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Published Articles

The Volume 18, No 2, June 2013

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Forced Response Approach of a Parametric Vibration

Dishan Huang, Chenchen Fu


In this paper, forecast modelling based on modulation feedback is used to investigate the forced response of parametric vibration with a damper. The system is excited by both the periodic coefficient and external force terms, which have different periods. In this study, the forced response is expressed as a linear combination of harmonic components. By applying harmonic balance, the parametric equation is converted into a set of infinite-order linear algebraic equations. Then, by taking the limit to infinity, all coefficients of the harmonic components in the forced response are fully expanded into a series. The advantages of the presented approach are (1) the forced response expressed as a trigonometric series is easier to apply in practice and (2) all coefficients of the harmonic components can be determined by numerical computation. The accuracy of the proposed approach has been verified by comparing resulting phase diagram trajectories with those obtained by the standard Runge-Kutta method. The results show that the presented approach is suitable for the forced response approach and the nonlinear characterization of parametric vibration.

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Gear Fault Diagnosis using Bispectrum Analysis of ANC based Adaptive Filtered Sound and Vibration Signal

Dibya Prakash Jena, S. N. Panigrahi


Fault diagnosis using acoustical and vibration signal processing has received strong attention from many researchers over the last two decades. In the present work, the experiment has been carried out with a customized gear mesh test setup in which the defects have been introduced in the driver gear. %The corresponding acoustic and vibration signals have been captured at different defect conditions such as defect in one tooth and defects in two teeth. Classical statistical analysis including higher-order statistics, namely bispectrum analysis, has been incorporated to detect the defects. However, in order to improve the signal-to-noise ratio of the captured signals for accurate defect detection, an adaptive filtering has been proposed. Active noise cancellation (ANC) has been applied on the acoustical and vibration signals as a denoising filter. The least mean square based ANC technique has been implemented considering the signals from healthy gear meshing as the background noise. The focus of this experimental research is to evaluate the appropriateness of the ANC technique as a denoising tool and the subsequent bispectrum analysis for identifying the defects. The performance of the ANC filtering was evaluated with most widely accepted standard filters. A synthetic signal, close in nature to the actual signal, has been investigated to ascertain the adequacy.

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Recent Advances in Muffler Acoustics

M. L. Munjal


Exhaust noise in engines has always been a major source of automotive noise. Challenges for muffler design have been constraints on size, back pressure, and, of course, the cost. Designing for sufficient insertion loss at the engine firing frequency and the first few harmonics has been the biggest challenge. Most advances in the design of efficient mufflers have resulted from linear plane wave theory, making use of the transfer matrix method. This review paper deals with evaluating approximate source characteristics required for prediction of the unmuffled intake and exhaust noise, making use of the electroacoustical analogies. In the last few years, significant advances have been made in the analysis of variable area perforated ducts, transverse plane wave analysis of short elliptical as well as circular chambers, double-tuned expansion chambers and concentric tube resonators, catalytic converters, diesel particulate filters, air cleaners, etc. The development of long strand fibrous materials that can be used in hot exhaust systems without binders has led to the use of combination mufflers in exhaust systems. Breakthroughs have been achieved in the prediction and control of breakout noise from the elliptical and circular muffler shell as well as the end plates of typical mufflers. Diesel particulate filters and inlet air cleaners have also been modeled acoustically. Some of these recent advances are the subject of this review paper.

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A Dynamic Model of a Reinforced Thin Plate With Ribs of Finite Width

Jaclyn E. Sylvia, Andrew J. Hull


This paper derives an analytical model of a thin plate of infinite extent stiffened by ribs that have a finite width. The governing model of the plate is the one-dimensional flexural wave equation, and the ribs were modelled as translational springs. The plate was excited by an external load that is harmonic in time and space. An orthogonalization procedure was developed, and the resulting system equations are an infinite set of algebraic equations containing a diagonal matrix that represents the plate dynamics and a full matrix that contains permutations of the Fourier coefficients of the Heaviside step function that represent the rib forces. This matrix equation is truncated and inverted and yields a solution of the plate displacements. An example problem is formulated, and the resulting displacement field is compared to a solution generated using finite element analysis for validation of the solution method. The system stop- and pass-band behaviour as a function of rib width is illustrated. It is shown that an increase in the width of the ribs results in greater stop-band behaviour of the system.

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A Simplified Formula for Calculating the Acoustic Power Radiated by Planar Structures

Yu Du, Jun Zhang


Based on the wave number transform, the sound power radiated by a planar structure embedded in a baffle can be derived theoretically as a double integral within the range of supersonic wave numbers. Due to the specific form of the integrand, a singularity problem is encountered at the integration boundary that leads to difficulties in evaluating the sound power directly. This technical note discusses a mathematical method for simplifying the original formula to avoid this singularity problem by using a technique of substituting variables. Compared to its original counterpart, the simplified formula not only eliminates the singularity points but also converges much more rapidly when evaluating the double integrals numerically.

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