Inherent Dissipation Research Articles

Vibration damping of large structures induced by attached small resonant structures

It is well known that the observed vibratory behavior of large and complicated structures usually indicates much more damping than can be accounted for by the inherent dissipation in the structural material. Several investigators have pointed out that greatly increased damping may result from vibratory power dissipated by the numerous small resonant substructures usually attached to the large main structure; C. Soize called them the ‘‘structural fuzzy’’ [J. Acoust. Soc. Am. 92, 2365 (A) (1992)]. This paper presents a simplified procedure for estimating the effect of these substructures when they have many resonances at frequencies near the excitation frequency. In this case, the increased damping of the large structure depends mainly on the total effective mass of all the substructures resonating within a frequency band (say a half-octave) centered at the excitation frequency, and is relatively independent of the specific amount of dissipation in the individual substructures. The effect of the substructures on the frequency response and vibration pattern of the main structure can also be accounted for in simple fashion. The influence of nonuniform spatial distributions of the attached substrates on the estimates is also discussed in terms of specific examples. [Work supported by ONR.]

Assessment of total variation diminishing schemes in compressible mixing flow computations

Numerical simulations of temporally developing mixing layers using high-resolution total variation diminishing (TVD) schemes have been carried out to investigate the effects of grid resolution and inherent scheme dissipation on the solution quality. Owing to the sensitivity of the turbulence results to grid resolution, mixing flow computations generally require high grid density to resolve the shear-layer dynamics and to interpret the mean and turbulent flowfield interactions. Various limiters were tested in examining the numerical dissipation effect for which essentially nonoscillatory (ENO) solution is taken as a benchmark basis. The computations performed for scheme evaluation covered a broad spectrum including subsonic, transonic, and supersonic convective Mach numbers. Among the schemes considered, the performance of a minmod and van Leer limiters comply more consistently with the ENO results for a wide range of convective Mach numbers, whereas the superbee limiter, being the test TVD scheme for subsonic and low transonic Mach number flow, suffers from overcompression, which may lead to nonphysical solutions at high supersonic convective Mach numbers. The result obtained by each TVD scheme is sensitive to the design of the limiter. Dissipation introduced by the limiting procedure should be kept as minimal as possible, but a nonsmooth minimization should be avoided, because it may result in nonphysical overcompression, particularly for high convective Mach number flows.

Artificial dissipation models for the Euler equations

Various artificial dissipation models that are used with central difference algorithms for the Euler equations are analyzed for their effect on accuracy, stability, and convergence rates. In particular, linear and nonlinear models are investigated using an implicit approximate factorization code (ARC2D) for transonic airfoils. Fully implicit application of the dissipation models is shown to improve robustness and convergence rates. The treatment of dissipation models at boundaries will be examined. It will be shown that accurate, error free solutions with sharp shocks can be obtained using a central difference algorithm coupled with an appropriate nonlinear artificial dissipation model. I. Introduction T HE solution of the Euler equations using numerical techniques requires the use of either a differencing method with inherent dissipation or the addition of dissipation terms to a nondissipative scheme. This is because the Euler equations do not provide any natural dissipation mechanism (such as viscosity in the Navier-Stokes equations) that would eliminate high frequencies which are caused by nonlinearitie s and especially shocks. A variety of numerical algorithms and computer codes for the Euler equations have been developed. Methods such as MacCormack's1 explicit

Design of electric wave filters with the aid of the electrolytic tank

The analogue representation of the properties (in terms of complex frequency λ) of image-parameter transfer functions of the Zobel type by current-flow in an electrolytic tank provides, in the first place, a convenient means of designing such filters, and it has the important consequence that the properties of these current-flow representations are found to lead to a process for the solution of the approximation problem in the insertion-loss theory of filter design. The paper is in two parts, of which Part 1 is devoted to the representation of image-parameter transfer functions by the electrolytic tank. The electrolytic tank itself is first considered to be of the double-layer form described in an earlier paper;2 for the accurate representation of functions of the filtering type, however, it is found more appropriate to work in a transformed version of the λ-plane in which the entire plane is represented in a finite rectangle—the electrolytic tank is then of particularly simple construction. In Part 2 of the paper, the use of the electrolytic tank as an aid to filter design on an insertion-loss basis is described. A transformation is developed, by means of which the approximation problem can be solved for a low-pass-filter specification of insertion loss, the poles and zeros of the insertion modulus function of the filter being accurately determined by simple measurements on the electrolytic tank. The transformation itself follows from the properties of image-parameter functions considered in Part 1. Detailed design procedures are given, including provision for the effects of inherent dissipation in the reactance elements of the filter. It is also found possible to extend the method of design to a general, unsymmetrical band-pass filter, and to apply the basic principles to certain root-finding operations involved in Darlington's method of network realization. Detailed examples and experimental results are given throughout the paper.