Acoustic Radiation Damping Research Articles

Measuring the internal damping of thin metal beams in flexure

Since the internal damping of most metals is a relatively small quantity, precise measurement requires that both acoustic radiation damping and boundary condition damping be either eliminated or highly minimized. In this talk, an experiment setup will be described which can measure the internal damping of metal beams in flexure. To perform a measurement, a beam specimen is placed on wire supports within a vacuum chamber and excited by an autonomous force hammer located within the chamber. The wire supports are located exactly at the nodal lines of the beam mode of interest, so that the frictional losses created by the wire supports are minimized. Once excited, the beam deflection is measured with a single point laser vibrometer. The signal decay measured by the vibrometer is used to estimate damping of the mode of interest using either the Hilbert transform or the half- power method. The wire supports are then moved, and the procedure is repeated for the next mode of interest. Results for several metal specimens will be presented and compared to Zener’s thermoelastic model, which describes the losses created by thermal currents for a beam in flexure, to demonstrate the accuracy of the measurement method.

Hybrid assessment of acoustic radiation damping combining in-situ mobility measurements and the boundary element method

A hybrid experimental-numerical approach is proposed for assessing acoustic radiation damping – a major energy dissipating mechanism in lightweight structures. The vibrational behavior is characterized by distributed mobility measurements using laser Doppler vibrometry allowing to realistically capture the mechanical behavior of the structure under test. The experimentally obtained matrix of mobilities are coupled to a boundary element model to evaluate the radiated sound power numerically. Thereby, acoustic measurements and associated low frequency limitations are avoided, which results in two salient features of the proposed hybrid approach: modeling of diffuse incident acoustic fields and consideration of acoustic short-circuiting induced by slits and gaps. These features contribute to an accurate and excitation-dependent estimation of acoustic radiation damping in the low frequency range. The proposed hybrid approach is applied to flat and C-shaped aluminum sandwich panels mounted onto a tub-shaped foundation. The results are compared to those obtained by a previously reported numerical method.

Theoretical and experimental studies on the hydrodynamic damping of elastic rotating propeller blades

The hydrodynamic damping characteristics of elastic rotating propeller blades are investigated theoretically and experimentally. Firstly, the modal hydrodynamic damping ratio of propeller blade rotating in water is theoretically predicted based on the cantilever plate theory. Then, a series of tests are designed to determine the mechanical, acoustic radiation and hydrodynamic damping of the first-order bending mode of the rotating blade. During the hydrodynamic damping test, the bending vibration of the blade is excited by the rotation-induced turbulence and measured by two strain gauges attached to the blade root. The results show that the theoretical prediction is in good agreement with the experimental results. The hydrodynamic damping increases linearly with the rotational speed of the propeller. Theoretical analysis also shows that the modal hydrodynamic damping ratio of the first-order bending mode is much larger than that of higher-order bending modes. The hydrodynamic damping decays exponentially with the increase of frequency ratio while increases slightly with the increase of propeller advance ratio which represents the ratio of free stream fluid speed to the propeller tip speed.

Mechanical and acoustic emission properties of vegetable fiber‐reinforced epoxy composites for percussion instrument drums

AbstractPercussion instrument drums are traditionally made of wood, which is becoming less available as environmental concerns grow. In order to replace wood in percussion instruments, four types of epoxy resin composites reinforced with fabrics of hemp, flax, ramie, and jute, respectively, are fabricated using vacuum assisted resin infusion molding. The tensile and flexural properties of the composites are measured and compared with those of ailanthus wood. The results show that the flexural strengths and moduli of the composites are either better or in between to those of the horizontal and vertical strips of the wood. An acoustic test method is developed to test the acoustic performance of the composites and the wood. The results show that the composites have lower acoustic dynamic moduli, acoustic radiation damping coefficients, sound velocity, and higher acoustic impedance than those of the wood due to their lower flexural moduli and higher specific densities. The shapes of the acoustic spectra for the composites are somewhat similar to those of ailanthus. The acoustic performance comprehensive scores of the four composites are also in between those of the vertical and the horizontal strips of ailanthus. It is possible to match the acoustic performance of ailanthus by increasing the flexural modulus and decreasing the specific density of the composites through reducing the yarn crimp, increasing the fiber volume fraction, and introducing microvoids into the composites.

Theoretical Improvement of a KZK equation for focused ultrasound in bubbly liquids with thermal effects

Toward medical applications such as HIFU treatment, weakly nonlinear evolution of focused ultrasound in initially quiescent bubbly liquids is theoretically investigated with a special attention to the consideration of a thermal effect. Although our group (Kanagawa, JASA, 2015) was derived a Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation for quasi-plane progressive ultrasound with initially nonuniform number density of microbubbles, thermal effects such as thermal conduction were completely neglected. In this paper, we modify our previous KZK equation by incorporating thermal effects, i.e., the thermal conduction and thermodynamics inside bubble, and the liquid viscous damping in bulk liquid. By using the method of multiple scales to basic equations for bubbly liquids introducing an energy equation proposed by Prosperetti (JFM, 1991), a revised KZK equation incorporating all the thermal effects was derived. Although a newly discovered dissipation term without differentiation corresponds to the thermal conduction, the coefficient of original dissipation term was expressed by the liquid viscosity and liquid compressibility (i.e., acoustic radiation damping). Hence, the physics of dissipation by thermal conduction differs that by liquid viscosity and compressibility. Furthermore, we emphasize that a thermal effect contributes the nonlinear effect, that is, nonlinear coefficient include the ratio of specific heats of the gas inside the bubble.

Effect of boundary conditions in the experimental determination of structural damping

Building a digital twin representing the dynamical behaviour of a structure requires knowledge of its material and geometrical properties. While geometry, mass and stiffness can often be characterised quite accurately, at least for homogeneous isotropic materials, the experimental quantification of structural damping is a time consuming endeavour. Furthermore, the chosen experimental set-up subjects the obtained damping values to uncertainties. In this context, the present study takes a closer look at the influence of the boundary conditions on experimentally obtained damping values. A solid plate made out of a commonly used aluminium alloy has been measured repeatedly with different boundary conditions. The plate is excited by an automated impulse hammer and a laser scanning vibrometry has been employed in order to record the structural response at a total of 165 equally distributed points per measurement. Hence, the modal damping values do not only correspond to a segment but to the entire structure. For each boundary condition, the specimen has been measured 20 times consecutively in order to determine the underlying variance. These data point out that experimentally obtained damping values are much more sensitive to the applied boundary conditions than the natural frequencies. Furthermore, it is indicated that the lowest damping values are obtained when suspending the structure at the nodal lines of the corresponding mode. In the second part of this study, the experimentally determined damping values are compared to numerically obtained values for acoustic radiation damping. This comparison suggests that at higher frequencies, the overall damping of the plate is more affected by energy dissipation due to sound radiation than at lower frequencies.

Investigation of radiation damping in sandwich structures using finite and boundary element methods and a nonlinear eigensolver.

The fully coupled vibroacoustic interaction of sandwich panels is studied using the finite and the boundary element methods. The extent of radiation damping is quantified for various configurations based on both harmonic response analyses and modal analyses. The underlying nonlinear eigenvalue problem is solved using a projection method based on contour integration yielding the shifted (wet) eigenfrequencies, modal radiation loss factors, and air-loaded structural modes. The numerical results clearly illustrate the relevance of air-loading when studying the vibration of sandwich structures. Further, the numerically obtained estimates for radiation damping are compared to both theoretical expressions and experimental results found in the literature. Although good agreement is observed in general, the comparison indicates the limited applicability of commonly used theoretical expressions when coincidence occurs in a frequency range where the modes are still well separated. Moreover, possible sources of error when experimentally determining radiation damping are discussed in detail. The results presented in this paper provide deep insights into the phenomenon of acoustic radiation damping and help to estimate its relevance in future research.

Identification of Radiation Damping Using a Coupled FE/BE Formulation and a Nonlinear Eigenvalue Solver

AbstractWhile acoustic radiation damping is a rather small and insignificant aspect of many engineering applications, it is the primary energy‐dissipating mechanism for lightweight structures with large radiating surfaces. Attempts to reduce the vibrational response of those lightweight structures by additional mechanical damping can only be successful if the extent of mechanical damping is comparable or larger than the extent of radiation damping. In this regard, engineers are in need of reliable and flexible methods for the quantification of radiation damping, as well as for the modeling of its effect in an early stage of the design process. In this paper, the modal radiation loss factors are obtained from an eigenvalue analysis of the coupled structural acoustic system. The equations of linear elasticity and acoustics are addressed by finite and boundary element methods respectively. The nonlinear eigenvalue problem is solved by contour integration. The thereby obtained modes represent the structural modes subject to acoustic loading. The modal radiation damping values can be obtained from the complex eigenvalues. The approach is verified based on the example of a honeycomb sandwich panel in air.

Ultra high quality factor resonators operated in fluids

Maximal quality factors are often a synonym for high performances for resonator based sensing devices. When vibrating within a fluid, several damping mechanisms dramatically reduce their performances. We propose a new concept to drastically reduce acoustic radiation damping. A specifically designed cavity enclosing the resonator is presented, able to couple the radiated field back in the resonator. Experiments on a custom tuning fork have been carried out and a cavity design is presented. This enclosing cavity tenfold its quality factor to reach Q = 75,000 in air at atmospheric pressure, passing through the established physical limits and setting a new record. The presented concept can be extended to many areas of physics employing high quality factor resonators, allowing the exploration of completely new geometries.

Predicting structural and acoustic-radiation loss factors using experimental modal analysis

Standard damping measurements cannot typically distinguish between structural losses and losses due to acoustic radiation. Since the trend in aerospace engineering is to use lighter and stiffer materials, aerospace panels often have their critical frequency at low to mid frequencies making the acoustic losses of comparable or greater value than the structural loss factors. A procedure for measuring acoustic radiation loss factors is presented based on experimental modal analysis. Experimental modal analysis was performed on a composite panel with carbon-fiber facesheets and an aluminum honeycomb core. The loss factors using the standard decay and modal methods are compared to an energy-based method based on the power injection method. The acoustic radiation loss factors were then estimated using boundary element computations of the radiated noise with the modally reconstructed velocity as input. The acoustic radiation damping was then removed from the total damping to predict the losses due to structural ...

Medium damping influences on the resonant frequency and quality factor of piezoelectric circular microdiaphragm sensors

Medium damping influences on the resonant frequency and quality factor of piezoelectric circular microdiaphragm sensors (PCMSs) are investigated theoretically and experimentally in this paper. The acoustic radiation and viscosity damping as the two main sources of energy dissipation in a medium virtually added the mass of the diaphragm and therefore decrease the frequency and Q-factor of the diaphragm. The magnitude of medium damping inversely depends on the radius-to-thickness ratio. An increase in this ratio is the trend in the fabrication of thin microdiaphragms by MEMS fabrication processes, which implies the higher influence of medium damping on the dynamic behavior of microdiaphragms. The fabricated PCMSs were tested in vacuum, air, and ethanol. The Q-factor and the resonant frequency of the device increase by almost seven times, 4.7% from air to 0.05 atmpressure, respectively. The Q-value drops from 111.195 in air to 23.908 in ethanol. Throughout this work, theoretical and experimental values were compared and a fairly good correlation was observed.

Damping and induced damping of a lightweight sandwich panel with simple and complex attachments

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.

Non-linear vibration analysis of an elastic plate subjected to heavy fluid loading in magnetic field

In the present study, the non-linear vibration of an elastic plate subjected to heavy fluid loading in an inclined magnetic field is investigated. The structural non-linearity, fluid non-linearity, and the effects of magnetic field are all incorporated in the formulations to derive the governing equation of the plate. The method of multiple scales is adopted to determine the eigenvalues and mode shapes of the linear vibration, and then the amplitude of the non-linear vibration response of the plate is calculated. Based on the assumptions of ordering and formulations of multiple scales, it can be concluded that the linear dynamic behavior of the plate under heavy fluid loading but weak near-resonant loading is influenced by the effects of the fluid loading, linear structural rigidity and linear magnetic field, furthermore, the non-linear dynamic behavior of the plate under heavy fluid loading but weak near-resonant loading is dominated and controlled by the effects of the fluid loading, non-linear structural rigidity and non-linear magnetic field. Both thick and thin plates are investigated; the contributions due to the structural non-linearity and acoustic linear radiation damping are of the same order for a rather thick plate. For a thin plate, the structural non-linearity completely controls the behavior of the plate, which implies that in this case the effect of fluid loading is considerably negligible. In general, it can be concluded that both the effects of magnetic field and structural non-linearity play important roles only on the first few modes of the plate.

Acoustic leakage in electromagnetic waveguides made from piezoelectric materials

We study the propagation of coupled acoustic and electromagnetic waves in a piezoelectric plate waveguide embedded in two half-spaces of another dielectric material. It is shown that certain waves are guided electromagnetically but not so acoustically and that these waves are effectively damped waves with acoustic leakage of energy. An estimate of the acoustic radiation damping is given.

On the modeling of sound radiation from poroelastic materials

Numerical approaches based on finite element discretizations of Biot’s poroelasticity equations provide efficient tools to solve problems where the porous material is coupled to elastic structures and finite extent acoustic cavities. Sometimes, it may be relevant to evaluate the radiation of a poroelastic material into an infinite fluid medium. Examples include (i) the evaluation of the diffuse field sound absorption coefficient of a porous material and/or the sound transmission loss of an elastic plate coupled to a porous sheet, (ii) the assessment of the acoustic radiation damping of a porous material coupled to a vibrating structure. The latter is particularly important for the correct experimental characterization of the intrinsic damping of the material’s frame. Up to now, the acoustic radiation of a porous medium into an unbounded fluid medium has usually been neglected. The classical approaches for modeling free field radiation of porous materials (i) assumes the interstitial pressure at the radiation surface to be zero or (ii) fixes the radiation impedance to an approximate value. This paper discusses the limitations of these assumptions and presents a numerical formulation for evaluating the sound radiation of baffled poroelastic media including fluid loading effects. The problem is solved using a mixed FEM-BEM approach where the fluid loading is accounted for using an admittance matrix. Both numerical examples and a transmission loss test are presented to illustrate the performance of the technique and its applications.

On the measurement of the mechanical properties of acoustic porous materials

This paper discusses the measurements and use of the mechanical properties of porous materials. It starts with a review of the classical methods currently used and concentrates in explaining the assumptions, difficulties and limitations of these methods. Next, it concentrates on two methods: a quasi-static approach accounting for the effect of shape factors on the measured properties and a hybrid inverse method similar to the vibrating beam method used for viscoelastic materials. Through full 3-D numerical simulations, both methods are simulated and their main features, assumptions, and limitations are investigated. In particular, the model uses full poro-elastic modeling and boundary element in order to investigate the effect of acoustic radiation damping and viscous damping. Using various types of materials, comparisons between these two methods and experimental data are also discussed.

Free-vibration tests on rigid and flexible roofed cavity models with wall openings

Results are presented from free-vibration tests, in still air, on two Helmholtz resonator models, one with rigid walls and one with interchangeable rigid or flexible walls. The results differ from previous studies concerning Helmholtz resonance in building models because of the relative lengths of the orifices. Orifice inertia coefficients were determined from the measured Helmholtz frequency of rigid walled models; bulk modulus ratios were determined from the Helmholtz frequencies of flexible-walled resonators. Damping factors at the Helmholtz frequency, as a fraction of critical, were determined from free-vibration decay data. Acoustic radiation damping was shown to be negligible for the majority of configurations tested.

Acoustic radiation damping of flat rectangular plates subjected to subsonic flows. Part II: Composite

The acoustic radiation damping for various laminated composite and aluminum plates subjected to a uniform, subsonic, and steady flow has been predicted. The predictions are based on the linear equations of motion of a flat plate. The fluid loading is characterized as the perturbation pressure derived from the linearized Bernoulli and continuity equations of fluid mechanics. Parameters varied in the analysis include Mach number and plate material properties and ply lay-up. Results show that the fluid loading can significantly affect realistic plate responses. Universal curves are presented where the acoustic radiation damping normalized by the mass ratio is a smooth function of the reduced frequency. A separate curve was required for each Mach number and plate aspect ratio. Generally, graphite/epoxy and carbon/carbon plates have higher acoustic radiation damping values than similar aluminum plates, except near plate divergence conditions resulting from aeroelastic instability. In addition, acoustic radiation damping values can be greater than or equal to the structural damping ratio component (assumed as 0·01) for the higher Mach numbers.

Acoustic radiation damping of flat rectangular plates subjected to subsonic flows. Part I: Isotropic

The acoustic radiation damping for various plates and semi-infinite strips subjected to a uniform, subsonic and steady flow has been predicted. The predictions are based on the linear vibration of a flat plate. The fluid loading is characterized as the perturbation pressure derived from the linearized Bernoulli and continuity equations. Parameters varied in the analysis include Mach number, mode number and plate size, aspect ratio and mass. Results show that the fluid loading can significantly affect realistic plate responses. In addition, acoustic radiation damping values can be greater than or equal to the structural component of the modal critical damping ratio (assumed as 0·01) for the higher subsonic Mach numbers.

Toward a hydrodynamic theory of sonoluminescence

For small Mach numbers the Rayleigh–Plesset equations (modified to include acoustic radiation damping) provide the hydrodynamic description of a bubble’s breathing motion. Measurements are presented for the bubble radius as a function of time. They indicate that in the presence of sonoluminescence the ratio of maximum to minimum bubble radius is about 100. Scaling laws for the maximum bubble radius and the temperature and duration of the collapse are derived in this limit. Inclusion of mass diffusion enables one to calculate the ambient radius. For audible sound fields these equations yield picosecond hot spots, such as are observed experimentally. However, the analysis indicates that a detailed description of sonoluminescence requires the use of parameters for which the resulting motion reaches large Mach numbers. Therefore the next step toward explaining sonoluminescence will require the extension of bubble dynamics to include nonlinear effects such as shock waves.