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The interaction between vibrations in solids and fluids is gaining emphasis in many areas of engineering design. Computational technology is a critical asset in determining the severity, nature, and quality of structural-acoustic vibrations, and the recent advances in the field have made this class of analysis much more common. This talk will discuss briefly the history of computational analysis in structural acoustics, the wide scope of applications, and describe some trends that can be expected to affect a variety of engineering enterprises in the near future.
The term "structural-acoustics" is subject to various interpretations. The physical phenomenon involves waves of various types – compression, shear, bending, and complex combinations – propagating or standing in a coupled mechanical system involving fluids and solid media. The complexity of the subject is immediately evident if one considers the vibrations of an aircraft or vehicle, composed of many different materials, containing and immersed in fluids of various densities, transferring energy and momentum continuously. This continuous transfer may be intentional – an audio device, for example – or undesirable, as in the noise from an aircraft engine intruding into the passenger compartment.
Products with acoustic performance as a primary design requirement, such as sonar transducers and hearing aids, are typically subjected to rigorous structural-acoustic analysis as a matter of course. These applications created the initial impetus for computational acoustic analysis, of course, and it should be no surprise that in these fields the analytical methodologies are well advanced, highly varied, and well accepted by engineers. To some degree, the criticality of acoustic performance has driven innovation and acceptance of new methods in this area, however, the early adoption of computational technology has also led to a broad swathe of entrenched tools, which may need to be displaced before innovation in computational acoustics occurs.
Increasingly, automobiles, consumer products, and aircraft are judged in the marketplace by their acoustic qualities. Automobile technology has advanced so significantly that customer perception of ride comfort and the particular sound the driver expects from a specific brand have become critical to sales. A vehicle with excellent performance and quality but which sounds harsh, overly loud, or inconsistent with the characteristic note of the brand may simply be unacceptable to the end-user. Aircraft, as well, must be designed with acoustic emissions in mind although, in this case, overall levels inside and out are generally more important than sound quality.
Moreover, exterior noise levels for aircraft, particularly on takeoff and landing, are strictly regulated. The commercial success of an aircraft design may be severely limited by noise, as was seen with the European Concord supersonic transport.
In many other systems, structural-acoustic vibration can cause severe degradation in performance, or even loss of function. A recently fielded warship, for example, failed to meet its design speed because of extreme global vibrations not predicted by conventional design methods. The vibrations in the ship in-water, involving transfer of momentum between the hull and the fluid, were quite different than the dry-ship modes; failure to predict their effects resulted in significant delay and cost. A similar phenomenon plagued the battleship USS North Carolina, whose keel was laid in 1937. Seventy years hence, ship designers are expected to avail themselves of computational technology rather than risk costly refits.
As mentioned above, a fairly wide range of computational methods have been applied to structural acoustics, and innovative methods continue to be developed. Yet, as in so many other areas of engineering technology, the finite element method has emerged as the premiere technology, due to its versatility, efficiency, and the facility by which complex analyses can be executed by engineers reliably. However, several factors impeded the progress of FEA in structural acoustics, and challenges remain which inhibit its wider adoption in this field.
Structural acoustics analyses nearly always remain in the linear regime, which is to say that the response of a system is doubled if the loads are. Consequently, it is tempting to believe that these problems are not challenging, or at least less so than nonlinear phenomena. However, the demands for accuracy, the length scales, unknown material properties, exterior acoustics, and latent nonlinearities undercut this facile conclusion.
There is a legitimate expectation that linear analysis should match experimental or closed-form solutions with very low errors. Achieving this level of performance in computational structural acoustics can be done, and is on a regular basis, yet analysts working in this field understand that the bar is set fairly high.
Structural acoustics involves the propagation of waves, and the wavelengths dictate a length scale. Any finite element mesh constitutes a low-pass filter, with the pass band proportional to the size of the finite elements. Therefore, the intuition we develop as engineers, to create finite element meshes with decreasing degrees of refinement away from the areas of greatest interest, fails. Meshes need to have uniformly high levels of refinement to preserve accuracy, establishing a floor on the minimum element size, and the mesh may need even higher refinement in critical areas. Consequently, finite element analysis of structural acoustic phenomena most often involves very large models; indeed, overcoming this limitation has been an area of intensive activity and innovation.
When damping is low, structural acoustic systems respond just like all linear dynamic systems, dominated by the nearby resonant frequencies in the system. All real systems at frequencies of interest, however, exhibit energy and momentum losses as waves propagate. Reliably quantifying these effects in modern structural systems is extremely challenging, as is even measuring the properties once appropriate material models are identified.
The finite element method does not naturally handle the coupling of a structure to a large exterior region of fluid. For example, when a submarine, automobile, or loudspeaker transmits wave energy into the external fluid, the waves generated in the fluid can be thought of as travelling infinitely far before they return. This effect is hard to manage in a finite element mesh of finite size. In fact, accurate and efficient finite element computations under these conditions are a fairly recent development, and the difficulty inherent in exterior problems was a major barrier to acceptance of FEA for structural acoustics.
While structural acoustic problems are usually linear in terms of response, realistic systems exhibit nonlinear dependence on frequency of excitation and boundary conditions. A lightly damped system may respond over ranges of orders of magnitude, depending on the proximity of the excitation frequency(s) to the system resonances. Moreover, small changes within manufacturing tolerances can result in significant changes in system response.
Computational analysis of structural acoustics no longer presents insurmountable problems in engineering practice. Reliable technology is available in a variety of commercial codes, and a broad range of laboratory and research codes. Standard practice has emerged, centred on the finite element method. Structures and acoustic volumes are meshed, with due consideration to the wavelengths of interest, and modal analysis is performed on the structure and fluids separately. These modes are used to create a reduced-order model of the coupled system, from which damped, transient or steady state forced response can be quantified. This approach, standard in the automotive industry and many others, dates to the sixties and has proven to be quite robust.
Challenges emerge, however, for which this approach is inefficient or inaccurate. When the fluid and the structure couple strongly, for example with ships in water, using the modes of the decoupled ship and fluid may not work very well. When frequencies are "high" (approaching the available limit for the computers at hand), the cost of computing and using the needed modes may be overwhelming. When exterior effects are prominent (submarines, ultrasound), modal approaches may also not be optimal. Finally, the analyst must quantify the quantities of interest to the engineering manager or project leader, in the presence of uncertainties of geometry and damping, and with a range of engineering changes of materials, subsystems, and geometries.
The engineering community is responding, and these challenges define the trends we observe in computational structural acoustics. This talk will discuss some of these new technologies in more detail. Finite element technology at the level of formulation is addressing exterior problems, high frequencies, and uncertainties. Solution technology also improves rapidly – particularly in the computation of modes, reduced-order models, and transient effects. Of equal importance, acoustic physicists and engineers increasingly accept the finite element method as the preferred approach to structural acoustics problems. Finally, commercial software technology has made such progress in streamlining FEA interfaces that structural acoustics, formerly regarded as something of an arcane specialty, has emerged onto the desktop of almost any competent finite element analyst.
Matthew Ladzinski, NAFEMS North America
Dr. Jeffrey Cipolla, Weidlinger Associates, Inc.
Dr. Jeffrey Cipolla, Weidlinger Associates, Inc.
Dr. Cipolla has spent the last sixteen years developing computer codes and performing calculations for the transient and time-harmonic dynamic analyses of complex, coupled structural systems, such as ships, automobiles, aircraft, and hardened structures. Dr. Cipolla was the principal developer of the Abaqus Acoustics and Undex software. This general-purpose finite element code was extended to analyze structures and the acoustic wave propagation effects through the surrounding media under his supervision. He led research in iterative solution methods for non-Hermitian coupled fluid-solid forced-response and in innovative finite elements for the Office of Naval Research. He has also led the development and validation of finite element software enhancements for the analysis of rolling tires for Yokohama Rubber Corporation. Dr. Cipolla led and managed the development of Undex software for the QinetiQ corporation. He led the developments in heat transfer and in some other proof-of-concept research for Dassault Systemes Simulia Corporation.
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