Richard H. Lyon

Noise Reduction of Rectangular Enclosures with One Flexible Wall

The noise reduction produced by a small rigid enclosure with one flexible wall is computed. It is assumed that the critical frequency of the wall lies above the first acoustic resonance of the enclosure. The noise reduction is computed for very low frequencies where both wall and enclosed volume are stiffness‐controlled, for frequencies where the wall is resonant and the volume is stiff, and for frequencies where both the wall and the acoustic space have resonant behavior. In the last case, a comparison made with the usual noise‐reduction calculations based on forced wave‐transmission loss. The noise reduction computed in this paper turns out to be less than the value computed by that more “classical” approach.

Random Vibration of Connected Structures

The sharing of energy by connected, randomly vibrating structures can be estimated, using a statistical approach. Modal energy is taken as the primary variable; the structures are described statistically by their modal densities, masses, and loss factors. Average response levels are computed. In addition, response variations are calculated to establish confidence coefficients for estimates related to these average levels. The method is applied to two cases: a single resonator attached to a plate and two plates attached together. Experimental studies are reported that support the methods.

ROLE OF MULTIPLE REFLECTIONS AND REVERBERATION IN URBAN NOISE PROPAGATION

Various studies of sound transmission in urban areas that involve multipath propagation or multiple reflections are reviewed. Studies of propagation in a single street or corridors display important descrepancies between theoretical analyses and field experiments. Model studies suggest that scattering may play an important, but as yet unexplained role. Sources above the street show good correspondence between field and laboratory data and theory. Intrusion of aircraft noise into an urban area shows that sound may be slightly amplified above an open‐terrain condition due to channeling effects. The general urban background noise appears to be accounted for by surface transportation sources distributed over the city, aside from a shielding factor of 10–15 dB of as yet undetermined origin.

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.

Response of Strings to Random Noise Fields

A formulism for predicting the motion of continuous systems excited by random noise fields is applied to the special case of a one‐dimensional string. Several examples are attacked: (1) Brownian motion of finite strings, (2) response to a spatially stepped‐temporally delayed noise field, (3) response of finite ribbon to moving, random pressure fluctuations, (4) response of an infinite ribbon to moving, random pressure fluctuations. Cases (2) and (3) are investigated experimentally, the latter by using flowing turbulence.In case (2) appears the interesting phenomenon of the capability of the string “remembering” or “forgetting” a signal which it received in the past. The larger the damping of the string, the sooner it will forget a previous signal. In cases (3) and (4) a coincidence effect appears between the flow velocity of the forcing field and the velocity of waves on the ribbon. Here again, the phenomenon of forgetting appears and sharply determines the magnitude of any coincidence effect which may ap...

On the Vibration Statistics of a Randomly Excited Hard‐Spring Oscillator

Previous calculations of the statistical behavior of a hard spring oscillator excited by purely random and Gaussian noise are extended. The moments of the displacement and its extrema are found in an analytic form and their interrelations are exploited. Recurrence relations, asymptotic expressions, and computations of the moments are presented. Envelope autocorrelations for three narrow‐band linear filters are found, and the mean size of clumps of cycles exceeding predetermined levels is obtained. For the hard‐spring oscillator we find that the relative envelope fluctuation is less than that of a linear oscillator and that the mean clump size is also smaller in general.

Cepstral analysis as a tool for robust processing, deverberation and detection of transients☆

Abstract A transient pulse generated by excitation from most machine components contains useful information for diagnosing the machines condition and for analysing structural characteristics. A direct measurement of an excitation pulse, however, is not simple because locating sensors at the exact source location is not practical in many engineering applications. In this paper, an indirect method for detecting a transient source waveform is introduced. A vibration response signal that includes information on an excitation pulse and dispersive structural characteristics is monitored by using a sensor at a remote position. Then, cepstral analysis plays the role of a robust inverse filter to smooth out the transmission path and deverberate the complicated vibration response. Examples of deverberation and detection of excitation pulses using the cepstrum are presented.

Progressive phase trends in multi‐degree‐of‐freedom systems

The relative phase of the response of a dynamical system to its excitation has been largely ignored in problems dealing with noise response of such systems. This is because mean‐square amplitude functions are able to predict many of the quantitites that one is interested in such as crack growth, noise radiation, and clearance impact probabilities without concern for phase. But phase has an essential role in other cases, such as phase coherence of vibration fields, or the design of filters to ‘‘dereverberate’’ a received signal. This paper describes some early results of the analysis of phase response of multi‐degree‐of‐freedom systems, using ideas that are closely related to statistical energy analysis, until now, used exclusively for the kinds of problems listed above that tend to ignore phase. The present results show good agreement between simple theory and experiments, but more importantly, they suggest directions for further work that should have significant payoff in the future.

SOUND RADIATION FROM A BEAM ATTACHED TO A PLATE

The sound power radiated by acoustically slow waves scattered by a beam is computed. An acoustic radiation resistance per unit length of beam is computed based on the radiated power and the mean‐square transverse plate velocity in the absence of the beam. For a diffuse reverberant vibrational field and supported, clamped, or edge supported lines, explicit expressions for the radiation resistance are obtained. The reduction of radiation coupling due to beam vibration is also computed.

Response of a Nonlinear String to Random Excitation

The response of a perfectly flexible string with longitudinal deformation to random excitation is studied in some detail. The equations of motion are essentially those of Carrier [Quart. Appl. Math. 3, 157–165 (1945)]. The modified mean square response for the “elastic” string is discussed and it is shown that the mean square deflection is diminished from the linear case. From a study of the fourth moments, it also appears that the shape of probability distributions of the transverse displacement are altered, the response to gaussian noise being in general nongaussian.