Random Mobility Variation of Disordered Periodic Structures

1991 ◽  
Author(s):  
G. Q. Cai
Keyword(s):  
Wave Propagation ◽  
Periodic Structures ◽  
Excitation Frequency ◽  
Normal Modes ◽  
Computational Procedure ◽  
Energy Concentration ◽  
Periodic Cell ◽  
Structure Response ◽  
Spatially Periodic ◽  
The Mean

Abstract Due to material, geometric and manufacturing irregularities, a structure designed to be spatially periodic cannot be exactly periodic. The departure from perfect periodicity is referred to as disorder, and it is known to cause spatial localization of normal modes and attenuation of wave propagation even if the structure is undamped. In this paper, another effect of disorder is investigated; namely, possible energy concentration near where a excitation is applied, thus, inducing higher level of structure response, A computational procedure is developed for calculating the mobility, or mechanical admittance, of deterministically disordered periodic structures based on wave propagation theory, and then extended to the case of randomly disordered periodic structures. It is shown that, given the probability distribution of the disordered parameters of a periodic structure, the mean and standard deviation of the mobility magnitude can be obtained. The results are exact if the number of the periodic cell units is not large, and approximate if the number is large. Depending on the excitation frequency, the mean mobility magnitude of a disordered system may be either greater or smaller than that of the perfectly periodic counterpart.

Dynamics of Disordered Periodic Structures

1996 ◽  
Vol 49 (2) ◽  
pp. 57-64 ◽  
Author(s):  
Y. K. Lin
Keyword(s):  
Wave Propagation ◽  
Frequency Response ◽  
Periodic Structures ◽  
Dynamic Properties ◽  
Periodic Pattern ◽  
Structural System ◽  
Space Antenna ◽  
Spatially Periodic ◽  
Main Construction ◽  
The Ideal

For functional or aesthetic reasons, many a structural system is designed to be spatially periodic; namely, it is composed of identical sub-units which are connected to form a spatially periodic pattern. The main construction of the hull of a ship, the fuselage of an aircraft, and a space antenna are examples. Such a structure possesses interesting dynamic properties. However, due to material, geometric and manufacturing variabilities, an ideally periodic structure does not exist. The departure from the ideal designed configuration is known as disorder, which can cause drastic change in the dynamic behavior. The present paper gives a review of some recent works on wave propagation and frequency response of disordered periodic structures, of interest to researchers on vibration and noise control.

Design of Disordered Periodic Structures for Mode Localization

2017 ◽  
Author(s):  
Gabriele Cazzulani ◽  
Emanuele Riva ◽  
Edoardo Belloni ◽  
Francesco Braghin
Keyword(s):  
Wave Propagation ◽  
Periodic Structures ◽  
Unit Cell ◽  
Band Gaps ◽  
Mode Shapes ◽  
Mode Localization ◽  
Geometrical Properties ◽  
Unit Cells ◽  
The Mean ◽  
Propagation Properties

Periodic structures are the repetition of unit cells in space, that provide a filtering behavior for wave propagation. In particular, it is possible to tailor the geometrical, physical and elastic properties of the unit cells, in order to attenuate certain frequency bands, called band-gaps or stop-bands. Having each element characterized with the same parameters, the filtering behavior of the system can be described through the wave propagation properties of the unit cell. This is technologically impossible to obtain, therefore the Lyapunov factor is used, in order to define the mean attenuation of a quasi-periodic structure. Tailoring Gaussian unit cell properties potentially allows to extend the stop-bands width in the frequency domain. A drawback is that some unexpected resonance peaks may lie in the neighborhood of the extended regions. However, the correspondent mode-shapes are localized in a particular region of the structure, and they partially decrease the global attenuating behavior. In this paper, the aperiodicity introduced in the otherwise perfect repetition is investigated, providing an explanation for the mode-localization problem and for the stop-bands extension. Then, the proposed approach is applied to a passive quasi-periodic beam, characterized from a localized peak within a designed band-gap. The geometrical properties of its aperiodic parts are changed in order to deterministically move the localization peak in the frequency response. Numerical and experimental results are compared.

Periodic structure with interconnected nonlinear electrical networks

2016 ◽  
Vol 28 (2) ◽  
pp. 204-229 ◽  
Author(s):  
Linjuan Yan ◽  
Bin Bao ◽  
Daniel Guyomar ◽  
Mickaël Lallart
Keyword(s):  
Wave Propagation ◽  
Periodic Structure ◽  
Wave Attenuation ◽  
Periodic Structures ◽  
Short Circuit ◽  
Electrical Network ◽  
Electrical Networks ◽  
Mechanical Wave ◽  
Matrix Formulation ◽  
Structure Response

This article aims at investigating the filtering abilities of periodic structures with nonlinear interconnected synchronized switch damping on inductor electrical networks. Periodic structures without electrical networks themselves naturally have the function of filtering since the structure response breaks into pass bands and stop bands when the structure is excited by an external force with multiple or varying frequencies. Introduction of linear electrical networks in the periodic structure makes stop bands of the structure wider than that of the structure without electrical networks. However, nonlinear piezoelectric electrical networks may have better effect on the mechanical wave attenuation than linear piezoelectric electrical networks in terms of frequency band. Therefore, this article proposes a piezoelectric periodic structure with nonlinear interconnected synchronized switch damping on short-circuit/synchronized switch damping on inductor electrical network. A transfer matrix formulation including the interconnected electrical network is also proposed for deriving the characteristics of elastic wave propagation. The results show that the proposed technique permits enhancing the damping abilities in particular frequency bands compared to electrically independent periodic cells, which, combined with structural tailoring, would allow achieving high damping performance.

A Physical Interpretation for Broken Reciprocity in Spatiotemporal Modulated Periodic Rods

2017 ◽  
Author(s):  
Jacopo Marconi ◽  
Gabriele Cazzulani ◽  
Massimo Ruzzene ◽  
Francesco Braghin
Keyword(s):  
Wave Propagation ◽  
Vibration Suppression ◽  
Periodic Structures ◽  
Previous Analysis ◽  
Travelling Waves ◽  
Periodic Systems ◽  
Mathematical Methods ◽  
Elastic Structures ◽  
The Mean ◽  
And Control

Periodic systems have long been known for their peculiar characteristics in wave propagation and have been studied in many fields over the last century, going from electro-magnetics and optics to elastic structures, which drew an increasing interest in structural and mechanical engineering for vibration suppression and control spanning over broadband frequency ranges. Recently, on the stream of other studies conducted in different fields, spatiotemporal modulated elastic structures have been studied, showing promising results for wave control in that one-way propagation in the so called directional-bands can be achieved, constituting what may be called a mechanical diode. Despite of the fact that mathematical methods for the analysis of such structures have already been developed, often physics behind them is difficult to grasp. In this work, a simplified interpretation of the undergoing phenomena is thus given relating wave propagation in the mean to its physical characteristics as well as to modulation parameters. Exploiting Doppler effect and passive equivalent structures, it is shown that the broken reciprocity is due to the fact that opposite travelling waves effectively see two different periodic structures. To this aim the rod case is analysed for low modulation speeds and low modulation amplitudes; finally, in the light of the previous analysis, an explanation for First Brillouin Zone’s asymmetry is given.

Nonlinear Modal Analysis and Energy Localization in a Bladed Disk Assembly

2008 ◽  
Author(s):  
F. Georgiades ◽  
M. Peeters ◽  
G. Kerschen ◽  
J. C. Golinval ◽  
M. Ruzzene
Keyword(s):  
Modal Analysis ◽  
Nonlinear Oscillations ◽  
Periodic Structures ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Energy Localization ◽  
Bladed Disk ◽  
Bladed Disk Assembly ◽  
Nonlinear Modal Analysis ◽  
Nonlinear Normal

The objective of this study is to carry out modal analysis of nonlinear periodic structures using nonlinear normal modes (NNMs). The NNMs are computed numerically with a method developed in [18] that is using a combination of two techniques: a shooting procedure and a method for the continuation of periodic motion. The proposed methodology is applied to a simplified model of a perfectly cyclic bladed disk assembly with 30 sectors. The analysis shows that the considered model structure features NNMs characterized by strong energy localization in a few sectors. This feature has no linear counterpart, and its occurrence is associated with the frequency-energy dependence of nonlinear oscillations.

Wave Propagation in Two-Dimensional Nonlinear Periodic Lattices

2009 ◽  
Author(s):  
Raj K. Narisetti ◽  
Massimo Ruzzene ◽  
Michael J. Leamy
Keyword(s):  
Wave Propagation ◽  
Linear Models ◽  
Periodic Structures ◽  
Harmonic Wave ◽  
Excitation Amplitude ◽  
Pass Band ◽  
Perturbation Approach ◽  
Nonlinear Stiffness ◽  
Two Dimensional ◽  
Low Amplitude

This paper investigates wave propagation in two-dimensional nonlinear periodic structures subject to point harmonic forcing. The infinite lattice is modeled as a springmass system consisting of linear and cubic-nonlinear stiffness. The effects of nonlinearity on harmonic wave propagation are analytically predicted using a novel perturbation approach. Response is characterized by group velocity contours (derived from phase-constant contours) functionally dependent on excitation amplitude and the nonlinear stiffness coefficients. Within the pass band there is a frequency band termed the “caustic band” where the response is characterized by the appearance of low amplitude regions or “dead zones.” For a two-dimensional lattice having asymmetric nonlinearity, it is shown that these caustic bands are dependent on the excitation amplitude, unlike in corresponding linear models. The analytical predictions obtained are verified via comparisons to responses generated using a time-domain simulation of a finite two-dimensional nonlinear lattice. Lastly, the study demonstrates amplitude-dependent wave beaming in two-dimensional nonlinear periodic structures.

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