Rayleigh Integral Research Articles

Acoustic response behavior of porous 3D graphene foam plate

Sound radiation and sound transmission loss (STL) behavior of porous 3D graphene (3D-GrF) foam plate are presented. Two variable refined plate theory which includes both transverse bending and shear stresses is used to model the plate and Navier’s solution is used to calculate the vibration responses while Rayleigh integral is used to analyze the acoustic response. Variation in free vibration frequencies with the nature of porosity distribution is significant for the 3D-GrF plates having higher porosity co-efficient. The natural frequency of the 3D-GrF plate with more porosity around the center and less porosity at the outer surfaces is high. However, resonant amplitudes of the responses and STL of the plates are controlled by both the nature of the porosity distribution pattern and porosity co-efficient. In general, STL of the plate with less porosity around the center and high porosity at the extreme surfaces is high compared to the other cases.

Thermal ablation of biological tissue by high intensity ultrasound

The paper discusses the effect of a series of focused high-intensity ultrasound pulses from a multi-element transducer on the biological tissue. The simulation of the ultrasound intensity field in a homogeneous medium uses the Rayleigh integral. The thermal problem modelling is based on the numerical solution of the heat equation. The advantages of processing a given volume of tissue with pulses, whose focal points over time consistently diverge from the geometric focus of the transducer, have been demonstrated. The effect of the time delay between pulses on the nature of tissue heating and the size of the thermal ablation region is analyzed. The issues of scaling for the problem of heat distribution are discussed.

Sound Radiation Analysis of Functionally Graded Porous Plates with Arbitrary Boundary Conditions and Resting on Elastic Foundation

In this paper, the sound radiation behaviors of the functionally graded porous (FGP) plate with arbitrary boundary conditions and resting on elastic foundation are studied by means of the modified Fourier series method. It is assumed that a total of three types of porosity distributions are considered in the present study. The material parameters are determined according to the porosity coefficient used to denote the size of pores in the plate. The governing equations of the FGP plate are derived by utilizing the Hamilton’s principle on the basis of the first-order deformation theory (FSDT). Each displacement component of the FGP plate is expanded as the Fourier cosine series combined with auxiliary polynomial functions introduced to enhance the convergence rate of the series expansions. The acoustic response of the FGP plate due to a concentrated harmonic load is calculated by evaluating the Rayleigh integral. Good agreements are attained by comparing the present results with those in available literatures, which show the accuracy and versatility of the developed method in this paper. Finally, the influences of the porosity distribution type, porosity coefficient, boundary condition and elastic foundation on the sound radiation of the FGP plate are analyzed in detail.

Acoustic Overpressure Signals from Fully Confined and Vented Chemical Explosions

ABSTRACT We analyzed acoustic overpressure signals generated by overburied underground chemical explosions conducted in hard rock in New Hampshire in 2018. The explosions had comparable yields between 62.8 and 82.6 kg trinitrotoluene equivalent and were buried at depths between 12 and 13 m. Two explosions resulted in crater formation and gas venting, whereas the remaining explosions were fully confined and did not result in ground failure. Acoustic signals from the confined explosions were produced by the ground shock near ground zero. Acoustic signals from cratered explosions represent a combination of a ground shock signal and a time-delayed high-amplitude signal generated by gas venting. The cratering and venting occurred during the free-fall phase observed on the near-source accelerograms. We argue that the main reason for the cratering in this experiment is the low-rock porosity, preventing postexplosion pressure relief in the cavity and promoting long fracture formation during the unloading phase and subsequent containment failure. The ground-shock-induced signals were modeled using the Rayleigh integral of the near-source ground acceleration. The equations of nonlinear acoustics were used to model the observed gas venting signals produced by the gas flow from the explosion cavity to the surface. By comparing the near-source signals produced by venting to theoretical signals from surface blasts we have shown that the venting signals have significantly lower peak pressures and longer signal durations compared to surface blasts of the equivalent impulse. The observed amplitudes of the acoustic signals produced by the venting are significantly higher than the ground-shock related signals expected from overburied explosions. This is important to consider because higher acoustic amplitudes may potentially lead to errors in yield estimation.

Mechanism of a periodic chiral lattice coating on sound radiation suppression at the strong radiation mode of a stiffened hull plate

The development of acoustic coatings is of interest for underwater acoustic stealth to control structure-borne sound radiation of ships. The ship hull is composed of finite stiffened plate structures. The structural discontinuity introduced by the stiffeners will result in uncancelled volume velocity in regions in proximity to the stiffeners, which will produce dominant sound radiation and named as strong radiation mode. Control of this strong radiation mode is of interest. In this study, a periodic chiral lattice coating is proposed, which makes use of the rotation of ligaments of chiral lattice to change the volume velocity distribution on the radiation surface. In order to reveal the vibration attenuation and sound radiation suppression mechanism, dynamic models of a stiffened plate applied with a single-layer chiral lattice coating under point mechanical excitation are established. The chiral lattice coating is composed of ligaments, nodes and air voids between them. The vibro-acoustic responses are studied by employing the finite element method (FEM) and Rayleigh integration. The influence of the acoustic medium in the air voids is also taken into account. Then the vibration suppression and sound insulation performance of the chiral lattice coating is investigated. Experimental study of a stiffened plate applied with the single-layer chiral lattice coating is carried out in a semi-anechoic chamber by employing a Laser Doppler Vibrometer (LDV) scanning system. In comparison, a non-stiffened plate applied with the same periodic chiral lattice coating and the same stiffened plate applied with a periodic non-chiral lattice coating is also studied. It is shown that non-stiffened plate will not have the strong radiation mode and the chiral-lattice rubber coating is not as effective as it for the stiffened plate. The non-chiral lattice coating is not effective as the chiral lattice coating in suppressing the sound radiation at the strong radiation mode. Both numerical and experimental studies show that the single-layer chiral lattice coating is capable to effectively suppress the sound radiation at the strong radiation mode. The suppression mechanism of the chiral lattice coating is two-fold, vibration amplitude reduction and vibration distribution alteration on the sound radiation surface, of which the latter is dominant and lowers the sound radiation efficiency.

GPU Accelerated Acoustic Field Determination for a Continuously excited Circular Ultrasonic Transducer

Abstract This work presents a GPU algorithm to calculate the acoustic field generated by a circular ultrasonic transducer radiating in water a continuous wave. The acoustic pressure in a space point in front of the transducer is calculated by Rayleigh integral, which uses the Huygens principle to compose the field as the sum of contributions from an infinite number of point sources. Because the pressure at each spatial point can be calculated independently, the solution algorithm can run in parallel, taking advantage of the GPU cores. Some experiments were performed in a frequency range from 0.25 to 5.0 MHz. The radiating surface was discretized in order to have a fixed number of elemental areas per wavelength. Results showed the validity of the acoustic fields simulated. In addition, a performance analysis showed that the GPU was 50 times faster than CPU for the most demanding problems.

Optimization and modelling methodologies for electro-viscoelastic sandwich design for noise reduction

In this paper a multilayered laminated sandwich with viscoelastic core, surface bonded piezoelectric patches and shunted damping is optimized in order to reduce sound radiation. The viscoelastic core is used since it is especially effective in damping higher frequencies while the piezoelectric patches can actuate on the lower end by tuning its circuit accordingly. Firstly, a single objective optimization is conducted to obtain the optimal stacking parameters of the laminate. Secondly, a multi-objective optimization approach is developed to distribute the piezoelectric shunted patches on the top of the sandwich panel, where the objectives are to reduce the weight, the sound radiation, and the number of shunted RL circuits. The sound radiation characteristics of different configurations are assessed by calculating their radiated sound power through the Rayleigh integral. Finite element analyses are conducted with the use of commercial software ANSYS© and the optimization procedures are implemented with the use of MATLAB© functions.

Numerical study of the reflected elastic waves using Rayleigh diffraction integral

In this work, the transient ultrasonic waves radiated by a linear phased array transducer in a liquid then reflected at a liquid solid interface is studied. A model based on the Rayleigh integral is used where the reflection at the plane interface is considered by using the reflection coefficients for harmonic plane waves. The transient field is obtained by an inverse Fourier transform of the harmonic field. The obtained results highlight the different components of the ultrasonic field: the direct and edge waves as well as the longitudinal head waves or leaky Rayleigh waves. The temporal representation of these waves has been analyzed and discussed by the rays’ model. Instantaneous cartographies allowed a clear description of all the waves which appear at the liquid-solid interface. The results have been compared to those obtained by using a finite element method.

Simulation of nonlinear trans-skull focusing and formation of shocks in brain using a fully populated ultrasound array with aberration correction.

Multi-element high-intensity focused ultrasound phased arrays in the shape of hemispheres are currently used in clinics for thermal lesioning in deep brain structures. Certain side effects of overheating non-targeted tissues and skull bones have been revealed. Here, an approach is developed to mitigate these effects. A specific design of a fully populated 256-element 1-MHz array shaped as a spherical segment (F-number, F# = 1) and filled by randomly distributed equal-area polygonal elements is proposed. Capability of the array to generate high-amplitude shock fronts at the focus is tested in simulations by combining three numerical algorithms for linear and nonlinear field modeling and aberration correction. The algorithms are based on the combination of the Rayleigh integral, a linear pseudo-spectral time domain Kelvin-Voigt model, and nonlinear Westervelt model to account for the effects of inhomogeneities, aberrations, reflections, absorption, nonlinearity, and shear waves in the skull. It is shown that the proposed array can generate nonlinear waveforms with shock amplitudes >60 MPa at the focus deep inside the brain without exceeding the existing technical limitation on the intensity of 40 W/cm2 at the array elements. Such shock amplitudes are sufficient for mechanical ablation of brain tissues using the boiling histotripsy approach and implementation of other shock-based therapies.

Thermal buckling and sound radiation behavior of truss core sandwich panel resting on elastic foundation

Due to high stiffness and other potential multifunctional application characteristics, truss core sandwich structure offers a promising alternative to traditional stiffened or corrugated sandwich plates used in aerospace and marine industry. And sound radiation from plate structures is a design factor indicating the power reduction, which can help the lattice truss core sandwich structure meet the acoustic requirements for practical engineering design, but the sound radiation performance of this sandwich structure remains unclear. Based on that, the thermal buckling and sound radiation behavior analyses of truss core sandwich structure resting on elastic foundation in thermal environment are presented in this paper. The mechanical behavior of structure–foundation interaction is modeled as two-parameter model including Winkler and shear foundation. The sound radiation due to a concentrated harmonic force in thermal environment is computed by solving the Rayleigh integral. By comparing with numerical simulation results calculated by commercial finite element software, the accuracy and feasibility of theoretical model developed in this paper are validated. The effects of several key parameters including the truss core radius, inclination angle and height, temperature field and elastic foundation stiffness coefficient on thermal buckling and sound radiation behavior have been subsequently investigated.

Vibratory response and acoustic radiation behavior of laminated functionally graded composite plates in thermal environments

The present study is concerned with vibro-acoustic behavior analyses of laminated functionally graded carbon nanotube reinforced composite plates based on Reddy’s higher order shear deformation theory. Four types of carbon nanotubes distributions along the plate thickness are considered, which include uniformly distributed and three other functionally graded distributions. Governing differential equations are derived by means of Hamilton’s principle. The sound pressure and radiation efficiency are calculated with Rayleigh integral. A numerical comparison with available results in the literature is carried out to show the validity of the present model. Furthermore, effects of the carbon nanotubes volume fraction, different thermal environments, lamination angle and carbon nanotubes distribution types on the structural and acoustic response of laminated functionally graded carbon nanotube reinforced composite plates are also investigated.

An Edge-Based Smoothed Finite Element Method for Analyzing Stiffened Plates

In this paper, an edge-based smoothed finite element method with the discrete shear gap using triangular elements (ES-DSG3) is presented for static, free vibration and sound radiation analyses of plates stiffened by eccentric and concentric stiffeners. In the present model, the ES-DSG3 for the plate element with the isoparametric thick-beam element is employed to formulate stiffened plate structures. The deflections and rotations of the plates and the stiffeners are connected at tying positions. By using Rayleigh integral, sound radiation of stiffened plates subjected to a point load can be obtained. The edge-based gradient smoothing technique is employed to perform the related numerical integrations over the edge-based smoothing domains. Compared with the original DSG3 model, the present ES-DSG3 model is relatively softer as a result of the edge-based gradient smoothing technique. From several numerical examples, it is observed that the ES-DSG3 can produce more accurate numerical solutions than the original DSG3 for stiffened plates.

The potential of stop band material in multi-frequency ultrasonic transducers

Ultrasonic transducers play a major role in surround sensing for automotive and industrial applications. The development of autonomous driving functions is one of the top challenges for mobility solutions of the 21st century. In this context, surround sensing systems with high performance serve as a key enabler. This leads to an increasing number of sensors which are desired to operate in parallel or in shorter intervals. Hence, measurements should be conducted with two different frequencies to discriminate the sensor signals. Known multi-frequency ultrasonic transducers mostly employ multiple electro-mechanical coupling elements which require more complex sensor electronics.To overcome this issue, the authors present a study on multi-frequency ultrasonic transducers using only one electro-mechanical coupling element. In order to achieve suitable sound radiation properties at two well separated operating frequencies, spatially distributed stop band material is employed. As a result, the operational deflection shape can be controlled at a certain frequency. In finite element simulation, the relation between spatially distributed stop band material and the resulting operational deflection shapes is investigated. The sound radiation behavior is estimated using the numerical results from a harmonic analysis as input for the Rayleigh integral. In experimental investigations, the presented approach is validated. Finite element simulation and experimental testing show good accordance. Based on the results of the presented study, it is possible to realize a multi-frequency ultrasonic sensor with one electro-mechanical transducer element only and suitable sound radiation behavior at multiple operating frequencies.

Comparison for the Effect of Different Attachment of Point Masses on Vibroacoustic Behavior of Parabolic Tapered Annular Circular Plate

In this paper, a comparison for the effect of different arrangement of point masses on vibroacoustic behavior of parabolic tapered annular circular plate with different taper ratios are analyzed by keeping the total mass of the plate plus point masses constant. Three different arrangement of thickness variation are considered. The mathematical tool FEM using ANSYS is used to determine the vibration characteristic and both FEM and Rayleigh integral is used to determine the acoustic behavior of the plate. Further, Case II plate (parabolic decreasing increasing thickness variation) for all combination of point masses is found to have reduction in natural frequency parameter in comparison to other cases of parabolic tapered plate. In terms of acoustic behavior, sound power levels of different cases of plate with different point mass combination are observed. It is observed that the Case II plate with two point masses combination shows the highest sound power and the Case III plate for all cases of point mass combination is least prone to acoustic behavior. Furthermore, It is observed that at low forcing frequency average radiation efficiency of parabolic tapered plate for different arrangement of point masses is almost same, but at high forcing frequency average radiation increases for higher taper ratio. Finally, a brief discussion of peak sound power reduction and actuation for different arrangement of point masses with different taper ratios are provided.

Mathematical modeling for estimation of acoustic radiation from clamped free tapered annular circular plate having different parabolically varying thickness

In this study, a comparison of sound radiation characteristic of a clamped free annular circular plate with different parabolically varying thickness with different taper ratios 0.25, 0.50 and 0.75 with different excitation locations are analyzed by keeping the mass of the plate constant. Rayleigh integral is applied to determine the acoustic behavior of the plate. The same problem is also solved by FEM to draw the comparison. It is observed that excitation locations and modes have a significant effect on sound power level in comparison to stiffness variation due to different taper ratios. Further, the variation of peak sound power level is investigated with different taper ratio with different excitation locations. Finally, the design options for peak sound power are suggested for different excitation locations with different taper ratios.

Theoretical and Numerical Estimation of Vibroacoustic Behavior of Clamped Free Parabolic Tapered Annular Circular Plate with Different Arrangement of Stiffener Patches

This paper compares the vibroacoustic behavior of a tapered annular circular plate having different parabolic varying thickness with different combinations of rectangular and concentric stiffener patches keeping the mass of the plate and the patch constant for a clamped-free boundary condition. Both numerical and analytical methods are used to solve the plate. The finite element method (FEM) is used to determine the vibration characteristic and both Rayleigh integral and FEM is used to determine the acoustic behavior of the plate. It is observed that a Case II plate with parabolic decreasing–increasing thickness variation for a plate with different stiffener patches shows reduction in frequency parameter in comparison to other cases. For acoustic response, the variation of peak sound power level for different combinations of stiffener patches is investigated with different taper ratios. It is investigated that Case II plate with parabolic decreasing–increasing thickness variation for an unloaded tapered plate as well as case II plate with 2 rectangular and 4 concentric stiffeners patches shows the maximum sound power level among all variations. However, it is shown that the Case III plate with parabolically increasing–decreasing thickness variation with different combinations of rectangular and concentric stiffeners patches is least prone to acoustic radiation. Furthermore, it is shown that at low forcing frequency, average radiation efficiency with different combinations of stiffeners patches remains the same, but at higher forcing frequency a higher taper ratio causes higher radiation efficiency, and the radiation peak shifts towards the lower frequency and alters its stiffness as the taper ratio increases. Finally, the design options for peak sound power actuation and reduction for different combinations of stiffener patches with different taper ratios are suggested.

Equivalent-Source Acoustic Holography for Projecting Measured Ultrasound Fields Through Complex Media.

Holographic projections of experimental ultrasound measurements generally use the angular spectrum method or Rayleigh integral, where the measured data are imposed as a Dirichlet boundary condition. In contrast, full-wave models, which can account for more complex wave behavior, often use interior mass or velocity sources to introduce acoustic energy into the simulation. Here, a method to generate an equivalent interior source that reproduces the measurement data is proposed based on gradient-based optimization. The equivalent-source can then be used with full-wave models (for example, the open-source k-Wave toolbox) to compute holographic projections through complex media including nonlinearity and heterogeneous material properties. Numerical and experimental results using both time-domain and continuous-wave sources are used to demonstrate the accuracy of the approach.

Assessment of the airborne sound insulation from mobility vibration measurements; a hybrid experimental numerical approach

A new measurement procedure is proposed to assess the airborne sound insulation of a partition under diffuse sound field excitation using mobility measurements combined with a numerical procedure. The advantage of this hybrid approach is that the diffuse acoustic field does not need to be physically created, thus avoiding problems related to the generation of such fields at low frequencies. Furthermore, the acoustic properties of both the source and receiving rooms will not affect the determination of the sound reduction index R. The proposed method is especially suited for frequencies below the so called Schroeder frequency of the room, and is complementary to the standardized measurement approaches as described in ISO 10140-2:2010. The measurement part of the proposed procedure involves the measurement of the mobility by forcing the partition along a grid of excitation points (e.g. by means of a shaker) and measuring its response along a grid of response points (e.g. by means of a scanning laser Doppler vibrometer). Using the resulting matrix of mobility transfer functions, the vibrational response of the partition excited by a diffuse acoustic field is numerically calculated, from which the radiated sound power is computed using the Rayleigh integral. Thus the reliance on source and receiving rooms used in standard sound insulation testing is removed entirely. The proposed method provides an estimate that only depends on the properties of the partition. The method was tested in an acoustic laboratory on a single layer glass plate of 1.35 × 1.54 m2, as well as on a funicular shell structure with dimensions of 3 × 3 m2. Comparisons with analytical models and standardized ISO10140-2:2010 measurements confirm the validity of the results.

Effect of static load on vibro-acoustic behaviour of clamped plates with geometric imperfections

The effect of static load on the vibro-acoustic behaviour of clamped rectangular plates with various geometric imperfections is further investigated in this paper. An effective method applying static load on the plate subjected to dynamic excitations is proposed in the experiment. The Von Karman nonlinear incremental strain-displacement relationship is utilized to describe the large deflection and initial geometric imperfection. Based on the assumed mode method and Hamilton's principle, the nonlinear vibration governing equations of an imperfect plate considering the added effect in the experimental implementation are formulated. Firstly, the nonlinear static deflection is solved iteratively. Then the tangent stiffness matrix is utilized to calculate the linear vibration at the equivalent static position. The acoustic radiation can be derived hereof by Rayleigh integral. The theoretical, numerical and experimental results coincide well. The results show that the natural frequencies of the imperfect plate are higher than those of the original flat one. Under static load, different from the flat plate which is stiffened, the imperfection may lead to either stiffening or softening of the plate depending on the imperfection shape and the static load direction. And the vibro-acoustic characteristics are affected accordingly. It is noted that when the imperfection gets larger, snap-through may occur under static pressure. Furthermore, comparison of vibration characteristics among different load locations with the same static load is also discussed.

Vibro-acoustic response of a clamped rectangular sandwich panel in thermal environment

Composite sandwich structures are extensively applied in the automotive, marine and aircraft industries owing to their superior stiffness-to-weight ratio. This paper is concentrated on the vibro-acoustic characteristics of a clamped rectangular sandwich panel in high temperature environments. The analytical solution of vibration and acoustic responses for the fully clamped boundary condition is derived. Firstly, natural frequencies and corresponding modes in thermal environment are derived using the piecewise shear deformation theory. Thermal buckling temperatures and corresponding modes are obtained to investigate the buckling characteristics of the sandwich panel. The vibration response is acquired by applying the mode superposition method. The sound pressure distribution is derived by applying the Rayleigh integral, and the sound radiation efficiency is obtained in sequence. Sound transmission loss (STL) of the sandwich panel is also obtained in theory. Next, numerical simulations and experimental result are carried out to verify the accuracy of the analytical solutions. Finally, focus is placed on the influence of several key parameters including temperature, boundary condition, thickness of the core and dimension of the sandwich on vibro-acoustic characteristics of sandwich panel.