underwater panel excited by a point drive and by turbulent boundary layer flow. To facilitate more efficient analysis, an uncorrelated pressure assumption is made for the turbulent boundary layer forcing function. The thicknesses of groups of elements were used as the design variables with an adaptive covariance matrix evolutionary strategy as the search algorithm. The objective function was a weighted sum of total sound power and panel mass and the Pareto front was computed to show the optimum trade-off between the two objectives. The optimal designs are presented which illustrate the best methods for reducing radiated sound and mass simultaneously.

Structural–acoustic optimization of a pressurized, ribbed aircraft panel

A method to reduce the noise radiated by a ribbed, aircraft panel excited by turbulent boundary layer flow is presented. To compute the structural-acoustic response, a modal approach based on finite element/boundary element analysis was coupled to a turbulent boundary flow forcing function. A static pressure load was also applied to the panel to simulate cabin pressurization during flight. The radiated sound power was then minimized by optimizing the horizontal and vertical rib location and rib cross section using an evolutionary search algorithm. Nearly 10 dB of reduction was achieved by pushing the ribs to the edge of the panel, thus lowering the modal amplitudes excited by the forcing function. A static constraint was then included in the procedure using a low-frequency dynamic calculation to approximate the static response. The constraint limited the amount of reduction that was achieved by the optimizer.

Structural-Acoustic Topology Analysis Based on Evolutionary Structural Optimization

Application of the evolutionary structural optimization (ESO) approach for structural acoustic optimization is investigated. Combining the sizing optimization, a more appropriate rejection criterion for ESO was put forward. There is a trial of applying modified evolutionary structural optimization (MESO) method in dynamic response problem. Finally, the topology optimization of plate structure under harmonic loading as example, the MESO approach is conducted. The numerical results show that the MESO is feasible in topology optimization analysis; and it expands the application of traditional ESO theory.

The Structural-Acoustic Optimization Analysis Based on Material Selection Optimization Approach

The problem of application of the material selection optimization approach for structural-acoustic optimization is investigated. By introducing the stacking sequence hypothesis of metal material, the mechanical parameters of the material and plies number are defined as design variables; the mathematical model of material selection optimization for reducing acoustic power is established. Take a hexahedral box structure for example; the material selection optimization is carried out. The example shows that the vibration and acoustic radiation of composite laminated can be reduced by using material selection optimization method.

A study on the application of material selection optimization approach for structural-acoustic optimization

Issues of application of the material selection optimization approach for structural-acoustic optimization is investigated herein. By introducing the stacking sequence hypothesis of metal material, the mechanical properties parameters and plies’ numbers of the metal material or composite material are defined as design variables; the mathematical formulation about material selection optimization approach is established. Finally, a hexahedral box structure is taken as an example, and the material selection optimization is conducted. By introducing genetic algorithm (GA), the optimization problem is solved. The numerical example shows the effectiveness of the proposed stacking sequence hypothesis of metal material.

Structural-Acoustic Optimization of Laminated Composite Structures Based on Response Surfaces Method

Based on Mindlin first order shear effect plate theory, the structural-acoustic optimization of laminated composite structures under external loading was investigated. For improving the optimization efficiency, the response surfaces method (RSM) is introduced, and the uniform Latin square method was used to select the most appropriate sample points. In the end, taking the laminated composite plate acoustic radiation as an example, the mathematical model of structural structural-acoustic optimization is established. The results show that the acoustic radiation of laminated composite structures can be reduced by optimizing the stacking sequence parameters such as layers thickness and layers angle. The results prove the validity of the calculating ways.

Structural acoustic optimization of ribbed panels excited by complex forcing functions

Structural acoustic optimization is performed on a ribbed panel exited by diffuse acoustic field and turbulent boundary layer (TBL) flow. In order to vary the rib location during the optimization, component mode synthesis (CMS) was used with the rib and plate treated as separate substructures. The CMS approach couples the individual modes of the rib and plate using impedances at the connection points thus only requiring full eigenanalysis and radiation resistance calculations once and allowing for more rapid function evaluation during the optimization. The optimization was then performed using an evolutionary strategy with covariance matrix adaption. The rib location and properties were varied by the optimizer to find the best low-noise panel. An exhaustive search was performed to verify the optimum solution and compare results for several objective functions. Alternative design variables and constraints will also be discussed.

Vibro-Acoustic Optimization of Turbulent Boundary Layer Excited Panel with Curvilinear Stiffeners

The present work addresses the structural-acoustic design optimization study of straight or curvilinearly stiffened panels excited by turbulent boundary layer (TBL) pressure fluctuation. The Corcos model of representing TBL is used to capture the correlation of TBL pressure excitation. Validation of the Corcos TBL model, implemented in a framework, named EBF3PanelOpt, is also performed. For a comparative study, two optimal baseline designs are obtained for a panel with two and four stiffeners, respectively. The optimal designs obtained by performing acoustic optimization have reduced the maximummean square pressure radiated in the far field by 11.4 dB for a panel with two stiffeners and 18.5 dB for a panel with four stiffeners. The reduction of mass and the acoustic response during structural-acoustic optimization are conflicting in nature. Therefore, amulti-objective design optimization using the nondominated sorting genetic algorithm-II (NSGA-II) in VisualDoc is performed. The best Pareto-optimal design with four stiffeners, obtained using the multi-objective design optimization approach, has reduced the maximum mean square pressure radiated in the far field by 4.8 dBwhen comparedwith the baseline designwith four stiffeners. The obtained optimal designs meet all of the constraints, such as buckling eigenvalue, von Mises, and crippling stresses.

Study on the Coupled Structural-Acoustic Systems for Transport Aircraft

The applications of sandwich structures in industry are numerous. The optimization of such structures with high strength and light weight have been the topic of interest for many researchers. There have also been a few studies on the vibration and sound transmission across these structures. This dissertation presents the structural and acoustic studies of sandwich structures for transport aircraft applications. The analysis of fully coupled structural-acoustic systems is presented in this paper. A method for the analysis of such coupled systems is developed using a particular solution approach. A simple two-dimensional rectangular cavity is used as an example to illustrate the solution approach in detail. Extensive numerical simulations have been done to investigate the effect of structural-acoustic coupling on the resonant frequencies and mode shapes of the system. The Galerkin and the Rayleigh-Ritz methods are used to obtain the coupled modal equations for the system which are solved using a state space formulation, which would provide the reference to the coupled structural-acoustic systems optimization.

A New Hybrid Design of Experiments Approach for Optimization in Structural Acoustics

a new hybrid optimization method including of simplex method and method of design of experiments is developed. The objective of the optimization includes the minimization of the root mean square level of structure borne sound. Application of this new hybrid optimization method is experienced on a square plate. The shape modification concept is considered. The structure’s local geometry modification values at the selected surface key-points are considered as design variables. It is shown that the presented hybrid optimization method is able to reduce the value of objective function with a few number of objective function evaluations.

Structural-acoustic optimization of a rectangular plate: A tabu search approach

In this paper, the application of tabu search method for optimization in structural acoustics is introduced. A shape modification concept is used to change the vibrational and acoustical properties of the finite element model. Objective of optimization process is to minimize the root mean square level of structure borne sound for a quadratic plate made of steel. The comparison of results from this study with other previously published works shows that tabu search method can give a suitable performance for using it in structural acoustic optimization applications.