J. Gregory McDaniel

Power flow to a cylindrical shell with an attached structure

This paper presents an analytical framework for understanding and controlling the physical mechanisms which govern power flow to infinitely long cylindrical shells from applied point forces. It has been observed by others that the power flow to an empty shell peaks dramatically when the excitation frequency is near the cutoff frequency of a wave in the shell. In this paper, these observations are explained and generalized by a new analytical expression for power flow based on classic analyses of a shell’s response to an applied point force. This expression quantifies the partition of power among propagating waves excited by an applied force. Furthermore, the expression confirms that power flow increases dramatically as a propagating wave is excited in the vicinity of its cutoff frequency. In the context of this understanding, the attachment of a passive structure to the shell is explored as a means of controlling power flow. The nonlinear problem of designing a structure which satisfies practical constraints and minimizes power flow is formulated in such a way as to be solvable by a variety of optimization techniques. The formulation, which can be extended to other structures, is based on an expression for power flow in which the impedance of the attached structure acts in mechanical parallel with the shell’s impedance at the points of attachment. An example indicates that a significant reduction in power flow can be achieved by the attachment of a passive structure whose parameters have been optimized by a genetic algorithm.

Computation of complex wave numbers and amplitudes on vibrating structures from response data

This work demonstrates a robust approach for computing complex wave numbers and amplitudes of waves in structures from experimental or numerical data. The approach postulates a wave field, which is a linear combination of damped waves. The number of waves and initial estimates of the complex wave numbers are based on any a priori physical knowledge and on the results of standard analyses of the data, such as wave‐number transforms and spatial attenuation rates. Given these initial estimates of wave numbers, associated wave amplitudes are computed by linear least‐squares inversion to data. Optimization algorithms improve these estimates by searching for complex wave numbers and amplitudes that minimize the normalized mean‐square error between the data and the wave field. This approach is often more robust than Prony‐based techniques, which require equally spaced data and are more sensitive to noise or unmodeled components. The approach is demonstrated on experimental vibration measurements of a damped box ...

Toward a design methodology for equipment emulators in the shock testing of large structures

In a variety of situations, an undesired shock excitation is applied to a master structure which supports shock‐sensitive equipment. Often, one wishes to design and test a master structure which transmits the least amount of shock energy to the attached equipment. In scaled testing of new designs, a major task is to design and construct ‘‘equipment emulators,’’ inexpensive mechanical systems which approximately mimic the dynamic behavior of the actual full‐scale equipment as seen by the master structure. This presentation will present new methodologies for designing equipment emulators, assessing their fidelity, and interpreting test data taken in the presence of imperfect emulators. Starting with frequency‐domain impedance descriptions of the master structure and actual equipment at the attachment points, this work develops sensitivity metrics which directly relate the fidelity of the emulator to its structural complexity. These ideas may provide a path by which experimentalists can efficiently arrive at...

Spatial scales on fluid‐loaded plates and shells

This paper attempts to quantify in a general way the spatial scales that occur on fluid‐loaded plates and shells for the purpose of assessing various modeling techniques. Modelers using the SARA finite‐element code typically follow a ‘‘quarter‐wavelength rule,’’ which states that the size of a quadratic element should be less than a quarter of the minimum wavelength in the problem. The minimum wavelength for fluid‐loaded plates and shells is often the flexural wavelength. Questions naturally arise regarding the accuracy of this rule near discontinuities. In this paper, a straightforward theoretical justification for the quarter‐wavelength rule is presented in terms of a Taylor series expansion of the wave field. This justification is extended to the local evanescent fields generated near discontinuities. The complex wave numbers describing these fields, as well as SARA finite‐element data for some canonical problems, are examined to determine the expected accuracy of a given discretized model. The fundame...

Applications of the causality condition to acoustic scattering

The causality condition states that the response of a passive system cannot precede the cause. Under certain conditions, the causality condition leads to a Hilbert transform relation between the magnitude and phase of the complex Fourier transform of a system’s response. This relation has profound implications for those attempting to design passive structures whose desired scattering characteristics are expressed in the frequency domain. Unless the causality condition is satisfied in the frequency domain, the structure is not physically realizable. In this presentation, some novel applications of this relation are developed for a one‐dimensional fluid‐loaded structure which scatters incident sound in the backward and forward directions. In each application the reflection and transmission coefficients, which are the complex Fourier transforms of the reflected and transmitted pressures due to an impulsive incident pressure wave, are subject to the causality condition. The Weiner–Lee transform, which is deri...

Structural wave reflection coefficients of cylindrical shell terminations: Numerical extraction and reciprocity constraints

A fluid-loaded cylindrical shell guides vibratory energy along its axial direction in the form of a finite set of distinct traveling wave types. On a finite shell, the energy incident upon a termination is redirected into reflected waves of all types and into sound radiated into the farfield. (The total field near the termination also includes various evanescent components.) Reflection coefficients relate the amplitudes of individual reflected wave types to the amplitudes of individual incident wave types. In this paper, values for the reflection coefficients of several terminations have been extracted from results of finite element analysis for the forced response of a finite structure excited by a variety of different sources. The numerical results exhibit good agreement with the analytical constraints consequent to the principle of reciprocity. The constraints are developed here by an analysis adaptable to other multimodal waveguides by appropriate modification of detail.

Wave propagation on coated cylindrical shells

This presentation describes methods of using an approximate elasticity formulation to compute natural wave numbers of waves in coated cylindrical shells. The efficient computation of these wave numbers is critical to coating design. A previously developed displacement‐based variational formulation for coated shells [J. G. McDaniel and J. H. Ginsberg, J. Appl. Mech. 60, 463–469 (1993)] retains the accuracy of analytical formulations, but avoids the computational burdens associated with special functions of complex argument. This formulation, which was previously applied to two‐dimensional problems, is extended to address wave propagation in the axial coordinate for each circumferential harmonic. Because the formulation is energy based, one has ready access to the strain energy distributions of each wave. For a specified real axial wave number, one obtains an easily solvable generalized eigenvalue problem for complex natural frequency. For a specified real frequency, the search for complex axial wave number...

Comments on ‘‘Sound radiation from finite cylindrical coated shells, by means of asymptotic expansion of three‐dimensional equations for coating’’ [J. Acoust. Soc. Am. 96, 277–286 (1994)]

The idea of expanding elastic variables in powers of a thickness coordinate is not new, having been employed by Bassett as early as 1890 [Philos. Trans. R. Soc. Ser. A 181, 433–480]. A variety of works over the past decade, which were heavily influenced by Mindlin [‘‘An Introduction to the Mathematical Theory of Vibrations of Elastic Plates,’’ A Monograph Prepared for U.S. Army Signal Corps Engineering Laboratories, Fort Monmouth, NJ (1955)], have established that such expansions should introduce readily identifiable approximations. McDaniel and Ginsberg [J. Acoust. Soc. Am. 90, 2341 (1991) and J. Appl. Mech. 60, 152–157 (1993)] successfully addressed this idea with displacement expansions used in conjunction with Hamilton’s principle. The resulting formulation avoids many of the assumptions and complications that appear in the recent asymptotic analysis by Laulagnet and Guyader [J. Acoust. Soc. Am. 96, 277–286 (1994)], including assumptions on thickness relative to radius and to characteristic wavelength...

Reflection of axisymmetric waves from an arbitrary termination of a fluid‐loaded semi‐infinite cylindrical shell

This work proposes an approximate theory for the reflection of axisymmetric waves on a semi‐infinite fluid‐loaded shell from an arbitrary termination. The reflected and incident waves are described by wave numbers and wave shapes derived from the standard thin‐shell equations for an infinite shell with fluid loading. The termination is characterized by an admittance matrix that relates stress resultants within the shell wall to axial, radial, and rotational velocities of the midsurface. The admittance matrix is determined for arbitrary terminations by finite element experiments on a fluid‐loaded finite shell. An example focusing on variations in the axial admittance shows the effect of added mass at the termination. Results include the reflection and coupling between surface, longitudinal, and evanescent waves. [Work supported by ONR.]

Mid‐frequency endcap reflection and radiation coefficient extraction from FEM data

The response of a simple cylindrical shell terminated by rigid endcaps to various axisymmetric mechanical excitations is determined using the SARA 2‐D finite element code. By assuming that the response of the shell is primarily composed of structural waves, which satisfy the fluid‐loaded shell equations, the structural wave reflection matrix of the endcap is determined through an over‐constrained system of equations. Results for the frequency range, 2<k0a<6, show that for this type of endcap, the reflection process may be parametrized with a smooth function in frequency that is dependent on a small number of variables. Using a similar approach, the far‐field radiation patterns of the endcap due to each incident structural wave type are also determined and parametrized. This work suggests that at mid frequencies and away from trace‐matched angles, many of the essential elements of the axisymmetric elastic structural response of simple shells may be modeled using a one‐dimensional ray picture where all the ...