Benjamin M. Goldsberry

A three-dimensional, longitudinally-invariant finite element model for acoustic propagation in shallow water waveguides

A three-dimensional, longitudinally-invariant finite element (FE) model for shallow water acoustic propagation is constructed through a cosine transform of a series of two-dimensional FE models at different values of the out-of-plane wavenumber. An innovative wavenumber sampling method is developed that efficiently captures the essential components of the integral as the out-of-plane wave number approaches the water wavenumber. The method is validated by comparison with benchmark solutions of two shallow water waveguide environments: a flat range independent case and a benchmark wedge.

Negative stiffness honeycombs as tunable elastic metamaterials

Acoustic and elastic metamaterials are media with a subwavelength structure that behave as effective materials displaying atypical effective dynamic properties. These material systems are of interest because the design of their sub-wavelength structure allows for direct control of macroscopic wave dispersion. One major design limitation of most metamaterial structures is that the dynamic response cannot be altered once the microstructure is manufactured. However, the ability to modify wave propagation in the metamaterial with an external stimulus is highly desirable for numerous applications and therefore remains a significant challenge in elastic metamaterials research. In this work, a honeycomb structure composed of a doubly periodic array of curved beams, known as a negative stiffness honeycomb (NSH), is analyzed as a tunable elastic metamaterial. The nonlinear static elastic response that results from large deformations of the NSH unit cell leads to a large variation in linear elastic wave dispersion ...

Normal Mode Analysis of Three-Dimensional Propagation Over a Small-Slope Cosine Shaped Hill

Three-dimensional propagation over an infinitely long cosine shaped hill is examined using an approximate normal mode/parabolic equation hybrid model that includes mode coupling in the out-going direction. The slope of the hill is relatively shallow, but it is significant enough to produce both mode-coupling and horizontal refraction effects. In the first part of the paper, the modeling approach is described, and the solution is compared to results obtained with a finite element method to evaluate the accuracy of the solution in light of assumptions made in formulating the model. Then the calculated transmission loss is interpreted in terms of a modal decomposition of the field, and the solution from the hybrid model is compared to adiabatic and N × 2D solutions to assess the relative importance of horizontal refraction and mode-coupling effects. An analysis using a horizontal ray trace is presented to explain differences in the modal interference pattern observed between the 3D and N × 2D solutions. The detailed discussion provides a thorough explanation of the observed 3D propagation effects and demonstrates the usefulness of the approximate normal mode/parabolic equation hybrid model as a tool to understand measured transmission loss in complex environments.

Three-dimensional propagation: Comparison of finite element and coupled-mode solutions

Three-dimensional propagation over an infinitely long cosine-shaped hill is studied using finite element and coupled-mode models. The finite element approach is based on a longitudinally invariant solution technique. The solution is formulated in a Cartesian coordinate system and a cosine transform is applied to eliminate the range-independent dimension. The resulting equation is two dimensional and the solution is calculated for a sufficient range of values of the transform variable. Then the spatial solution is obtained using an inverse cosine transform. The coupled-mode model is formulated in a cylindrical coordinate system, and the solution is obtained using a separation of variables. Modal amplitudes are calculated from the horizontally separated part of the Helmholtz equation using a hybrid technique such that a parabolic solution provides the description of horizontal refraction in the azimuthal direction and a stepwise coupled-mode technique accounts for mode-coupling in the radial direction. The ...

Inversion of shear wave speed in coastal sediments using interface waves

Shear speeds in semi-consolidated and consolidated shallow water sediments can significantly impact compressional wave attenuation and arrival times of acoustic normal modes. In addition shear properties of sediments are directly related to the strength of the sediments in geotechnical applications. All of these factors emphasize the importance of estimating shear speeds in shallow water sediments. One of the most promising approaches to estimate shear speed is to invert the shear speed profile using the dispersion of interface waves (Scholte waves). Interface wave data from a small scale experiment conducted in very shallow water in coastal Rhode Island will be presented. The University of Rhode Island’s shear measurement system consisting of vertical axis and 3-axis geophones were used to collect data in 3 m of water. Interface waves were excited by dropping a weight from a research vessel. Modeling of interface waves will be carried out using Finite Element Method (FEM) and a dynamic stiffness matrix m...

Shear wave inversion in a shallow coastal environment

Estimation of the shear properties of seafloor sediments in littoral waters is important in modeling the acoustic propagation and predicting the strength of sediments for geotechnical applications. One of the promising approaches to estimate shear speed is by using the dispersion of seismo-acoustic interface (Scholte) waves that travel along the water-sediment boundary. The propagation speed of the Scholte waves is closely related to the shear wave speed over a depth of 1–2 wavelengths into the seabed. A geophone system for the measurement of these interface waves, along with an inversion scheme that inverts the Scholte wave dispersion data for sediment shear speed profiles have been developed. The components of this inversion scheme are a genetic algorithm and a forward model which is based on dynamic stiffness matrix approach. The effects of the assumptions of the forward model on the inversion, particularly the shear wave depth profile, will be explored using a finite element model. The results obtained from a field test conducted in very shallow waters in Davisville, RI, will be presented. These results are compared to historic estimates of shear speed and recently acquired vibracore data. [Work sponsored by ONR, Ocean Acoustics.]

Comparison of two-dimensional axial-symmetric and longitudinally invariant methods for three-dimensional shallow water acoustic propagation using finite element methods

In shallow water acoustic propagation, performing a fully three-dimensional finite element model is currently unfeasible due to difficulty in implementation and limits in computational power. Therefore, alternative representations of the 3D acoustic field are sought. Two promising methods to represent the 3D field are the longitudinally invariant (LI) method, and a 2D axial-symmetric reduction of the 3D Helmholtz equation. When a spherical source is used, azimuthal symmetry of the acoustic propagation is assumed, and these two methods can be compared in 2D planes of the 3D field. Because the LI method takes more computational time than the axial-symmetric method, the accuracy of the pressure field are compared to see if the axial-symmetric method can be used in place of the LI method. First, the two methods are compared for a flat ocean surface with stratified media. Then, a wedge-shaped ocean surface is considered, and the two methods are compared with 2D PE solutions. These comparisons will show if the axial-symmetric method produces similar results to the LI method, and if so, under which geometrical and physical situations the axial-symmetric method can be used in place of the LI method. [Work sponsored by the Office of Naval Research, Ocean Acoustics.]

Guided waves at bianisotropic fluid interfaces

Willis fluids are characterized by constitutive relations that couple the pressure and momentum density to both the particle velocity and the volume strain. This effective dynamic response coupling may arise due to microstructural asymmetry, long range order, or time-varying material properties and has been shown to be analogous to electromagnetic bianisotropic media [Phys. Rev. B 96, 104303 (2017)]. In this study, we report on the existence of guided waves at the interface between two fluids when at least one displays Willis coupling. Criteria for the existence of these waves are discussed in terms of the material properties, frequency, and wave number, and expressions for the dispersion relation and rate of spatial decay away from the interface are obtained analytically. We demonstrate that interface waves are supported when one of the fluids possesses Willis coupling, in contrast to an interface between two classical isotropic fluids, which cannot support interface waves. Special cases are highlighted via numerical examples. [Work supported by ONR, NSF, the Applied Research Laboratories at The University of Texas at Austin, and the NRC Research Associateship Program.]

Non-reciprocal bilinear structures

Structures that display non-reciprocal behavior resulting from nonlinear effects are presented. The nonlinear mechanism is bilinear stiffness, also known as bimodular elastic response. Specific realizations considered are in the form of bilinear springs in series making a finite degree of freedom uni-dimensional nonlinear structure. Recall that a system is reciprocal if FB uB,A = FA uA,B where is uB,A (respectively uA,B) is the displacement at point B (A) resulting from a force FA applied at A (FB applied at B). We say the system is fully non-reciprocal if the reciprocity relationship is violated for any sign of the applied forcing, positive or negative, compressive or tensile. Perhaps the simplest system displaying full non-reciprocity is a two degree-of-freedom spring-mass-spring-mass-spring structure, fixed at both ends. We first describe the static and low frequency behavior, illustrating full non-reciprocity. Similar systems with many bilinear springs and masses display nonlinear traveling wave effects, including pulse spreading and shock formation depending on whether the leading edge of the incident pulse is compressive or tensile, respectively. The talk will also discuss fabrication and optimization of the bilinear springs using additive manufacturing. Work supported by NSF-EFRI.Structures that display non-reciprocal behavior resulting from nonlinear effects are presented. The nonlinear mechanism is bilinear stiffness, also known as bimodular elastic response. Specific realizations considered are in the form of bilinear springs in series making a finite degree of freedom uni-dimensional nonlinear structure. Recall that a system is reciprocal if FB uB,A = FA uA,B where is uB,A (respectively uA,B) is the displacement at point B (A) resulting from a force FA applied at A (FB applied at B). We say the system is fully non-reciprocal if the reciprocity relationship is violated for any sign of the applied forcing, positive or negative, compressive or tensile. Perhaps the simplest system displaying full non-reciprocity is a two degree-of-freedom spring-mass-spring-mass-spring structure, fixed at both ends. We first describe the static and low frequency behavior, illustrating full non-reciprocity. Similar systems with many bilinear springs and masses display nonlinear traveling wave ef...

Bianisotropic acoustic metasurfaces for wavefront manipulation

Materials with sub-wavelength asymmetry and long-range order have recently been shown to respond to acoustic waves in a manner that is analogous to electromagnetic biansiotropy [Sieck et al. Phys. Rev. B 96, 104303, (2017)]. A characteristic of these materials is the generation of dipolar scattering when subjected to a uniform time-varying pressure field. This behavior leads to a characteristic acoustic plane-wave impedance that has a preferential direction, known as a polarization, which results in direction-dependent magnitude and phase of an acoustic field scattered from bianisotropic acoustic media. These materials can therefore be used as acoustic metasurfaces to control the reflected or transmitted acoustic fields. This work presents the use of bianisotropic acoustic media for wavefront manipulation through analytical and finite element modeling and discusses potential acoustic analogues to existing bianisotropic electromagnetic metasurfaces. [This work was supported by ONR and the National Science Foundation.]Materials with sub-wavelength asymmetry and long-range order have recently been shown to respond to acoustic waves in a manner that is analogous to electromagnetic biansiotropy [Sieck et al. Phys. Rev. B 96, 104303, (2017)]. A characteristic of these materials is the generation of dipolar scattering when subjected to a uniform time-varying pressure field. This behavior leads to a characteristic acoustic plane-wave impedance that has a preferential direction, known as a polarization, which results in direction-dependent magnitude and phase of an acoustic field scattered from bianisotropic acoustic media. These materials can therefore be used as acoustic metasurfaces to control the reflected or transmitted acoustic fields. This work presents the use of bianisotropic acoustic media for wavefront manipulation through analytical and finite element modeling and discusses potential acoustic analogues to existing bianisotropic electromagnetic metasurfaces. [This work was supported by ONR and the National Science ...