K.P. Byrne

Analysis of a random repeated impact process

A simple random repeated impact process similar to the classical random walk process is analyzed. The process, which consists of a ball bouncing on a randomly vibrating surface, is analogous to loss-of-contact situations which can occur in linkages and vibrating tools. It also has relevance to rolling contact where the rolling element may separate from the surface and sustain repeated impacts. A coefficient of restitution is used to describe impact, and some important assumptions limit the analysis to values of this coefficient greater than 0°8. The Markov nature of the process is demonstrated by its one-step “memory”. It may be regarded as a discrete Markov process “imbedded” in continuous time. A difference equation governing the process is developed and analyzed for the case where the vibrating surface has a Gaussian distribution of velocities. With the one-step transition probability density function a linear weighting function is used to account for the weighting effect of the balls velocity on the distribution of table velocities at impact. The resulting integral equation is solved iteratively to yield the probability density function of ball velocities after impact. This information may then be used to predict the magnitudes of the impacts and the time between them.

Experimental investigation of a random repeated impact process

Abstract A simple random repeated impact process which has previously been investigated theoretically has now been investigated experimentally. The process, which consists of a ball bouncing on a randomly vibrating surface, is analogous to loss of contact situations which can occur in machinery and transportation systems where a hard rolling element separates from the rolling surface. Experimental data was acquired and processed by using a digital data acquisition system and associated software. The results were obtained in the form of histograms which could be directly compared with the predicted probability density functions. The agreement between the predicted behaviour and the measured results was excellent, and confirmed the dependence of the behaviour of the random process on the coefficient of restitution and the excitation level. Also, it was verified that the probability density function of table velocities at impact was distinct from the Gaussian density function of the excitation. Consequently the theoretical analysis previously developed has been validated with sufficient confidence to enable it to be applied to predictions of acoustic noise generated by the impact process.

Impact statistics for a simple random rattling system

Abstract A small mass (called the ball) constrained to move along a slot of fixed length in a large mass which is vibrating randomly in the direction of the slot is taken as a model of a randomly driven vibroimpact system. Numerical simulation analysis has been used to determine the statistics of the impacts between the rattling ball and the large randomly driven mass. These statistics include the probability densities of the magnitudes of the impacts and the times between impacts. The results presented provide fundamental information which can be used to estimate noise and wear in systems with clearances.

On the growth rate of bending induced edge cracks in panels excited by convected random pressure fields

Abstract Parts of an aircraft structure may be made to vibrate as a result of acoustic waves generated by various aircraft noise sources impinging on the structure. The stresses associated with this acoustically induced vibration may be sufficiently large to result in fatigue failure of portions of the structure. If acoustically induced fatigue cracks occur in the stiffened skin structure widely used in aircraft construction they may initiate in the skin panels near the stiffener attachment points. The initiation and subsequent propagation of these cracks at the panel edges is primarily due to the bending stresses arising from the out-of-plane vibration of the individual skin panels. The emphasis of the work described in this paper is on devising a method of predicting the growth rate of an edge crack in a panel which is excited by a convected random pressure field.

Effects of a porous jacket on sound radiated from a pipe

Conventional pipe laggings incorporate a porous jacket and an impervious outer cladding sheet. It has been observed during investigations of such pipe laggings that a simple porous jacket applied by itself to a pipe can actually increase the sound radiated. Reasons for this phenomenon are discussed. The effect of a rigid frame porous jacket around a pipe is examined theoretically for the breathing, bending, and ovalling modes of pipe vibration. The predicted insertion loss associated with the bending mode of pipe vibration is compared with the corresponding experimental result and some of the results of a parametric study are given.

On the growth rate of bending induced edge cracks in acoustically excited panels

Abstract Parts of an aircraft structure may be made to vibrate as a result of acoustic waves generated by various aircraft noise sources impinging on the structure. The stresses associated with this acoustically induced vibration may be sufficiently large to result in fatigue failure of portions of the structure. If acoustically induced fatigue cracks occur in the stiffened skin structures widely used in aircraft construction they may initiate in the skin panels near the stiffener attachment points. The initiation and subsequent propagation of these cracks at the panel edges is primarily due to the bending stresses arising from the out-of-plane vibration of the individual skin panels. The emphasis of the work described in this paper is on examining the growth rate of edge cracks in acoustically excited panels. A single panel with an edge crack is considered and this structural element is modelled as a flat plate clamped on three edges and part of the fourth. The crack is represented by the unclamped part of the fourth edge. Fracture mechanics principles are used to predict the crack growth rates associated with the first two modes of vibration of the edge cracked panel. The crack tip stress intensity factors associated with these panel modes are estimated by a technique based on finding the nominal bending stresses at the crack tips. The nominal bending stresses are in turn found from mode shapes determined by the Rayleigh Principle. The validity of the various assumptions is assessed by comparing the predicted crack growth rates with measured growth rates in panels representative of those used in aircraft construction.

Calculating the acoustical properties of fabric constructions

Architects are using fabric structures more frequently, not only because of the aesthetic appeal of such structures, but also because of their low initial and operational costs. A common application of fabric structures is in community buildings such as shopping malls and recreation centres. Fabric structures are also now used in industrial noise control applications. The constructions used in fabric structures incorporate one or more porous or impervious fabric sheets which may carry high in-plane tensions. Sometimes layers of porous materials may also be included. The acoustical performance of a fabric construction is usually adequately described by the diffuse field sound absorption cofficient, α (Δf), and the diffuse field sound reduction index, R(Δf), in frequency bands. A procedure for calculating these quantities is described. For this procedure, a fabric sheet is characterized by its mass per unit area, flexural stiffness, flexural loss factor, specific flow resistance, and the magnitudes and directions of the principal biaxial in-plane tensions. A porous layer is characterized by its thickness, flow resistivity, and position relative to the fabric sheets. The first part of the calculation procedure is concerned with finding the sound reflection and transmission coefficients for a plane wave of given frequency and direction. These calculations are based on the successive application of two types of formulae. The first type of formulae relate the surface or wave impedances across the fabric sheets and the porous layers or air spaces between them, and the second type relate the acoustic pressures across these elements. The second part of the calculation procedure involves integrating the frequency and direction dependent plane wave coefficients to give the diffuse field coefficients. The results of the application of the procedure to some representative situations are given and are compared with experimental results.

Acceleration noise generated by a random repeated impact process

Abstract Acceleration noise levels generated by a random repeated impact process have been predicted and compared with experimental measurements. The process consisted of a ball bouncing on a randomly vibrating surface, and is an idealized representation of random impact phenomena which can occur in machinery and transportation systems where a rolling element is in intermittent contact with the rolling surface. Predictions of the magnitudes of impacts and the times between them have been used in conjunction with established acoustic theory to estimate acceleration noise levels generated by the impacting ball. Measured sound pressure levels were in excellent agreement with the predicted levels.