A new method of analyzing wave propagation in periodic structures; Applications to periodic timoshenko beams and stiffened plates
TL;DR: In this article, a response function is derived for an infinite, uniform, one-dimensional structure which is subjected to an array of harmonic forces or moments, spaced equidistantly, and which have a constant phase or ratio between any adjacent pair.
About: This article is published in Journal of Sound and Vibration.The article was published on 1986-01-08. It has received 188 citations till now. The article focuses on the topics: Timoshenko beam theory & Infinite set.
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1,197 citations
TL;DR: A review of dynamic modelling of railway track and of the interaction of vehicle and track at frequencies which are sufficiently high for the track's dynamic behaviour to be significant is presented in this paper.
Abstract: A review is presented of dynamic modelling of railway track and of the interaction of vehicle and track at frequencies which are sufficiently high for the track's dynamic behaviour to be significant. Since noise is one of the most important consequences of wheel/rail interaction at high frequencies, the maximum frequency of interest is about 5kHz: the limit of human hearing. The topic is reviewed both historically and in particular with reference to the application of modelling to the solution of practical problems. Good models of the rail, the sleeper and the wheelset are now available for the whole frequency range of interest. However, it is at present impossible to predict either the dynamic behaviour of the railpad and ballast or their long term behaviour. This is regarded as the most promising area for future research.
615 citations
TL;DR: In this paper, an exact analytical approach based on a combination of the spectral element method and periodic structure theory is proposed for the prediction of all the band edge frequencies in an exact manner without the need to calculate propagation constants.
304 citations
TL;DR: In this article, a mathematical model is developed to predict the response of a rod with periodic shunted piezoelectric patches and to identify its stop band characteristics, and the model accounts for the aperiodicity, introduced by proper tuning of the shunted electrical impedance distribution along the rod.
Abstract: Shunted piezoelectric patches are periodically placed along rods to control the longitudinal wave propagation in these rods. The resulting periodic structure is capable of filtering the propagation of waves over specified frequency bands called stop bands. The location and width of the stop bands can be tuned, using the shunting capabilities of the piezoelectric materials, in response to external excitations and to compensate for any structural uncertainty. A mathematical model is developed to predict the response of a rod with periodic shunted piezoelectric patches and to identify its stop band characteristics. The model accounts for the aperiodicity, introduced by proper tuning of the shunted electrical impedance distribution along the rod. Disorder in the periodicity typically extends the stop bands into adjacent propagation zones and, more importantly, produces the localization of the vibration energy near the excitation source. The conditions for achieving localized vibration are established and the localization factors are evaluated for different levels of disorder on the shunting parameters. The numerical predictions demonstrate the effectiveness and potentials of the proposed treatment that requires no control energy and combines the damping characteristics of shunted piezoelectric films, the attenuation potentials of periodic structures, and the localization capabilities of aperiodic structures. The theoretical investigations presented in this paper provide the guidelines for designing tunable periodic structures with high control flexibility where propagating waves can be attenuated and localized.
233 citations
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TL;DR: In this paper, a general theory of harmonic wave propagation in one-dimensional periodic systems with multiple coupling between adjacent periodic elements is presented, where the motion of each element is expressed in terms of a finite number of displacement coordinates.
490 citations
TL;DR: In this paper, the authors considered the free harmonic motion of infinite beams on identical, equi-spaced supports and derived the flexural propagation constants for beams on rigid supports which exert elastic rotational restraint.
409 citations
TL;DR: In this paper, the nature of the characteristic wave motions is studied, and a characteristic receptance matrix for a characteristic wave is defined, and the equations governing the reflection process are set up, and used to formulate the equations for the natural frequencies and modes of a finite periodic system with arbitrary boundaries.
268 citations
TL;DR: In this paper, a solution for the response of stiffened beams due to a spatial and temporal harmonic pressure has been obtained in the form of a particular series of space harmonics, evolved from considerations of progressive wave propagation, applied to obtain the r.m.s. curvature at a point on a periodically supported beam excited by a random acoustic plane wave or boundary layer pressure fluctuation.
145 citations
144 citations