Logic design for a self-contained diver navigation system

A major criterion in the design of a diver-held acoustic navigation system we are developing is that it must be very compact so that a diver can operate it easily and safely. With space at a premium, a logic circuit has been designed as a convenient way of measuring and storing the relative distances of the diver from up to four fixed transponders. A battery-powered microprocessor allows the diver's location to be computed. With one of the logic circuits the location can be found in two-dimensional space in the plane of three transponders; with two or three logic circuits the location can be found in three-dimensional space using four transponders. The circuit could be used in any other application which involves measuring the relative arrival times of acoustic pulses at a receiver.     

The measurement of the free field impulse response of microphones in a laboratory environment

A method is presented of measuring the free field frequency and impulse response of microphones by using a pulse technique in an ordinary laboratory environment. The pressure transient generated by exciting a loudspeaker with a narrow pulse is detected at some point in the loudspeaker's far field by a “reference” microphone whose response is assumed flat over the frequency range of interest. The microphone to be tested is then substituted in exactly the same position and its response to the transient measured. The outputs of the two microphones are accurately sampled and deconvolved by using a discrete Fourier transform technique to give the magnitude and phase parts of the “test” microphone's frequency response, and hence, via the discrete Fourier transform, its response to a delta function of pressure propagating in the free field. The computed impulse responses are presented and the accuracy of the method discussed.To illustrate the use of the method, the free field frequency response and free field correction curves of a one inch instrumentation microphone are measured. The method is then used to measure the pressure which occurs at the centre of the flat end-face of a long a cylinder when excited by an impulse of acoustic pressure propagating in the free field from various angles of incidence.     

An analog simulation study of the rocking response of a railroad freight vehicle

The steady state response of a single large capacity railroad freight vehicle is presented. The vehicle is described through an appropriate multi-degree of freedom non-linear mathematical model. The equations of motion of the system are derived by using Lagrange's procedure. The analog computer is employed for solving the non-linear differential equations of motion for obtaining the system's rocking response in the time domain. The vehicle steady state frequency response is derived from a sequence of time responses. By utilizing the frequency response plots a complete study of the system sensitivity to variation in the suspension parameters is carried out. The study shows that a possible practical solution to the freight car rocking problem can be achieved by using additional stabilizing devices consisting of friction and viscous dampers.     

Field-theoretic approach to the properties of the solid state

The techniques of quantum field theory are used to investigate the thermodynamic ion displacement correlation function—or Green's function of the phonon field—in a crystal and especially in a metal. The structure of thermodynamic Green's functions is outlined and the method for solving for them at finite temperature is fully discussed.The analytic structure of the phonon Green's function is then considered. This function is shown to be bounded and invertible everywhere off the real axis; a spectral form is derived for its inverse. The symmetries imposed by the point group of the crystal are then discussed.Assuming small ionic oscillations, we find the inverse of the phonon Green's function as a linear function of the electronic contribution to the dielectric response function of the metal. This dielectric function is shown to be simply related to the longitudinal part of the conductivity tensor that gives the response of the electrons to the effective electric field in the metal. The assumption of translational invariance then leads to an explicit expression for the phonon Green's function in terms of this conductivity.The deformations in the lattice induced by an arbitrarily time varying external force are calculated in terms of the retarded phonon Green's function. In the static long wavelength limit the phonon Green's function yields the macroscopic elastic constants of the crystal. Their relation to the conductivity is exhibited, and several elastic constants are estimated. We also see that the complete phonon spectrum and the lifetimes of the phonon states may be calculated from this Green's function. A relation between the long wavelength acoustic attenuation in metals and the de conductivity is derived, which is in good agreement with recent experiments. Furthermore, the ions in a metal are shown to have a high-frequency oscillation along with the electrons, at essentially the electron plasma frequency.     

Machinery noise predictions at the design stage using acoustic modelling

This paper presents a simple method of predicting the $\text{L}{}_{\mathrm{eq}}$ sound pressure levels in the operator's position for a machine, whilst the latter is still at the design stage. Simple acoustic models are used to estimate mean values for the transfer functions between vibrational response and sound pressure at a point. Given a force input to a structure (machine) and the subsequent vibration response, which can be calculated by finite element or other means, it provides a quick and easy method of accurately predicting overall rms sound levels. The method is applied and provided with data obtained from a full-scale industrial drop hammer. It is applicable to any machine which can be identified as a distribution of separate sound sources.     

The acoustic response in a liquid layer overlying a multi-layered viscoelastic half-space

A Green function is constructed that represents the steady-state acoustic response in a liquid layer overlying a Voigt viscoelastic multi-layered half-space. The effect of the solid half-space is characterized by a ratio related to the impedance of the sub-bottom. This ratio is evaluated by first developing a matrix recurrence relation for the potentials in the solid which, when repeatedly applied, directly relates the first viscoelastic layer's response to the last layer's. After boundary conditions are applied at the liquid-solid interface, the impedance ratio is obtained from another matrix relation. The result is in a form convenient for digital computer calculations. The response for the homogeneous single layer or half-space is shown to be consistent with existing results.     

Elastic properties of dilute palladium-hydrogen solid solutions

A thin-line pulse-echo technique has been used to measure the variation of the Young's modulus of super-pure palladium as a function of temperature and hydrogen concentration. The resulting measurements have been analyzed so as to yield approximate information relating to the change to be expected in the partial thermodynamic functions of the system due to the lattice relaxation at constant pressure.     

The thermalization length by the green function method

We study the concept of the thermalization lenght by the Green function method, using Sobolev's escape and destruction probabilities. A unique analytical procedure yields the usual numerical estimates for the noncoherent scattering case (with complete redistribution in frequency) as well as for the case of coherent scattering. The on-the-spot approximation is used to remove the assumption of an infinite geometry. Rybicki and Hummer's longest flight approximation is shown to yield the on-the-spot approximation. A generalization to the multilevel case is sketched.     

Use of lagrange multipliers with polynomial series for dynamic analysis of constrained plates part I: Polynomial series

A theory for prediction of the dynamic response of a constrained plate is presented here. The boundaries of the plate may be partially fixed, its dynamic loading is due to elastically mounted vibrating machines and its constraints include beam-like stiffeners. The theory yields the eigenvalues and modal shapes of the plate and stiffeners which comprise the system. The solution, given in Part I, is based on Galerkin's method combined with use of special polynomial series presented by Kantorovich and Krylov. These eigenvalues are used in Part II [1] for response analysis of the complete system and the eigenvalues of the complete system will be obtained by the application of Lagrange equations and multipliers. The various coefficients used in the process are presented in the Appendices to the work. Comparisons with published results show good agreement.     

A computer orientated calculation method of the Nernst-Einstein relation in the presence of an electric field

Manning's method of calculating the ratio of mobility and diffusion coefficient in ionic conductors, sensitive to the type of particle jumps, is analytic. This paper presents a computer orientated treatment in terms of an averaging procedure recently proposed.     

Evaluation of photometric spectral line profiles by digital computer methods

A computer method for the transformation of photographic spectra into the intensity scale has been derived and applied to the radial distribution of spectral line shapes and continuum intensities as obtained from the side-on spectra of a plasma light-source of rotational symmetry by the use of Abel's inversion.     

A selective two microphone acoustic intensity method

A multiple input, two output model is proposed which enables the two microphone acoustic intensity method to decompose the intensity vector into contributions from individual sources, even when they are coupled and in close proximity within the measurement surface. By treating characteristic signals from each source as the inputs, and the sound pressure signals from the two closely spaced microphones as the outputs, the model's frequency response functions are developed from a least squares approximation. The cross spectrum between the two microphones can then be expressed as a function of the input signal spectra and the model's frequency response functions. By manipulating the model terms the selective cross spectrum associated with the radiation from each individual source can then be estimated. The selective cross spectrum is then processed via standard methods to obtain the acoustic intensity vector from each source. A series of laboratory experiments is summarized which demonstrates that the technique can accurately decompose the acoustic intensity vector from highly coherent sources (γ₁₂² > 0·9) buried in background noise in a semireverberant environment, to within 1 dB of the directly measured intensities.     

Equation of state of sodium chloride up to 32 kbar and 500°C2

The length change of a 25mm long single crystal of NaCl has been determined as a function of hydrostatic pressure up to 32 kbar and temperatures up to 500°C using an electrical contact piezometer with tungsten carbide as a standard. The measurements were carried out in an end loaded piston cylinder apparatus. The length change of the tungsten carbide standard is small compared to that of NaCl and therefore reliable data are obtained. Compression data by Bridgman[1] and thermal expansion data by Kennametal Inc. were used for the equation of state of tungsten carbide. We estimated an absolute uncertainty in the length change measurement of NaCl of ±0.7%. The temperature was accurate within 0.3°C. The uncertainty in pressure is ±0.4%. The results are compared with Decker's [2] equation of state which is frequently used when NaCl is taken as a standard in high pressure work. At room temperature we find a smaller compression of NaCl than Decker and find excellent agreement with Bridgman's[3] data. At higher temperatures we find very good agreement between our data and Decker's equation of state.     

A statistical approach to quantum mechanics

A Monte Carlo method is used to evaluate the Euclidean version of Feynman's sum over particle histories. Following Feynman's treatment, individual paths are defined on a discrete (imaginary) time lattice with periodic boundary conditions. On each lattice site, a continuous position variable x_i specifies the spacial location of the particle. Using a modified Metropolis algorithm, the low-lying energy eigenvalues, |ψ₀(x)|², the propagator, and the effective potential for the anharmonic oscillator are computed, in good agreement with theory. For a deep double-well potential, instantons were found in our computer simulations appearing as multi-kink configurations on the lattice.     

A recursive approach to prony parameter estimation

The Prony series method of fitting a series of complex exponentials to a time series can be applied to many acoustic and vibration signals. For example, in the analysis of a structure's response to transient excitation the Prony series method can be used to find the natural frequencies, damping ratios, amplitudes and relative phases of the modes of the structure. One of the main problems with this method is the need to calculate and invert matrices. In this paper an algorithm that combines the Prony series method with the recursive least squares algorithm is described. This eliminates the need to invert any matrices and also requires only part of the data to be available at one particular time. The method is applied to analyze a simulated structure's response and also to analyze the response of a beam to transient excitation.     

Binary space-integrating acousto-optic processor for vector-matrix multiplication

A binary acousto-optic processor for high accuracy vector-matrix multiplication is described. The processor's operation is based on the formation of inner products. Digitsl products are formed via analog convolution. A spherical lens is used to form both the necessary convolution integral as well as the summation of different digital products. The resulting system requires a single detector for inner product detection. The processor's performance and characteristics are discussed along with possible solutions for performance improvements.     

Relation between the Grüneisen ratio and the pressure dependence of Poisson's ratio for metals

The Grüneisen ratio of crystalline solids is shown to be dependent on a parameter n whose values are characteristic of each solid, and can be determined by two independent ways: from experimental shock data and from the pressure derivative of Poisson's ratio. The determinations are made for several metals, using data on the pressure derivatives of polycrystalline elastic moduli or of the second order elastic constants measured on single crystals, and giving the pressure derivatives of Poisson's ratio by means of the Voigt-Reuss-Hill averaging procedure. The values of the parameter n deduced from shock data are found to be in good agreement with those deduced from the pressure derivatives of Poisson's ratio. Positive and negative values of parameter n correspond respectively to increasing and decreasing Poisson's ratio with increasing pressure. Discussion of the results is made using the linear and the quadratic relationships between shock velocity and particle velocity. It is shown that shock wave data cannot yield directly an accurate estimation of the derivative of the initial slope of the Hugoniot.     

Comparison of the molecular cluster model with the phonon model for Jahn—Teller active impurities in crystals

For comparing the molecular cluster model with the phonon model in describing the Jahn-Teller interaction for magnetic impurities in crystals, the Jahn-Teller energy and the Ham reduction factors are expressed in terms of the phonon Green's function of the host crystal for an orbital triplet coupled to E_g modes of vibrations. Numerical results for the case of MgO lattice have been obtained using the phonon Green's function derived from the breathing shell model.     

Vibration of complex structures: The modal constraint method

A method is described for establishing the natural frequencies of an arbitrary structure with arbitrary supports. The method is based on the modal constraint technique described in a previous paper [1]. As shown in the present paper Weinstein's theory for the intermediate problem can be regarded as equivalent to the Lagrangian multiplier method: i.e., both methods result in the same eigenvalue equations. Weinstein's theory deals with modifications of base differential operators whereas the Lagrangian multiplier method deals with modifications of base energy functionals. The modal constraint technique is an extension of Weinstein's theory, or in energy terms the generalized Fourier expansion of the Lagrangian multiplier. The merits of this method lie in the fact that the eigenvalues and eigenfunctions of structures are used as base structures. The coupling of these structures are taken into account by Lagrangian generalized forces of the constraint acting on the base structures. Some examples are given and the results compared with known solutions.