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This paper presents a case study for measuring and simulating the vibration and radiated sound for a large complex industrial chiller. We describe a simulation framework based on statistical energy analysis (SEA), which is populated using a hybrid mix of analytic, numerical, and measurement techniques. This hybrid approach was motivated by preliminary measurements of vibration and sound from the operating chiller, as well as a series of vibroacoustic transfer functions measured during quiescent non-operating conditions. Some components, like the chiller condenser shell, are modally dense and well suited to statistical estimates of SEA parameters like modal density and coupling between the shell modes and internal and external acoustic spaces. Other components, like the discharge pipe between the compressor and condenser shell, have only a few well separated modes with low damping. This component is better modeled using mobilities either measured or calculated using finite element analysis. We estimate other parameters like internal and coupling loss factors using a mix of analytics and measurements where appropriate. We validate the general model by comparing simulated and measured transfer functions between the discharge pipe and condenser shell — the components that radiated the most sound. We estimate structure-borne and fluid-borne input powers from the compressor using inference techniques based on transfer function measurements at quiescent conditions and averaged surface vibrations measured at operating conditions. This inference approach allows for estimating input powers over any chiller operating condition. Simulated vibrations and radiated sound are generally within 3 dB of measurements for several operating conditions. This case study provides a useful general methodology for modeling and measuring the vibroacoustics of chillers and other complex machinery

Any vibrating structure is loaded by the fluid surrounding it. Whether air, water, or something else, the fluid loading adds a spatially distributed resistance (in phase with the vibration) and reactance (out of phase with the vibration) over the structural surfaces. The resistance absorbs energy, and damps structural vibrations. The reactance is either mass-like, effectively adding to the structural density, reducing resonance frequencies and vibration amplitudes; or stiffness-like, increasing resonance frequencies. Usually, mass-like reactance is caused by fluids external to a structure, and stiffness-like reactance is caused by enclosed volumes of fluids. This tutorial uses analytic methods to compare and contrast external and internal fluid loading on a flat rectangular plate and demonstrates the effects of fluid loading on plate vibration and radiated sound. The well-known stiffening effect of the internal Helmholtz resonance is demonstrated for a thin panel and a shallow entrained cavity. The differences between heavy (water) and light (air) external fluid loading are also demonstrated, with significant reductions in resonance frequencies and peak vibration amplitudes for water loading.

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.

The vibration responses of three flat rectangular plates excited by turbulent boundary layer flow are calculated and compared to measured data. The measurements were made in three different facilities by Wilby at ISVR [1] (high speeds typical of aircraft), Han at Purdue University [2] (moderate speeds typical of automobiles), and Robin at University of Sherbrooke [3] (lowest speeds), spanning 50 years of time. The plates are different sizes, made from different materials, and have different boundary conditions. The boundary layers have different heights and flow speeds. The ratios of plate flexural and convective wavenumbers kb/kc over the three cases range from about 0.1 to 2. Plate vibrations are normalized by wall pressure fluctuation autospectra measured by the previous investigators. This wide range of structural and flow conditions and the use of plate vibration spectra normalized by wall pressure autospectra allows for an objective assessment of various TBL wall pressure fluctuation cross-spectral empirical models. Two cross-spectral models are considered: the widely used Corcos model [4] and the less well-known elliptical extension by Mellen [5]. Smolyakov’s empirical models for convection velocity and streamwise and spanwise surface pressure length scales [6] supplement the Corcos and Mellen models. Calculations using the Corcos cross-spectral model overestimate the vibrations by about an order of magnitude at lower speed (and lower kb/kc) conditions. Including Smolyakov’s convection velocity and length scale formulations improves accuracy at low frequencies. The Mellen cross-spectral pressure model, supplemented with Smolyakov’s empirical models for convective wave speed and streamwise and spanwise surface pressure length scales, is therefore well suited for calculating plate vibrations due to TBL flows with flow speed/flexural wave speed ratios ranging from 0.1 to 2.

Lock-in flow tones can occur for many different types of flow instabilities and structural-acoustic resonators at low Mach number. This paper examines the interaction between a shear layer instability generated by flow over a shallow cavity and the modes of an elastic cantilevered beam containing the cavity. A describing function model indicates that a cavity shear layer instability capable of producing lock-in with acoustic pipe resonances cannot achieve lock-in with equivalent structural beam resonances, particularly resonances of submerged structures. Fluid-elastic cavity lock-in is unlikely to occur due to the high level of damping that exists for a submerged structure, the high fluid-loaded modal mass, and the relatively weak source strength a cavity generates. Limited experimentation using pressure, acceleration, and particle image velocimetry (PIV) measurements has been performed which are consistent with the describing function model. A stronger source produced by a larger scale flow instability—separated flow over a bluff body—was able to lock-in with modes of the same submerged structure, further demonstrating that the concern for lock-in from a cavity shear layer instability is isolated to systems capable of stronger coupling or those dominated by fluid-acoustic resonances.

Machines, buildings, and vehicles often use fasteners to connect structural elements. Screws and bolts introduce a pressure profile on joint interfaces that varies under different material parameters, preloads, and assembly conditions. Characterization of interfacial pressure at the faying surface of a joint is helpful for understanding the dynamics of the entire built-up system. Examples of interfacial measurements in the literature utilize ultrasonic methods. Some of these previous studies have used separate calibration specimens to convert qualitative ultrasonic measurements to quantitative pressure at an interface. An experiment presented here measured the quantitative distribution of pressure between fastened aluminum plates using an ultrasonic probe and force-sensing washer, without the need of a calibration specimen and test. Beyond traditional measurement methods of this type, boundary effects near the fastener were also accounted for. Scans using this method match finite element results, lending to the utility of the new procedure. The new method has shown to be accurate and more advantageous when compared to previous methods.

As part of the Sound-Structure Interaction course, offered through the Penn State Graduate Program in Acoustics, a set of demonstrations was developed to help reinforce structural acoustics theory. A common test article, a simply supported plate, was developed for a set of four demonstrations. The simply supported plate was used to demonstrate the concepts of mobility functions, radiated sound directivity, fluid loading and acoustic transmission loss. A modal impact hammer, accelerometers, microphones, a sound level meter and a sound intensity probe were used in combination with National Instruments compact DAQ systems and LabVIEW software to develop these custom demonstrations. Basic theory and setup of the demonstrations are presented as well as links to the videos of the demonstrations themselves.

Bolts, screws, rivets, and pins can significantly complicate the prediction of damping, stiffness, and resonance frequencies of built-up systems. Because the interaction of interfacial joints is not well understood, current predictive models incorporating fastened joints often require over-designing for safety. To better understand the behavior of fastened joints, several experiments have been performed on a built-up structure with two rectangular 1/4″ plates fastened together by two screws on a 1/2″ thick flange. The structure was excited via acoustic excitation, and acceleration was measured at multiple locations on the flange and plate during and after ensonifying. While the energy input to the system may be lower for acoustic excitations than other direct contact methods, the results in this paper show that ensonifying the structure has two important advantages over traditional impact hammer and shaker methods. First, resonances of the structure can be excited and analyzed individually in both steady state and free-decay conditions, which is an advantage over impact excitation. Second, the excitation method is non-intrusive and does not change the system properties, which is an advantage over shaker excitation. The proposed method is shown to be an effective way to excite structures for both steady-state and decay measurements.

The panel vibrations induced by fluctuating wall pressures within wall-bounded jet flow downstream of a high aspect ratio rectangular nozzle are simulated. The wall pressures are calculated using a Hybrid RANS/LES method, where LES models the large-scale turbulence in the shear layers downstream of the nozzle. The convecting turbulence in the shear layers loads the structure in a manner similar to that of turbulent boundary layer flow. However, at supersonic discharge conditions the shear layer turbulence also scatters from shock cells, generating backward-traveling surface pressure loads that drive the structure at low frequencies. The panel is rectangular with clamped edges along the sides oriented in the flow direction and free edges at the nozzle discharge and downstream edge. The panel modes of vibration are simulated with Finite Element Analysis. The structural vibration time histories are simulated by Fourier transforming the loading to the complex frequency domain, combining with the structural frequency response functions and inverse transforming the response back to the time domain. Simulated wall pressures and structural vibration agree well with measurements at on-design and underexpanded (about 50% higher pressure ratio) nozzle operating conditions. Filtering the negative wavenumber components from the loading and recomputing the structural response shows that the backward-traveling loading is responsible for about 12% of the overall structural vibration at on-design conditions and 25% of the response at underexpanded conditions.

The United States Nuclear Regulatory Commission (USNRC) has approved several extended power uprates (EPU) for Boiling Water Reactors (BWRs). In some of the BWRs, operating at the higher EPU power levels and flow rates led to high-cycle fatigue damage of Steam Dryers, including the generation of loose parts. Since those failures occurred, all BWR owners proposing EPUs have been required by the USNRC to ensure that the steam dryers would not experience high-cycle fatigue cracking. This paper provides an overview of BWR steam dryer design; the fatigue failures that occurred at the Quad Cities (QC) nuclear power plants and their root causes; a brief history of BWR EPUs; and a discussion of steam dryer modifications/replacements, alternating stress mechanisms on steam dryers, and structural integrity evaluation methods (static and alternating stress).

Many structural acoustics problems involve a vibrating structure in a heavy fluid. However, obtaining fluid-loaded natural frequencies and damping experimentally can be difficult and expensive. This paper presents a hybrid experimental-numerical approach to determine the heavy-fluid-loaded resonance frequencies and damping of a structure from in-air measurements. The approach combines in-air experimentally obtained mode shapes with simulated in-water acoustic resistance and reactance matrices computed using boundary element (BE) analysis. The procedure relies on accurate estimates of the mass-normalized, in vacuo mode shapes using singular value decomposition and rational fraction polynomial fitting, which are then used as basis modes for the in-water BE analysis. The method is validated on a 4.445 cm (1.75 in.) thick nickel-aluminum-bronze rectangular plate by comparing natural frequencies and damping obtained using the hybrid approach to equivalent data obtained from actual in-water measurements. Good agreement is shown for the fluid-loaded natural frequencies and one-third octave loss factors. Finally, the limitations of the hybrid approach are examined.

The modal wavenumber of rectangular, simply supported, isotropic thin plates was theoretically shown to be related to the zeros in the wavenumber spectrum and not to the peaks, resulting in an error between the actual modal wavenumber and location of the wavenumber spectrum peak for low mode orders. This theoretical proof is confirmed by experimental results reported in this letter.

The resonance frequency, stiffness, and damping of a structure with screws, bolts, or rivets is strongly influenced by the nonlinear interaction of connected faying surfaces. During the design phase of built-up systems, those system properties and their uncertainty must be understood to meet vibroacoustic design criteria. However, the frictional interaction of fastened joints is poorly understood, and hypotheses are still being made in an attempt to explain the causes of damping in fastened joints. Friction models that do exist either require onerous methods or are overly simplistic. To provide measured data to support future model development, this research uses experimental modal analysis and a time-domain approach to track damping via the ringdown of a pair of plates with a fastened joint with varying applied torques. Amplitude-dependent plots of the loss factor for several modes are provided, which represent the system better than their single-value counterparts. Frequency decrements due to increased fastener torque were less than one-half of a percent in the presented modes. Counterintuitively, increasing fastener torque in the experiment increased the loss factor and slightly reduced the resonance frequencies of the presented modes. Loss factors vary by 67–96%; in the case of the second mode, loss factor depends heavily on vibration amplitude.

Fluid–structure interaction (FSI) is investigated in this study for vortex-induced vibration (VIV) of a flexible, backward skewed hydrofoil. An in-house finite element structural solver finite element analysis nonlinear (FEANL) is tightly coupled with the open-source computational fluid dynamics (CFD) library openfoam to simulate the interaction of a flexible hydrofoil with vortical flow structures shed from a large upstream rigid cylinder. To simulate the turbulent flow at a moderate computational cost, hybrid Reynolds-averaged Navier–Stokes–large eddy simulation (RANS–LES) is used. Simulations are first performed to investigate key modeling aspects that include the influence of CFD mesh resolution and topology (structured versus unstructured mesh), time-step size, and turbulence model (delayed-detached-eddy-simulation and k−ω shear stress transport-scale adaptive simulation). Final FSI simulations are then performed and compared against experimental data acquired from the Penn State-ARL 12 in water tunnel at two flow conditions, 2.5 m/s and 3.0 m/s, corresponding to Reynolds numbers of 153,000 and 184,000 (based on the cylinder diameter), respectively. Comparisons of the hydrofoil tip-deflections, reaction forces, and velocity fields (contours and profiles) show reasonable agreement between the tightly coupled FSI simulations and experiments. The primary motivation of this study is to assess the capability of a tightly coupled FSI approach to model such a problem and to provide modeling guidance for future FSI simulations of rotating propellers in crashback (reverse propeller operation).

A rotorcraft roof composite sandwich panel has been redesigned to optimize sound power transmission loss (TL) and minimize structure-borne sound for frequencies between 1 and 4 kHz where gear meshing noise from the transmission has the most impact on speech intelligibility. The roof section, framed by a grid of ribs, was originally constructed of a single honeycomb core/composite facesheet sandwich panel. The original panel has acoustic coincidence frequencies near 600 Hz, leading to poor TL across the frequency range of 1 to 4 kHz. To quiet the panel, the cross section was split into two thinner sandwich subpanels separated by an air gap. The air gap was sized to target the fundamental mass-spring-mass resonance of the panel system to less than 500 Hz, well below the frequency range of interest. The panels were designed to withstand structural loading from normal rotorcraft operation, as well as 'man-on-the-roof' static loads experienced during maintenance operations. Thin layers of viscoelastomer were included in the facesheet ply layups, increasing panel damping loss factors from about 0.01 to 0.05. Transmission loss measurements show the optimized panel provides 6-11 dB of acoustic transmission loss improvement, and 6-15 dB of structure-borne sound reduction at critical rotorcraft transmission tonal frequencies. Analytic panel TL theory simulates the measured performance within 3 dB over most frequencies. Detailed finite element (FE)/boundary element (BE) modeling simulates TL slightly more accurately, within 2 dB for frequencies up to 4 kHz, and also simulates structure-borne sound well, generally within 3 dB.

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.

A finite element model of a bare top plate with braces and a bridge plate was created using orthotropic material properties. The natural variation of the wood properties including dependence on moisture content was also determined. The simulated modes were then compared to experimentally obtained modes from top plate prototypes. Uncertainty analysis was also performed to determine the statistical bound of natural variability between wood samples. The natural frequencies of the model fall within the computed error bound. These results reinforce the importance of obtaining accurate material properties for acoustic guitar modeling.

The flow past a rigid-fixed cylinder and a self-oscillating cylinder is simulated at Re=5000. The finite-volume based CFD package OpenFOAM is used for flow computations for a rigid-fixed cylinder. Extensive mesh convergence and time-step studies are conducted for a cylinder span of 2D (twice the diameter). Spanwise-pressure correlations and spectral calculations are conducted using longer cylinder span lengths: 4D, 8D and 16D. As the cylinder span size increases, better spanwise correlations are obtained. For a self-oscillating cylinder, the numerical approach that tightly couples DDES and FEA based on a fixed point iteration is used to predict the amplitude response and drag in a lock-in condition. The results of the rigid-fixed and self-oscillating cylinder computations compare favorably with experimental data.

Fastened joints can significantly complicate the prediction of damping and resonance frequencies of built-up systems. This complexity often leads to over-designing for safety, which drives up manufacturing and operational costs. To improve understanding of the dynamic response of fastened joints, impact hammer and acoustically driven excitation of fastened plates at a flange have been measured. These findings add experimental data that are not well represented in the literature for such joints. The structure was excited acoustically, and acceleration was measured at multiple locations on the flange and plate. Backbone curves were generated with sinusoidal sweeps of acoustic input energy. These curves highlight the nonlinearity of the system, which varies according to fastener preload. Generally, as preload torque values decrease, nonlinearity increases with shifts observed in damping, stiffness, and resonance frequency. Data presented will be used to create a model for better predicting the global dynamic properties of built-up structures.

Rigid scatterers are fundamentally important in the study of scattering of many types of waves. However, in the recent literature on scattering of flexural waves on thin plates, a “rigid scatterer” has been used to represent a clamped boundary. Such a model physically resembles riveting the plate to a fixed structure. In this paper, a movable model for a rigid scatterer that allows rigid-body motion is established. It is shown that, when the mass density of the movable rigid scatterer is much greater than that of the host plate and at high frequencies, the movable rigid scatterer approaches the limiting case that is the riveted rigid scatterer. The single- and multiple-scattering by such scatterers are examined. Numerical examples show that, at the extreme end of lower frequencies, the scattering cross section for the movable model vanishes while that of the riveted models approaches infinity. An array of such movable rigid scatterers can form a broad and well-defined stop band for flexural wave transmission. With a volume fraction above 50%, the spectrum is rather clean: consisting of only an extremely broad stop band and two groups of higher frequency Perot–Fabry resonance peaks. Increasing either scatterer’s mass density or the lattice spacing can compress the spectral features toward lower frequencies.

A laboratory underwater acoustic measurement technique, Supersonic Intensity in Reverberant Environments (SIRE), is developed analytically and validated experimentally and numerically. Unlike standard free or diffuse field techniques, SIRE enables the measurement of narrowband sound power and directivity in an environment with inexact field conditions. The technique takes advantage of underwater vector sensors, measuring only acoustic pressure and the normal component of particle velocity/acceleration, and supersonic wavenumber filtering in the near field of a source. The result is outward-propagating acoustic waves separated from interfering incoming and/or evanescent waves. The SIRE technique was experimentally applied to monopole and dipole sources and the results are compared with theory and standard methods. SIRE is shown to accurately measure radiated sound power to within the limits of ANSI S12.51 and to accurately measure the directivity indices of simple sources to within ±3 dB. A coupled finite element/boundary element model of a point-driven, thin-walled cylinder is also developed to establish the limitations of the SIRE technique. The model results show that the measurement standoff distance should be less than the reciprocal of the largest wavenumber in the frequency band of interest. Furthermore, the maximum measurement grid spacing must be less than twice the standoff distance.

Underwater acoustic vector sensors, for measuring acoustic intensity, are typically used in open water where electromagnetic interference (EMI) is generally not a contributor to overall background noise. However, vector sensors are also useful in a laboratory setting where EMI can be a limiting factor at low frequencies. An underwater vector sensor is designed and built with specific care for EMI immunity. The sensor, and associated signal processing, is shown to reduce background noise at EMI frequencies by 10-50 dB and 10-20 dB across the entire frequency bandwidth, as compared to an identical unshielded vector sensor.

Recent work has shown that the Poisson’s ratio of an isotropic material can be determined using the anticlastic curvature that exists in certain mode shapes of a free, rectangular panel of that material. The shapes must be measured experimentally in order to determine the curvature that exists. The curvature is then related to Poisson’s ratio based on a relationship that depends on thickness and length-to-width ratio. For accurate determination of the anticlastic curvature, high spatial resolution is required. In this paper, high speed video is used to experimentally measure the mode shapes of a free, rectangular panel. The spatial resolution achieved is much higher than that obtained using traditional methods due to the inherent resolution of the camera. The high-speed video results are demonstrated and compared to modes using traditional modal techniques. The Poisson’s ratio is then computed and found to agree well with published values.Recent work has shown that the Poisson’s ratio of an isotropic material can be determined using the anticlastic curvature that exists in certain mode shapes of a free, rectangular panel of that material. The shapes must be measured experimentally in order to determine the curvature that exists. The curvature is then related to Poisson’s ratio based on a relationship that depends on thickness and length-to-width ratio. For accurate determination of the anticlastic curvature, high spatial resolution is required. In this paper, high speed video is used to experimentally measure the mode shapes of a free, rectangular panel. The spatial resolution achieved is much higher than that obtained using traditional methods due to the inherent resolution of the camera. The high-speed video results are demonstrated and compared to modes using traditional modal techniques. The Poisson’s ratio is then computed and found to agree well with published values.

The response of a structure to turbulent boundary layer (TBL) excitation has been an area of research for roughly 50 years, although uncertainties persist surrounding the low-wavenumber levels of the TBL surface pressure spectrum. In this experimental investigation, a cylindrical shell with a smooth internal surface is subjected to TBL excitation from water in fully developed pipe flow. The cylinder's vibration response to this excitation is used to determine low-wavenumber TBL surface pressure levels at lower streamwise wavenumbers than previously reported (k1/kc

The structure- and fluid-borne vibro-acoustic power spectra induced by turbulent fluid flow over the walls of a continuous 90° piping elbow are computed. Although the actual power input to the piping by the wall pressure fluctuations is distributed throughout the elbow, equivalent total power inputs to various structural wavetypes (bending, torsion, axial) and fluid (plane-waves) at the inlet and discharge of the elbow are computed. The powers at the elbow “ports” are suitable inputs to wave- and statistically-based models of larger piping systems that include the elbow. Calculations for several flow and structural parameters, including pipe wall thickness, flow speed, and flow Reynolds number are shown. The power spectra are scaled on flow and structural–acoustic parameters so that levels for conditions other than those considered in the paper may be estimated, subject to geometric similarity constraints (elbow radius/pipe diameter). The approach for computing the powers (called CHAMP – combined hydroacoustic modeling programs), which links computational fluid dynamics, finite element and boundary element modeling, and efficient random analysis techniques, is general, and may be applied to other piping system components excited by turbulent fluid flow, such as U-bends and T-sections.

The effect of placing a structural acoustic filter between water and the transducer elements of an array is investigated to help reduce undesirable grating lobes. A plate is mounted to transducer elements with a thin decoupling polyurethane layer between the transducer and the plate. The plate acts as a radiation/incidence angle filter to pass energy at angles near normal incidence, but suppress energy at large incidence angles. Grating lobe reduction is achieved at the expense of limiting the available steering of the main lobe. Within this steer angle limitation, the main lobe can be steered as normal while the grating lobe level is reduced by the plate’s angular filtering. The insertion of a plate structural filter provides an inexpensive and easily implemented approach to extend usable frequency bandwidth with reduced level grating lobes, without increasing the number of array elements. Even though some data matches theory well, a practical material has yet to be found that possesses optimal material properties. To the author’s knowledge, this work represents the first attempt to advantageously utilize a plate to provide angular dependent sound transmission filtering above the plate’s critical frequency (the supercritical frequency region). [Work sponsored by ONR Code 333, Dr. David Drumheller.]

Accurately estimating a structure's broadband response is highly dependent on a proper characterization of the system's internal damping as well as induced (or effective) damping when coupled systems are considered. In many aerospace and related applications a primary or master structure is loaded with equipment or substructures. The effects of these attachments on the master structure are often poorly understood and frequently overlooked, but in many cases can dominate the master structure's response. In this work various measures of damping of a lightweight aerospace panel (aluminum sandwich honeycomb core panel) with simple (lumped mass) and complex (electronic equipment) attachments are investigated using experimental techniques and simple statistical energy analysis models. The panel's various measures of damping in steady-state conditions are defined and explored. The panels with simple and complex attachments are experimentally evaluated using power injection methods. The results show that at different frequencies the simple panel's response is controlled by internal and then acoustic radiation damping. The complex attachment's induced damping effects, however, can far exceed both the structure internal and acoustic radiation components. A range of complex attachment configurations are evaluated and general design assessment procedures developed for use by designers. Future work is planned to explore the systems transient response and derived parameters, as well as investigate the effects when the attachment mass varies over a greater range of values, a realistic condition applicable to many aerospace systems.

This paper reviews the development of semi-empirical models which calculate the turbulent boundary layer wall pressure frequency spectra. Various models published from the late 1960s to 2004 are reviewed, and the pressure spectra calculated using these models are compared to measured data obtained at various flow conditions at a substantially wide range of Reynolds number and boundary layer thickness. The experimental data consists of flows on flat surfaces in air and cylindrical surfaces in water. A summary of the results on the applicability and limitation of each of the models compared is discussed. A model is identified that provides a good overall prediction of the frequency spectra for all cases evaluated. The readers may use the information presented to choose a model appropriate for their specific applications.

A stochastic model for the space–time turbulent boundary-layer wall-pressure spectrum is developed that uses statistical data from Reynolds-Averaged Navier–Stokes (RANS) solutions as input. The model integrates the source terms for the surface-pressure covariance across the boundary layer for user-specified space and time separations to form a discrete surface-pressure correlation function, the Fourier transform of which yields the surface-pressure wavenumber-frequency spectrum. By integrating RANS data into the model, it is able to respond to local geometry and flow conditions. Validation cases show that predicted surface-pressure power spectra respond appropriately to favorable, zero, and adverse pressure gradients. By operating as a post-processor of CFD RANS analyses, the model is a predictive tool that can be used in flow and flow-induced noise analyses. Because contemporary RANS models are able to predict flow statistics well for configurations of practical interest, this approach to modeling the turbulent boundary-layer forcing function is expected to generalize well to new flow configurations without requiring flow-specific tuning.

In this paper, the scattering of flexural waves on a thin Kirchhoff plate by an ensemble of through-thickness circular scatterers is formulated by using the concept of the T-matrix in a generalized matrix notation, with a focus on deterministic numerical computations. T-matrices for common types of scatterers, including the void (hole), rigid, and elastic scatterers, are obtained. Wave field properties in the multiple-scattering setting, such as the scattering amplitude, and scattering cross section, as well as properties of the T-matrix due to the energy conservation are discussed. After an extensive validation, numerical examples are used to explore the band gap formation due to different types of scatterers. One of the interesting observations is that a type of inclusion commonly referred to as the “rigid inclusion” in fact represents a clamped boundary that is closer to a riveted confinement than a rigid scatterer; and an array of such scatterers can block the wave transmission at virtually all frequencies.

A method to reduce the noise radiated by a ribbed 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.

Viscoelastic materials are often used to add damping to metal structures, usually via the constrained layer damping method. The added damping depends strongly on material temperature and frequency, as do the underlying material properties of the viscoelastomer. Several standardized test methods are available to characterize the dynamic material properties of viscoelastomers. However, they rely on limited test data which is extrapolated using the time—temperature superposition technique. The authors have found that the different testing methods typically produce significantly different dynamic material properties, or “master curves.” An approach for inferring viscoelastomer dynamic moduli with better accuracy is suggested here. Several metal bars are treated using constrained layer damping. Experimental modal analyses are conducted on the bars at different temperatures to produce sets of system resonance frequencies and loss factors. Corresponding finite element (FE) models of the treated bars are analyzed using assumed viscoelastomer material properties based on master curves generated using a standardized test technique. The parameters which define the master curves are adjusted by trial and error until the FE-simulated system loss factors match those of the measurements. The procedure is demonstrated on two viscoelastomers with soft and stiff moduli.

The structure-borne power in bending waves is well understood, and has been studied by many investigators in ideal beam and plate structures. All studies to date, however, have considered only the structural intensity induced by deterministic, localized drives. Since many structures of practical interest are excited by spatially random pressure fields, such as diffuse and turbulent boundary layer pressure fluctuations, techniques for measuring and predicting the structural intensity patterns in flat plates excited by such fields are presented here. The structural intensity at various frequencies in a simply supported, baffled, flat plate driven by a diffuse pressure field is simulated using analytical techniques and measured by post-processing data from a scanning laser Doppler vibrometer and reference accelerometer using finite differencing techniques. The measured and simulated fields are similar, and show intensity patterns different from those caused by deterministic point drives. Specifically, no clear source regions are apparent in the randomly driven intensity fields, although the energy flow patterns do clearly converge toward a point damper attached to the plate.

Particle impact dampers (PIDs) are enclosures partially filled with particles of various sizes and materials. When attached to a vibrating structure, they add damping by dissipating energy through inelastic particle-enclosure collisions as well as through momentum transfer. The development of a design curve that can be used to predict the damping characteristics of particle impact dampers is presented here. A power measurement technique enabled time-efficient measurement of the damping properties of the PID. This technique enjoys several advantages over traditional loss-factor measurements, including the flexibility to analyze the behavior of the PID at any frequency or amplitude of the excitation, and the ability to estimate the damping contribution for any structure operating within the bounds of the design curve. Using the power measurement technique, a large number of experiments were conducted to determine the effects of vibration amplitude, excitation frequency, gap size, nominal particle diameter, and particle mass on the dissipated power and effective mass of the PID. The power data were then systematically collapsed into a pair of two-dimensional master design curves with non-dimensional quantities for the axes. The quantities are comprised of combinations of design parameters. For specific applications, a damping efficiency of the PID may be predicted from the design curves. A physical interpretation of the design curves is given. The performance of a PID on a structure verified the predictive capabilities.

Plate vibrations due to turbulent boundary layer (TBL) excitation can depend strongly on the plate boundary conditions, especially when the flow convects over the plate at speeds much slower than those of the bending waves in the plate. The vibration response of a TBL excited baffled flat rectangular plate is analyzed with two sets of boundary conditions: (a) all four edges clamped, and (b) three edges clamped and one edge free, with the flow direction perpendicular to the free edge. A finite element model with discretization sufficient to resolve the convective wavenumbers in the flow excitation field is used for the study. Three TBL wall pressure excitation models are applied to the plates to represent the cross-spectra of the wall pressures: (i) a modified Corcos model, which includes all wavenumber components of excitation; (ii) a low-wavenumber excitation model previously derived by one of the authors, which only models the wavenumber-white region of the modified Corcos model; and (iii) an equivalent edge force model which only models the convective component in the modified Corcos model. The TBL wall pressure autospectrum is approximated using the model derived by Smolyakov and Tkachenko. The results obtained from applying models (ii) and (iii) to the clamped and free edge plates are compared to those generated using model (i). For the completely clamped boundary conditions, the low-wavenumber and Modified Corcos models yield nearly identical vibration spectra, indicating that surface interactions dominate the response of fully clamped plates excited by TBL pressures. For the free edge boundary condition, the vibrations predicted using the equivalent edge force and modified Corcos models match very well, showing that edge interactions between TBL pressures and structural modes dominate the vibrations of plates with free edges excited by TBL flow.

The wavenumber transform for rectangular, simply supported, isotropic thin plates has been rederived to correct a technical error found in the text Sound and Structural Vibration (Academic Press, 1985/2007) by Fahy/Fahy and Gardonio. The text states that the modal wavenumber corresponds to the peak of the wavenumber spectrum. While this is approximately true for higher-order modes, it does not hold for lower-order modes due to coupling between positive and negative wavenumber energy. The modal wavenumber is shown to be related to the zeros in the wavenumber spectrum by an integer multiple of 2π normalized by the plate length.

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.

When knowledge of material design parameters is lacking, it is important to understand how this uncertainty effects the system response. Generalized polynomial chaos (gPC) expansions provide a means for quantifying this uncertainty and typically show good agreement with Monte Carlo techniques at a much reduced cost [K. Sepahvand et al. / Applied Acoustics 87 (2015) 23-29]. In this work, we apply gPC expansions to study the effects of design parameter uncertainty on a structure’s modal characteristics—both eigenvalues and eigenfunctions. The gPC expansions permit the propagation of uncertainty from the design parameters to the modes and natural frequencies, which then characterize the vibration response of the system as a function of the random parameters. The response uncertainty can then be described using the solutions of the deterministic system sampled carefully over the parameter space. Uncertainty in the forcing function can also be included in this formulation. Numerical calculations demonstrate th...