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.

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.

scholarly journals Analysis of Vibration and Wave Propagation in Cylindrical Grid-Like Structures

2004 ◽  
Vol 11 (3-4) ◽  
pp. 311-331 ◽  
Author(s):  
Sang Min Jeong ◽  
Massimo Ruzzene
Keyword(s):  
Wave Propagation ◽  
Wave Attenuation ◽  
Periodic Structures ◽  
Interpolation Method ◽  
Dynamic Properties ◽  
Element Formulation ◽  
Two Dimensional ◽  
Combined Application ◽  
Cylindrical Grid ◽  
Phase Constant

The wave propagation in and the vibration of cylindrical grid structures are analyzed. The grids are composed of a sequence of identical elementary cells repeating along the axial and the circumferential direction to form a two-dimensional periodic structure. Two-dimensional periodic structures are characterized by wave propagation patterns that are strongly frequency dependent and highly directional. Their wave propagation characteristics are determined through the analysis of the dynamic properties of the unit cell. Each cell here is modelled as an assembly of curved beam elements, formulated according to a mixed interpolation method. The combined application of this Finite Element formulation and the theory of two-dimensional periodic structures is used to generate the phase constant surfaces, which define, for the considered cell lay-out, the directions of wave propagation at assigned frequencies. In particular, the directions and frequencies corresponding to wave attenuation are evaluated for cells of different size and geometry, in order to identify topologies with attractive wave attenuation and vibration confinement characteristics. The predictions from the analysis of the phase constant surfaces are verified by estimating the forced harmonic response of complete cylindrical grids, obtained through the assembly of the unit cells. The considered analysis provides invaluable guidelines for the investigation of the dynamic properties and for the design of grid stiffened cylindrical shells with unique vibration confinement characteristics.

Analysis of Vibration and Wave Propagation in Cylindrical Grid-Like Structures

2003 ◽  
Author(s):  
Sang Min Jeong ◽  
Massimo Ruzzene
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Periodic Structures ◽  
Dynamic Properties ◽  
Unit Cell ◽  
Element Formulation ◽  
Two Dimensional ◽  
Curved Beams ◽  
Cylindrical Grid ◽  
Phase Constant

The wave propagation in and the vibration of cylindrical grid structures are analyzed. The considered grids are composed of a sequence of identical elementary cells repeating along the axial and circumferential directions to form a two-dimensional (2D) periodic structure. Two-dimensional periodic structures are characterized by wave propagation patterns that are strongly frequency dependent and highly directional. Such unique characteristics can be utilized to design structures able to confine external perturbations to specified regions. The wave propagation characteristics of 2D periodic structures are determined through the analysis of the dynamic properties of the unit cell, which is described by its Finite Element mass and stiffness matrices. The cell is composed of curved beams to form a cylindrical grid. The combined application of the Finite Element formulation and the theory of 2D periodic structures yields the phase constant surfaces, which define, for the considered cell lay-out, the directions of wave propagation for assigned frequency values. The predictions from the phase constant surfaces analysis are verified by estimating the forced harmonic response of the complete grid. The results demonstrate the unique characteristics of this class of grid structures, and suggest how they may be designed to enhance attenuation capabilities of shell structures commonly used in aerospace or naval applications. Design configurations can be identified so that the transmission of vibrations towards specified locations and at certain frequencies is minimized. The study can be extended to include the optimization of the geometry and topology of the unit cell to achieve desired transmissibility levels in specified directions and for given excitation frequencies.

Response Prediction and Dynamic Substructuring for Coupled Structures in the Frequency Domain

2020 ◽  
Vol 36 (6) ◽  
pp. 867-879
Author(s):  
X. H. Liao ◽  
W. F. Wu ◽  
H. D. Meng ◽  
J. B. Zhao
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Dynamic Properties ◽  
Main Idea ◽  
Prediction Method ◽  
Response Prediction ◽  
Synthesis Methods ◽  
Dynamic Substructuring ◽  
Coupled Structures

ABSTRACTTo evaluate the dynamic properties of a coupled structure based on the dynamic properties of its substructures, this paper investigates the dynamic substructuring issue from the perspective of response prediction. The main idea is that the connecting forces at the interface of substructures can be expressed by the unknown coupled structural responses, and the responses can be solved rather easily. Not only rigidly coupled structures but also resiliently coupled structures are investigated. In order to further comprehend and visualize the nature of coupling problems, the Neumann series expansion for a matrix describing the relation between the coupled and uncoupled substructures is also introduced in this paper. Compared with existing response prediction methods, the proposed method does not have to measure any forces, which makes it easier to apply than the others. Clearly, the frequency response function matrix of coupled structures can be derived directly based on the response prediction method. Compared with existing frequency response function synthesis methods, it is more straightforward and comprehensible. Through demonstration of two examples, it is concluded that the proposed method can deal with structural coupling problems very well.

scholarly journals A Parameter Study of Localization

1996 ◽  
Vol 3 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Sandor Stephen Mester ◽  
Haym Benaroya
Keyword(s):  
Periodic Structures ◽  
Numerical Study ◽  
Vibration Characteristics ◽  
Periodic Pattern ◽  
Parameter Study ◽  
Structural Damping ◽  
One Dimensional

Extensive work has been done on the vibration characteristics of perfectly periodic structures. Disorder in the periodic pattern has been found to lead to localization in one-dimensional periodic structures. It is important to understand localization because it causes energy to be concentrated near the disorder and may cause an overestimation of structural damping. A numerical study is conducted to obtain a better understanding of localization. It is found that any mode, even the first, can localize due to the presence of small imperfections.

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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