David Newland

Wavelet Analysis of Vibration: Part 1—Theory

The purpose of this paper is to introduce and review the theory of orthogonal wavelets and their application to signal analysis. It includes the theory of dilation wavelets, which have been developed over a period of about ten years, and of harmonic wavelets which have been proposed recently by the author

Harmonic Wavelet Analysis

A new harmonic wavelet is suggested. Unlike wavelets generated by discrete dilation equations, whose shape cannot be expressed in functional form, harmonic wavelets have the simple structure ω(x) = {exp(i4πx) - exp(i2πx)}/i2πx. This function ω(x) is concentrated locally around x = 0, and is orthogonal to its own unit translations and octave dilations. Its frequency spectrum is confined exactly to an octave band so that it is compact in the frequency domain (rather than in the x domain). An efficient implementation of a discrete transform using this wavelet is based on the fast Fourier transform (FFT). Fourier coefficients are processed in octave bands to generate wavelet coefficients by an orthogonal transformation which is implemented by the FFT. The same process works backwards for the inverse transform.

Ridge and Phase Identification in the Frequency Analysis of Transient Signals by Harmonic Wavelets

It is difficult to generate high-definition time-frequency maps for rapidly changing transient signals. New details of the theory of harmonic wavelet analysis are described which provide the basis for computational algorithms designed to improve map definition. Features of these algorithms include the use of ridge identification and phase gradient as diagnostic features.

Harmonic and Musical Wavelets

The concept of a harmonic wavelet is generalized to describe a family of mixed wavelets with the structure wm, n(x) = {exp (in2πx) – exp (im2πx)}/i(n – m) 2πx. It is shown that this family provides a complete set of orthogonal basis functions for signal analysis. By choosing the (real) numbers m and n (not necessarily integers) appropriately, wavelets whose frequency content ascends according to the musical scale can be generated. These musical wavelets provide greater frequency discrimination than is possible with harmonic wavelets whose frequency interval is always an octave. An example of the wavelet analysis of music illustrates possible applications.

Efficient computer simulation of moving granular particles

Abstract A two-dimensional model for computing contacts and motions of granular particles of different shapes, sizes and material properties is presented. The primary aim of this model is to achieve a high degree of computational efficiency, to allow simulations to be performed very rapidly on a modest sequential machine. The important features of the model are (i) a polar representation of particle shape, (ii) a simple algorithm for contact detection, (iii) a binary collision model using momentum exchange as the describing feature, (iv) energetic coefficients of restitution selected pseudo-randomly, (v) a Coulomb friction approximation to describe slip at impact, and (vi) an optimized move-update algorithm. Results in satisfactory agreement with analytical solutions and existing, less efficient computer simulations are presented.

Nonlinear Aspects of the Performance of Centrifugal Pendulum Vibration Absorbers

Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1963.

Calculation of power flow between coupled oscillators

Abstract A perturbation method is developed for calculating the statistics of the energy transfer process between weakly coupled oscillators. The method is used to calculate first-order approximations for (a) the mean value, and (b) the spectral density of the power flow between two stiffness coupled oscillators under white noise random excitation. The result for mean power flow is identical with that obtained by Lyon and Maidanik (1) using an ad hoc method of linearization. The present method is, however, more general in the sense that it allows more complicated statistics to be evaluated (for instance, the spectrum of the energy transmission process), and applies to cases with narrow-band as well as broad-band excitation. The present method also allows more accurate results to be obtained by calculating second and higher order approximations. Among other possible applications, the method looks promising as an additional tool for the study of noise transmission in structures.

Harmonic wavelets in vibrations and acoustics

Four practical examples from mechanical engineering illustrate how wavelet theory has improved procedures for the spectral analysis of transient signals. New wavelet–based algorithms generate better time–frequency maps which trace how the spectral content of a signal changes with time. The methods are applicable to multi–channel data and time–varying cross–spectra can be computed efficiently.

Isolation of Buildings from Ground Vibration: A Review of Recent Progress

Many buildings near railways are mounted on rubber springs to isolate them from ground vibration. This paper reviews the theory of resiliently mounted buildings and discusses recent calculations of the effects of (a) different damping models and (b) piled foundations. The paper also describes site measurements in London and laboratory tests in Cambridge which are being made to support new analytical work.

Power Flow between a Class of Coupled Oscillators

The equation of mean power flow between two groups of randomly excited oscillators is derived from first principles. Subject to the coupling satisfying certain requirements, it is shown that a new parameter—the average natural frequency shift of the oscillators owing to the coupling—determines the power flow between the two groups. Power flow is directly proportional to the natural frequency shifts and to the oscillator densities (modal densities) in each group. It is suggested that this formulation has advantages over the conventional “coupling‐loss‐factor” equation of the statistical energy approach to noise‐transmission problems.