Manfred Heckl

Investigations on the Vibrations of Grillages and Other Simple Beam Structures

In the first part of this paper, the transmission of bending and torsional waves on beams forming + or T‐shaped systems is investigated. Then, the propagation of two different wave types, such as bending and longitudinal or torsional waves, on beams with periodic discontinuities is studied theoretically. Finally, the results are applied to the vibrations of grillages.

The Tenth Sir Richard Fairey Memorial Lecture: Sound transmission in buildings

Sound transmission through walls, ceilings, windows, doors, etc., depends on (1) mass per unit area, (2) bending stiffness, (3) damping, (4) variation in bending stiffness (because of struts or other anisotropies), (5) stiffness and damping of interlayers and sound bridges (in cases of double walls), (6) size and shape of partitions, (7) mounting conditions, (8) influence of flanking walls, (9) unwanted effects such as slits, etc. The first three parameters and to a certain degree also the fourth and fifth can be dealt with theoretically by investigating walls of infinite size. In this way many of the results obtained in buildings can be explained at least qualitatively. The influences of size, shape, mounting conditions and the influence of flanking transmission can be understood best by applying energy balance equations, and in this way the average behaviour of reasonably large constructions can be explained. Even though sound transmission has been investigated for approximately 80 years, there still remain some open questions especially with respect to inhomogeneous walls and multiple walls of finite size.

VIBRATIONS OF POINT-DRIVEN CYLINDRICAL SHELLS

By using some approximations it is possible to get fairly simple approximate formulas for the number of resonance frequencies and for the point impedance of thin cylinders. Measurements of the resonance frequencies and of the number of resonances within a certain frequency range confirm the theoretical results.

Wave Propagation on Beam‐Plate Systems

Formulas for the attenuation of bending waves that travel over a beam‐plate system, containing one or several beams, are derived and compared with measurements. It is found that one beam gives an attenuation which is very small near the resonances of the beam and rather high elsewhere, but in the average over wide frequency bands the attenuation appears to go nearly like the square root of frequency. The addition of beams of the same material and dimensions does not give an appreciable increase in attenuation. Formulas for the force impedance and mean‐square velocity of beam‐plate systems are also given. Finally, the damping of a beam by a plate attached to it is discussed.

Response of Hard‐Spring Oscillator to Narrow‐Band Excitation

The response of an oscillator with a nonlinear stiffness of the hard‐spring type to narrow band Gaussian random noise is analyzed theoretically by using the method of quasi linearization. The particular point of interest is the possibility of an occurrence of multiple valued response or “jumps” such as one observes when the exciting force is sinusoidal. It is argued that while it does not seem possible to have multivalued response with wide‐band (white noise) excitation, the response to narrow band excitation might exhibit such behavior owing to the temporal correlation of the source with the response. Numerical computations of the response curves do suggest multivalued response. In experiments with a nonlinear oscillator, multivalued response was observed, but agreement between theory and experiment may only be claimed to be qualitative.

Measurements of Absorption Coefficients on Plates

A method equivalent to the reverberation chamber method of architectural acoustics was used to determine the absorption of vibratory energy at the connection of plates to substructures. The applications and the limitations of the method are discussed. Experimental results obtained on typical constructions show that some supporting substructures have an absorption whose frequency dependence is governed mainly by their geometries. Absorption may be accounted for by frictional and viscous losses at the substructure. As pointed out in the previous papers the results are of some interest for the calculation of the vibration of structures excited by sound fields. They also can be used to find the average response of systems excited by point forces. (Supported by Aeronautical Systems Division, Air Force Systems Command, U. S. Air Force.)

Vibrations of a periodic rail-sleeper system excited by an oscillating stationary transverse force

The rail-sleeper system is idealized as an infinite, periodic beam-mass system. Use is made of the periodicity principle for the semi-infinite halves on either side of the forcing point for evaluation of the wave propagation constants and the corresponding modal vectors. It is shown that the spread of acceleration away from the forcing point depends primarily upon one of the wave propagation constants. However, all the four modal vectors (two for the left-hand side and two for the right-hand side) determine the driving point impedance of the rail-sleeper system, which in combination with the driving point impedance of the wheel (which is adopted from the preceding companion paper) determines the forces generated by combined surface roughness and the resultant accelerations. The compound one-third octave acceleration levels generated by typical roughness spectra are generally of the same order as the observed levels.

Noise Source Mechanisms

Each property of a fluid flow is a function of position x and time t. The density ρ is the mass per unit volume. The specific volume, or volume per unit mass, is ρ−1. The velocity at a point is the speed and direction at which the fluid particle currently at that point is moving. The Eulerian approach considers conditions at a fixed point x as time progresses. The Lagrangian approach considers a particular fluid particle which occupies successively different locations x, as time progresses. Rates of change in a Lagrangian frame are rates of change as seen by an observer moving with the fluid velocity. This rate of change is written D/Dt. Thus

SOME MECHANISMS OF EXCITATION OF A RAILWAY WHEEL

Railway wheel vibrations are caused by a number of mechanisms. Two of these are considered: (a) gravitational load reaction acting on different points of the wheel rim, as the wheel rolls on, and (b) random fluctuating forces generated at the contact patch by roughness on the mating surfaces of the wheel and rail. The wheel is idealized as a thin ring, and the analysis is limited to a single wheel rolling on a rail. It is shown that the first mechanism results in a stationary pattern of vibration, which would not radiate any sound. The acceleration caused by roughness-excited forces is much higher at higher frequencies, but is of the same order as that caused by load reaction at lower frequencies. The computed acceleration level (and hence the radiated SPL) caused by roughness is comparable with the observed values, and is seen to increase by about 10 dB for a doubling of the wagon speed. The driving point impedance of the periodic rail-sleeper system at the contact patch, which is used in the analysis, is derived in a companion paper.

Narrow Band Excitation of the Hard Spring Oscillator

By using the technique of “quasi‐linearization,” the response of a hard‐spring oscillator to a band of random noise is calculated. Comparison is sought with the limiting cases of wide band (purely random) and determinate sinusoidal excitation. It is shown that the limiting cases are approached in a satisfactory manner. In particular, multivalued solutions are obtained as the bandwidth of excitation is diminished but do not occur when the bandwidth is suitably broad. Experimental illustration is included. (Supported in part by the Office of Naval Research and the National Science Foundation.)