Jane L. Horner

Prediction of vibrational power transmission through bends and joints in beam-like structures

Abstract This paper is concerned with the prediction of vibrational power transmission through bends or joints in beam-like structures, impinged on by either flexural or longitudinal waves. Models have been developed which determine the wave type which carries most power in each section of the system. By establishing the wave type which predominantly causes power transmission it is then possible to apply the most suitable vibration control technique.

Prediction of vibrational power transmission through jointed beams

Abstract When attempting to control the vibration transmitted from a machine into and through the structure upon which it is mounted, it is desirable to be able to identify and quantify the vibration transmission paths in the structure. Knowledge of transmission path characteristics enables procedures to be carried out, for example, to reduce vibration levels at points remote from the source, perhaps with the objective of reducing unwanted radiation of sound. One method for obtaining transmission path information is to use the concept of vibrational power transmission. This paper is concerned with the prediction of vibrational power transmission through a system of jointed beams carrying longitudinal and flexural waves. Models have been developed which determine the wave type which carries most power in each section of the system. By establishing the wave type which predominantly causes power transmission it is then possible to apply the most suitable vibration control technique.

Approximations for the scattered field potential from higher mode transmission in rectangular apertures

This paper considers the wave fields that result when a plane wave impinges at an arbitrary angle on a rectangular aperture in a rigid, thick wall. A nondimensional form of a prior Fourier transform solution of this problem is derived, from which it is more easy to appreciate the relationship between the physical attributes of the aperture and incoming wave and the resultant acoustic fields. The scattered field from the aperture is examined in detail, in particular the modal contributions to the driving function for the amplitude of the velocity potential. Although the full scattered field contains both modal sum and modal coupling effects, it is shown that neglect of the modal coupling effects introduces minimal error to the solution in certain situations. An approximate analytical solution to the uncoupled analysis is then developed, which is accurate provided that the aperture is acoustically large, such that there are several cut-on modes within the aperture. The full nature of the scattered field can...

Higher mode sound transmission from a point source through a rectangular aperture

This paper considers the higher-order scattered and transmitted wave fields that result when an acoustic wave from a point source impinges at an arbitrary angle on a rectangular aperture in a rigid, thick wall. In this analysis, it is assumed that free field conditions exist on both sides of the aperture. Although the full scattered and transmitted pressure fields contain both modal sum and modal coupling effects, the modal coupling effects of the higher-order modes are ignored such that an approximate analytical solution to the uncoupled analysis can be utilized. Experiments have been undertaken to measure the sound pressure levels in the transmitted field that result when sound from a point source impinges on the opposite side of a rectangular aperture. Measurements were made with the source located at the required position to drive a particular in-aperture higher-order mode. The source was also located at positions that did not directly excite any in-aperture higher-order mode at a cut-on frequency. These results indicate that the approximate analysis developed here gives accurate solutions whether or not any mode of the aperture is driven at cut-on. Thus, the method can be used for any relative location of a source from a rectangular aperture of any dimensions.

Approximations for modal coupling in scattered fields from orifices

Previous investigations have used Hankel transforms to establish the velocity potentials of the wave fields resulting from arbitrary angle plane wave impingement on a circular orifice in a rigid, thick wall. The scattered field from the orifice is examined, in particular the modal contributions to the amplitude of its velocity potential. For each m,n mode the amplitude is dependent upon the amplitude of the in-orifice waves and a driving term unique to each m,n mode. In establishing the amplitudes of the in-orifice waves, the effects of modal coupling are also considered. In this work these two components of the scattered wave amplitude are investigated on a modal basis and approximations given for coupling effects. These approximations are then used to calculate the scattered field and the results compared with conventional solutions that use full modal coupling.

An approximate method for determining the maximum amplitude of higher-order duct modes

Previous investigations have used Hankel transforms to establish the amplitudes of the wave fields resulting from arbitrary angle impingement on a circular orifice in a baffle. Investigations have also been undertaken on the effects of model coupling between the higher modes in the orifice. In particular, these studies concentrated on establishing the contributions at the cut-on wave number for a particular mode. This work is extended to introduce a method of simply approximating the complex amplitude of the forward and backward waves in the duct at the cut-on wave number, based only on the modal wave number. The interest focuses on the cut-on wave number because the forcing functions for the various fields will be at a maximum at cut-on. This technique is established by observing the relationships between the peak values of the driving functions and the modal wave number. If simple approximations are established for the in-duct field, it is also possible to approximate the maximum amplitude of the scatte...

Acoustic performance of finite‐length apertures using finite‐element analysis

There is a wide range of published literature covering ducts of infinite or semi‐infinite length and to a lesser extent there are studies on apertures having restricted dimensions. The work presented in this paper is taken from recent research into the characterization of acoustic devices in finite‐length apertures, which may need to allow for a flow of fluid. Results of a finite‐element solution for a short duct between two half spaces are presented, along with a closed‐form solution [K. H. Jun and H. J. Eom, J. Acoust. Soc. Am. 98, 2324–2327 (1995)] as a validation of the finite‐element method. Further results of more complicated aperture geometry, which are not easily amenable to such forms of solution, have also been investigated and are presented.

Measurement of vibrational energy and point mobility of a beam subjected to moment excitation using a finite difference approximation

Abstract Moment excitation is often neglected in structural vibration analysis because of difficulties in measuring the applied moment and the resulting wave motion in the structure. Further, it is often assumed that moment-induced vibrational energy is significant only in the high frequency region. However, recent studies have shown that moment excitation should be included in vibrational analysis at all frequencies, when the source location is in close proximity to a structural discontinuity. In this article, a novel method is presented to measure the point mobility and resulting vibrational energy of a beam subjected to moment excitation. The proposed method utilizes a finite-difference approximation to calculate the rotational motion of the beam at the point of excitation. Moment excitation is induced by a specially designed impact rig which applies two equal and opposite forces on two moment arms that are perpendicularly attached to the beam. It is shown that, using the newly developed technique, the measured point mobility follows the trend of the equivalent theoretical structure. The technique also showed good agreement over a wide frequency range between the measured input energy and the measured transmitted flexural wave energy along the beam.

Modal scattering from orifices

When considering a sound wave traveling through a circular orifice in a rigid baffle, both the reflected and scattered field have to be established on the incident side of the orifice. Previous investigations have used Hankel transforms to establish the amplitudes of these two waves. This study concentrates on the coupling of the modes in the scattered and reflected fields, with the object of the investigation being to determine if a modal approach may be taken to describe the reflected sound fields from such an orifice. Results are shown in the form of the modal contributions to the integrand which must be used to obtain the scattered field.

Vibrational power transmission in asymmetric framework structures

When attempting to control the vibration transmitted from, say, a machine into and through the structure upon which it is mounted, it is desirable to be able to identify and quantify the vibration paths in the structure. Knowledge of transmission path characteristics enables procedures to be carried out, for example, to reduce vibration levels at points remote from the source, perhaps with the objective of reducing unwanted radiation of sound. One method for obtaining transmission path information is to use the concept of vibrational power transmission. Many machines are installed on frameworks constructed from beamlike members. By using the concept of vibrational power it is possible to compare the contributions from each wave type. Wave motion techniques are used to determine the expressions for vibrational power for each of the various wave types present. The results from the analysis show the amount of vibrational power carried by each wave type and the direction of propagation. Consideration is given...