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Over the course of the past 40-45 years of computational modeling in the fields of structures, structural acoustics, and vibrations, there have been extreme advancements made in numerous areas that have greatly increased and improved the size, accuracy, efficiency, and complexity of numerical solutions possible. Most of this progress has been made through a combination of improvements in the distinct areas of computer processing approaches/speed and available memory, primarily evolutionary enhancements in detailed numerical material and continuum mechanics models, development of entirely new physics-based numerical vibroacoustic modeling approaches, etc. This paper presents a historical review of the detailed progress made in computational structural acoustics and vibration from the “early days” in the 1980s through current state-of-the-art advanced numerical approaches, much of which would not have been dreamed possible back four decades ago! While most of the examples utilized in this talk are pulled from the speaker’s specific technical area of undersea vehicle/ system structural acoustics, the overall trends presented are certainly represented across the broad spectrum of vibro-acoustics modeling applications.

Throughout the course of a relatively long career in science and engineering, including advanced degrees, teaching, and a host of other external technical activities, there are numerous lessons learned and perspectives gained that are frequently much more important than specific technical advice. Oftentimes, the most important and critical teachings to be passed on to fellow present and future researchers are not narrowly-focused but wide-ranging and generally applicable. The most essential of these “pearls of wisdom” are learned occasionally out of successes yet more often out of apparent failures and frustrations. Almost invariably, the most valuable information is wide-ranging and universal and independent of any particular scientific discipline or field. This paper presents numerous technical and life-/career-related lessons that are hopefully of value and interest to current and upcoming scientists, engineers, and students. In addition, time permitting, a particular specific technical case study is presented.

Structural acoustics may be defined as a multidisciplinary coupled field of physics usually referring to the characterization of either (1) the sound power emitted by a vibrating structure subjected to external dynamic excitation or (2) the vibrational response of structures excited by incident sound fields or fluid excitation. The Structural Acoustics and Vibration (SAV) Technical Committee is a diverse group of scientists and engineers sharing a common interest and shared stewardship in the health and advancement of the SAV technical discipline. In addition to the fundamental scientific study of the underlying SAV physics which is important to all SAV practitioners, there is also interest on the practical real-world, application of the SAV science to predict, control, and potentially reduce the vibroacoustic response of given structural acoustic systems. This paper begins by providing a fundamental definition of the underlying physics governing the SAV technical discipline. The numerous categories and subdivisions within the general SAV area are then addressed, along with illustrations of the broad array of scientific and engineering real-world applications in the field. Following that, examples of interesting career options as well as exciting new research areas in SAV are presented. Finally, this paper concludes with information regarding the makeup, functioning, and administrative philosophy of the SAVTC.Structural acoustics may be defined as a multidisciplinary coupled field of physics usually referring to the characterization of either (1) the sound power emitted by a vibrating structure subjected to external dynamic excitation or (2) the vibrational response of structures excited by incident sound fields or fluid excitation. The Structural Acoustics and Vibration (SAV) Technical Committee is a diverse group of scientists and engineers sharing a common interest and shared stewardship in the health and advancement of the SAV technical discipline. In addition to the fundamental scientific study of the underlying SAV physics which is important to all SAV practitioners, there is also interest on the practical real-world, application of the SAV science to predict, control, and potentially reduce the vibroacoustic response of given structural acoustic systems. This paper begins by providing a fundamental definition of the underlying physics governing the SAV technical discipline. The numerous categories and s...

The Structural Acoustics and Vibration (SAV) Technical Committee is a broad group of scientists and engineers sharing a common interest and shared stewardship in the health and advancement of the SAV technical discipline. Structural acoustics may be defined as a multidisciplinary coupled field of physics usually referring to the characterization of either (1) the sound power emitted by a vibrating structure subjected to external dynamic excitation or (2) the vibrational response of structures excited by incident sound fields or fluid excitation. While the fundamental scientific study of the underlying SAV physics is certainly important to SAV practitioners, there is also interest on the practical application of the prediction, control, and potential reduction of the vibroacoustic response of given structural acoustic systems. This paper first provides a fundamental definition of the underlying physics behind the SAV technical discipline. The many categories and subdivisions within the general SAV area are then addressed, along with illustrations of the broad array of scientific and engineering real-world applications in the field. Following that, examples of interesting career options as well as exciting new research areas in SAV are presented. Finally, the paper concludes with information regarding the makeup, functioning, and administrative philosophy of the SAVTC.The Structural Acoustics and Vibration (SAV) Technical Committee is a broad group of scientists and engineers sharing a common interest and shared stewardship in the health and advancement of the SAV technical discipline. Structural acoustics may be defined as a multidisciplinary coupled field of physics usually referring to the characterization of either (1) the sound power emitted by a vibrating structure subjected to external dynamic excitation or (2) the vibrational response of structures excited by incident sound fields or fluid excitation. While the fundamental scientific study of the underlying SAV physics is certainly important to SAV practitioners, there is also interest on the practical application of the prediction, control, and potential reduction of the vibroacoustic response of given structural acoustic systems. This paper first provides a fundamental definition of the underlying physics behind the SAV technical discipline. The many categories and subdivisions within the general SAV area are...

Two major areas of current research focus in Structural Acoustics and Vibration (SAV) are in (1) the development of advancements in the Physics-Based Modeling (PBM) and simulation of real-world, large-scale vibroacoustic systems and also in (2) the development and incorporation of novel engineered materials to improve structural acoustic response performance from a broad array of perspectives. This paper presents examples from a wide survey of recent SAV computational PBM research, from the inclusion of additional complex, coupled modeled phenomena, to improvements in modeling efficiency, accuracy, and/or full frequency spectrum response prediction, through computational advances in the ability to solve extremely large-scale, previously intractable, structural acoustics models. Related to the second materials-based SAV research concentration, recent advancements and innovations in SAV-relevant materials including acoustic metamaterials, zero- and negative-Poisson’s ratio materials, single crystal ceramics, nanomaterials, etc., are also presented.

A generalized model for characterizing nonlinear systems was originally proposed by Italian mathematician and physicist Vito Volterra (1860-1940). A further development by American mathematician and MIT Professor Norbert Wiener (1894-1964) was published in 1958. After direct involvement with Norbert Wiener publication, Albert H. Nuttall has recently made new inroads along with his coauthors in applying the Wiener-Volterra model. A general description of a nonlinear system to the third order is termed the Nuttall-Wiener-Volterra model (NWV) after its co-founders. In this formulation, two measurement waveforms on the system are required in order to characterize a specified nonlinear system under consideration: an excitation input, x(t) (the transmitted signal) and a response output, z(t) (the received signal). Given these two measurement waveforms for a given system, a kernel response, h= [h0,h1,h2,h3] between the two measurement points, is computed via a least squares approach that optimizes modeled kernel...

Experiments and analyses of Hughes et al., JASA, 2009 are the origins of this research where we study the in-air waveform generation and propagation of the acoustic signals generated by cicadas. The sound generation is studied in a Newtonian model and the sound propagation is analysis by a numerical solver for viscous Burgers’ equation. The time histories from the tymbal surface velocities recorded by a laser Doppler vibrometer to the microphones positioned near the cicadas provide the test data. The Newtonian model describes the sound production systems process to generate the mating call signal structure. The numerical solver employs weighted essentially non-oscillatory (WENO) reconstruction to approximate the first and second derivatives of the semi-discrete operator. The WENO is utilizes due to the non-smooth structure of the cicada propagating waveform. Principally, the cicada mating signal in question has sharp transitions, since spectral methods tend to produce spurious oscillations as a result of attempting to represent a discontinuous function by a Fourier basis expansion. Thus, these analytical models are computationally tested to determine if the results capture the sound production and the transmission of the cicada mating calls. To verify the models are meaningful, the simulations are verified with real experimental data.

The structural acoustics and vibration related to submerged, structurally driven elastic plates is germane to a wide range of applications in U.S. Navy undersea vehicle and system designs. Of particular interest to a recent specific Naval design application was the examination of effects on the acoustic radiation from a very large, fluid-loaded elastic plate joined with a “welded,” or strongly attached, smaller elastic plate subjected to force-loading excitation somewhere on the large plate. This paper presents the results following an examination of several theoretical approaches to predicting the radiated sound level (both levels and directivity) of an idealized infinite plate and perfectly attached thin, finite plate submerged in a heavy fluid and driven by a line-load at varying locations on the infinite plate. Parametric studies are also presented to both highlight the underlying basic physical mechanisms and also to investigate the effect on sound radiation of varying system parameters. Specifically, results of parametric variations in (a) location of the line force on the plate with respect to the attached finite plate, (b) length/size of the attached plate, (c) mass and/or stiffness of the attached plate, (d) frequency of the harmonic line-load, and, time permitting, and (e) the mechanical theory of the attached thin plate, are all presented herein.

Among a multitude of diverse applications, the acoustics of cylindrical shells is also an important area of study for its applicability to and representation of many US Navy undersea vehicles and systems. Examination of structural acoustic predictions of cylindrical-shell-based system designs are frequently made using a variety of analytical and computational approaches including closed-form 3D elasticity, numerous kinematic plate/shell theories, Finite Element Analysis (FEA), Energy-based FEA (EFEA) coupled with Energy Boundary Element Analysis (EBEA), and Statistical Energy Analysis (SEA). Each of these approaches has its own set of assumptions, advantages, and applicable frequency range which can make for confusion. This paper presents radiated noise solutions in the area of cylindrical shell structural acoustics from the above list of methodologies for the canonical problem of a point-excited, finite cylindrical shell with/without fluid loading. Specifically, far-field radiated sound power predictions...

The principal anatomical structures in the cicada that radiate sound are two platelets referred to as tymbals, which vibrate after being struck by ribs that have undergone buckling. This research effort investigates the sound of these ribbed finite plates connected to a parallel surface by a nonlinear spring. When individual ribs are placed under compression, the linearized version of the model predicts eventual exponential growth of the transverse displacement when the compressional load exceeds the buckling load. The nonlinear spring, however, stops this growth and a subsequent oscillation ensues. The actual anatomy of the cicada is more complicated than this basic model. However, this simplified mathematical explanation is given as a means to describe sound emitted in a sequence of closely spaced tone bursts. The energy from these sound impulses are stored in tensed muscles and released via buckling into the kinetic energy of ribs, which is similar to striking a drum. The tymbals “ring” at a frequency controlled by the mass of the tymbals and the air cavity “spring” within the abdomen. This ringing vibration affects the amplitude, cycles within each pulse, and the damping of the tymbal function to generate the efficiency of the cicada sound radiation.

A quantitative explanation is given of features of noise emitted by cicadas (classed as the loudest of all insects). Microphone data shows sounds are emitted in a sequence of closely spaced tone bursts. Listeners do not perceive the individual pulses because of the finite integration time of the ear. The principal sound radiators are two platelets referred to as tymbals, which vibrate after being struck by ribs that have undergone buckling. The energy of each sound pulse is initially stored in tensed muscles and is initially released via buckling into the kinetic energy of ribs, which strike the tymbals in a manner similar to that of a drumstick striking a drum. The tymbals “ring” at a frequency controlled by the mass of the tymbals and the springiness of the air cavity within the abdomen of the cicada. The wavelengths of the radiated sound are much larger than the tymbal radii but comparable to the overall dimensions of the cicada. The detailed theory explains the radiation pattern of the sound radiation, the amplitude of the sound, the number of cycles in each pulse, the radiation damping of the tymbal vibrations, and why the cicada is such an efficient radiator of sound.

Projection systems are considered where two or three frequencies (e.g., f1, f2, and/or f3) are simultaneously projected into water in a parallel fashion. High near-field amplitudes produce beams of frequencies equal to any linear combination of f1, f2, and f3, with integer coefficients n1, n2, and n3 (possibly zero or negative). Interest here is in the case where the magnitudes of the coefficients sum to three, associated with a third-order nonlinearity. The question addressed is that of how large the amplitude of the far-field signal will be. The considered causes of the nonlinearities are (1) the convective derivative term in the total time derivative of the fluid velocity, and (2) the higher coefficients in the expansion of the fluid density in terms of the deviation of the pressure from its ambient value. These coefficients are derived from data reported by Holton et al. [J. Acoust. Soc. Am. (1968)] on the sound speed in water. A perturbation technique is explored starting with the basic nonlinear equations of compressible time-dependent fluid dynamics, where at each step one has a simultaneous set of coupled linear and homogeneous equations with the source terms dependent on the solutions of the analogous equations corresponding to the previously considered orders.

Since the pioneering work of Preston Smith, Jr. and Richard Lyon in 1959 in the development of the theory of Statistical Energy Analysis (SEA), followed by many others in the 1960’s on through today, the US Navy has utilized the important SEA vibro-acoustic simulation approach for high frequency self- and radiated-noise predictions of a multitude of undersea vehicles and systems. As a tribute to Preston Smith, this talk will review the current state of research in the determination of the variance/probability distribution about the mean response of a system modeled in SEA. While the subject of system response variance (or confidence interval) has obviously been of interest since the inception of this energy-based statistical method, there has been significant recent research in the literature advancing this area that is worth reviewing. As an additional acknowledgement of Preston Smith’s later important work in the area of underwater cylindrical shell acoustics, the current presentation will also revisit ...

Recent research in very high speed underwater vehicles shows they require a much more streamlined vehicle nose than the present rather flat tactical scale vehicle nose. It has been found that the common forward‐facing transducer array with a constant thickness array window utilized on current lower speed vehicles is inadequate. Two newer alternate front‐end array concepts suitable for lower drag, higher speed vehicles being investigated are (a) a variable thickness, streamlined array window on a flat forward facing array and (b) a streamlined vehicle nose structure consisting of a built‐in distributed, conformal array. While these highly streamlined concepts are attractive from the standpoint of reducing vehicle drag at higher speeds, both require reexamination of the effects of high curvature on front‐end sonar array performance. In the present paper, both above streamlined array concepts are numerically examined using the sara2d dynamic structural‐acoustic Finite Element Analysis (FEA) code. First, the ...

Statistical energy analysis (SEA) modeling has been utilized for decades toward the prediction of both self‐ and radiated noise behaviors of undersea vehicles such as submarines, torpedoes, and unmanned underwater vehicles. Since these vehicles operate in a semi‐infinite or infinite seawater environment, it is difficult in SEA to account for any “intra‐model” acoustic propagation through this infinite seawater path. For example, an important source of undersea vehicle self‐noise arises due to acoustic propagation through the seawater environment from the vehicle’s aft propulsion system to the vehicle’s nose where the array is oftentimes located. To date, there has been no standard method published in the literature for how to accurately handle this important acoustic propagation path in SEA. The present paper investigates and compares several approaches that have been employed for properly accounting for aft‐to‐forward acoustic propagation through this infinite seawater environment path both for fully‐wetted and supercavitating, high‐speed undersea vehicle SEA models. A new hybrid method employing both finite acoustic volume and semi‐infinite SEA acoustic elements has recently shown promise and is presented for discussion.

The literature is full of technical papers that have examined the free vibration of cantilevered Bernoulli‐Euler beams with both rigidly and elastically‐attached point masses at the free end. Additionally, much work has been published in the last ten years on cantilevered Timoshenko beams (which includes the effects of shear deformation and rotatory inertia) with a similar, yet more restricted, set of free end boundary conditions. Rossit and Laura published in the Journal of the Acoustical Society of America in 2001 a formulation for a Timoshenko beam with a simple single DOF spring‐mass system attached to the free end. The present paper extends Rossit and Laura's mathematical formulation to account for a general, damped, multi‐DOF system point‐connected to a cantilevered Timoshenko beam's free end. To demonstrate the formulation, mathematical relations and numerical results for a single DOF damped system and both damped/undamped 2DOF vibration absorbers are presented.

The coupled structural, acoustic, and piezoelectric noise propagation physics within a layered 1‐3 composite, half‐wavelength resonator transducer array for high‐frequency, broadband underwater applications is modeled herein using dynamic finite element analysis (FEA). This analysis is being performed primarily to evaluate the complex steady‐state dynamic response of the multiple‐layered composite array in order to ensure bond structural integrity during high‐frequency operation. Specifically, various geometric configurations of the individual array layers will be examined to determine their effect on both array performance and structural integrity (e.g., relative PZT element spacing between layers, bond materials, joining layer thickness). The results of the present analysis will also be compared to experimental data being collected on prototype layered 1‐3 composite arrays.

Three‐dimensional nonlinear dynamic finite‐element analysis (FEA) is utilized herein in order to examine the coupled structural, acoustic, and piezoelectric noise propagation physics within a high‐frequency sonar array for a supercavitating underwater research vehicle. Specifically, steady‐state dynamic simulations of the sonar array’s coupled performance are carried out that model both (a) the acoustic radiation field resulting from electrically actuated ceramic array elements, and (b) the ceramic array element electrical response due to incident structure‐borne excitation; fluid‐borne excitation is being examined presently and may also be presented if completed in time. This paper focuses primarily on the interesting issues related to accurately modeling such a complex coupled system. For example, the frequency‐dependent properties of a nonlinear elastomer absorption material within the array must be carefully characterized at very high frequencies in order to gain accurate results. Additionally, determining electrical properties of the piezoelectric ceramic material can pose a significant problem. Finally, performing a three‐dimensional simulation at high frequencies with coupled physics analyses is not a trivial undertaking.. Laboratory shaker experiments performed in order to validate the modeling will also be presented.

The simulation of propagation of structureborne vibratory and acoustic energy within a supercavitating high‐speed underwater vehicle is studied herein. The supercavitating vehicle is rocket propelled and rides entirely within a cavity in order to reduce drag and allow for higher underwater speeds. A ventilation system exists within the vehicle to ensure the cavity completely encloses the vehicle. With the exception of isolated control surfaces, the only wetted portion of the vehicle is the cavitating sonar array at the vehicle nose. This paper focuses on the use of statistical energy analysis (SEA) to quantify and parametrize the high‐frequency transmission of vibro‐acoustic energy within the complex, multiply connected marine vehicle, as well as including contributions from the reverberant cavity and seawater acoustic paths. Additionally, an examination of the many potential noise sources is made, including a discussion on handling the effects of surface backscattering and volume reverberation within an SEA framework. Numerical case studies are performed to exercise the model in order to predict the effects of specific design modifications such as structural design variations, isolation mounting scenarios, etc.