Jerry H. Ginsberg

Complex power, reciprocity, and radiation modes for submerged bodies

This study of the surface interaction between a submerged body and the surrounding fluid begins by developing reciprocity relations between alternative pressure and normal velocity distributions on the wetted surface. A corollary of these principles is proof of the symmetry of the matrix representing the acoustic contribution to the structural impedance, even in situations where the acoustic relation between surface pressure and normal velocity is not symmetric. The reciprocity properties lead to two eigenvalue problems, whose solution yields velocity and pressure radiation modes, each of which decouples the complex surface acoustic power. The matrices required to obtain the eigensolutions are shown to arise in the ordinary course of modeling fluid–structure interaction. Further analysis reveals that the velocity and pressure modes occur in a one‐to‐one correspondence, with a relative phase angle that decreases monotonically as the radiated power increases relative to the reactive power. Using the radiati...

Asymmetric vibration of a heavily fluid‐loaded circular plate using variational principles

As an initial step in the extension of the surface variational principle (SVP) to an assumed modes analysis of vibratory displacement and surface pressure on submerged axisymmetric structures subjected to arbitrary nonsymmetric loading, the present study considers an arbitrary harmonic excitation of an elastic plate. Two configurations, in which the supporting baffle is a thin rigid disk or an infinite plane, are considered. Fourier series expansions of the azimuthal dependence of pressure and displacement are shown to be uncoupled, with each harmonic being governed by equations that are similar in form to those for the analogous axisymmetric problem. Recursion relations using coefficients developed in the course of solving the axisymmetric problem are shown to substantially expedite the evaluation of the additional azimuthal harmonics. Results for a force located at r=a/2 when ka=3.35, where a is the radius of the plate, are presented in terms of the radial variation associated with each harmonic, as wel...

Analysis using variational principles of the surface pressure and displacement along an axisymmetrically excited disk in a baffle

A discussion of the singularities that arise in a variational principle for the surface pressure resulting from a specified harmonic motion of an arbitrary surface leads to the observation that essentially the same formulation may be employed to study a thin disk in an annular baffle and a disk in an infinite baffle. This variational principle is implemented jointly with Hamilton’s principle for structural displacement to study the response of an axisymmetrically excited flexible disk (membrane or elastic plate) in a baffle. Surface pressure, as well as displacement, are represented in a series of assumed modal functions. The system equations reduce to a set of simultaneous equations for the complex amplitudes of the assumed modes, in which the inhomogeneous terms are the modal generalized forces, whereas the coefficients of the homogeneous terms arise from the isolated responses of the fluid and structural media, and from the fluid–structure coupling. The coefficients associated with surface pressure are...

Variational formulation of acoustic radiation from submerged spheroidal shells

The surface variational principle (SVP) governing acoustic interaction between a vibrating surface and a surrounding fluid is combined with the dynamic equations governing response of a shell of revolution subjected to axisymmetric harmonic excitation. Ritz series representations are used to represent the spatial dependence of the surface pressure and shell displacement components. Two formulations are presented, with the difference being whether an intermediate computation of the in‐vacuo modes is performed. The direct approach, in which the Ritz coefficients are determined directly from the coupled formulation, is used to validate the SVP approach for the case of a spherical shell, whose response is known analytically. For the case of a slender spheroidal shell, the direct approach is compared to the results obtained from the modal approach, in which a truncated set of in‐vacuo modes forms the basis functions representing displacement. The aspect ratio and shell properties for this evaluation are select...

Mode isolation: A new algorithm for modal parameter identification

Multiple degree of freedom (MDOF) algorithms are the dominant methods for extracting modal parameters from measured data. These methods are founded on the notion that because the response of a linear dynamic system is the sum of many modal contributions, the extraction technique must deal with all of the modal parameters in a simultaneous fashion. The Mode Isolation Algorithm (MIA) described here is a frequency domain formulation that takes an alternative viewpoint. It extracts the modal parameters of each mode in an iterative search, and then refines the estimation of each mode by isolating its effect from the other modal contributions. The first iteration estimates modes in a hierarchy of their dominance. As each mode is estimated, its contribution is subtracted from the data set, until all that remains is noise. The second and subsequent iterations subtract the current estimates for all other modes to identify the properties of the mode under consideration. The various operations are described in detail, and then illustrated using data from a four-degree-of-freedom system that was previously used to assess the Eigensystem Realization Algorithm (ERA) and Enhanced ERA. Eigenvalues and mode shapes are compared for each algorithm. Another example analyzes simulated data for a cantilever beam with three suspended one-degree-of-freedom subsystems, in which the parameters are adjusted to bring two natural frequencies into close proximity. The results suggest that MIA is more accurate, and more robust in the treatment of noisy data, than either ERA version, and that it is able to identify modes whose bandwidth is comparable to the difference of adjacent natural frequencies.

Modal properties and eigenvalue veering phenomena in the axisymmetric vibration of spheroidal shells

The axisymmetric free vibration properties of arbitrarily slender thin spheroidal shells are investigated by implementing the method of assumed modes in conjunction with energy functionals derived from classical linear bending theory. Loci depicting the dependence of the natural frequencies on aspect ratio are constructed for aspect ratios ranging from a sphere to a prolate spheroid whose length is seven times its diameter. At certain aspect ratios, loci associated with different eigensolutions come close, then veer away without intersecting. Modal properties, such as the number of nodes in the mode associated with increasing root number for the eigenvalue, are found to change irregularly when veering occurs. An analysis of the partitioning of strain energy between membrane and bending effects is performed in conjunction with an earlier general study of eigenvalue veering phenomena. The analysis demonstrates that veering results in mixing of membrane and bending effects, such that it no longer is meaningf...

Propagation of nonlinear acoustic waves induced by a vibrating cylinder. I. The two‐dimensional case

This study details the first successful uniformly valid expansion for a multidimensional nonlinear wave in a system described by curvilinear coordinates. The problem of interest is the steady‐state wave motion induced within an inviscid compressible fluid by an infinite circular cylinder executing a harmonic planar vibration in its nth circumferential mode. The solution is achieved by employing a regular perturbation series to obtain an outer expansion for the velocity potential. Then outer expansions for the pressure and the velocity components are derived by the method of renormalization. Finally, uniformly valid expansions for the response are determined by matching the outer solutions with the results of a linearized analysis, which represent the inner solutions. Examples considering the effect of the nondimensional parameters are treated by presenting pressure and velocity profiles, as well as nodal and antinodal lines of radial velocity. The range of validity for farfield approximations is discussed.

On Dowell's simplification for acoustic cavity-structure interaction and consistent alternatives.

A widely employed description of the acoustical response in a cavity whose walls are compliant, which was first proposed by Dowell and Voss [(1962). AIAA J. 1, 476-477], uses the modes of the corresponding cavity with rigid walls as basis functions for a series representation of the pressure. It yields a velocity field that is not compatible with the movement of the boundary, and the system equations do not satisfy the principle of reciprocity. The simplified formulation is compared to consistent solutions of the coupled field equations in the time and frequency domains. In addition, this paper introduces an extension of the Ritz series method to fluid-structure coupled systems that satisfies all continuity conditions by imposing constraint equations to enforce any such conditions that are not identically satisfied by the series. A slender waveguide terminated by an oscillator is analyzed by each method. The simplified formulation is found to be very accurate for light fluid loading, except for the pressure field at frequencies below the fundamental rigid-cavity resonance, whereas the Ritz series solution is found to be extremely accurate in all cases.

A Spectral Description of Inertial Effects in Fluid-Loaded Plates

The wavenumber-based formulation of the surface variational principle (SVP) describes the surface pressure and displacement as a comparatively small set of interacting waves. It enables one to pose questions of parametric sensitivity from a global perspective. The present paper is the first application of such an approach to the question of the level of detail to which a model must be constructed. It considers a two-dimensional problem of an elastic plate in an infinite baffle, with pinned boundary conditions. A study by Feit and Johnson (1991) demonstrated that the signal scattered by the plate is significantly altered by the presence of an attached mass, and that the distribution of mass as well as the total mass, is important. In order to explore these issues, a line mass attached to the plate is replaced in the SVP formulation by a continuous spatial distribution. The functional form of this distribution is described in a spectral manner using Fourier series, whose ascending orders represent successive stages in refinement of the scale to which a modeldescribes inertial effects. The excitation applied to the plate is taken as a concentrated line harmonic force. With the excitation held fixed, the influence of each spectral component of inertial distribution on the surface response and radiated power are assessed. Evaluations carried out for a range of frequencies shed light on how small scale inertial heterogeneities can influence macroscopic radiation features

A linear least-squares version of the algorithm of mode isolation for identifying modal properties. Part II: Application and assessment

The latest modifications of the algorithm of mode isolation (AMI) for identification of modal properties from frequency response data are tested with synthetic data derived from an analytical model of an elastic frame in which flexure and torsion are coupled. The parameters of this model are selected to cause the occurrence of localized modal patterns in two modes having close natural frequencies. The response data is contaminated with white noise at a level sufficient to almost mask the two close modes. Results for the real and imaginary part of the eigenvalues are tabulated. The analytical modal patterns of displacement and torsional rotation are depicted graphically, accompanied by the discrete values obtained from AMI. Excellent agreement is found to occur for each mode, other than one of the pair of close modes. The poorer quality of that mode’s identified properties is shown to be a consequence of its localized modal pattern. Results for the eigenvalues obtained by the rational fraction polynomial a...