Wave Propagation in One-Dimensional Structure of Periodic Inelasticity Composites

2011 ◽  
Author(s):  
Helio Aparecido Navarro ◽  
Meire Pereira de Souza Braun
Keyword(s):  
Wave Propagation ◽  
Vibration Suppression ◽  
Stop Band ◽  
Dimensional Structure ◽  
Material Models ◽  
One Dimensional ◽  
Elastic Plastic ◽  
Structural Problems ◽  
Plastic Damage ◽  
Non Linear

This study involves the analysis of elastic-plastic-damage dynamics of one-dimensional structures comprising of periodic materials. These structures are composed by multilayer unit cells with different materials. The dynamical characteristics of the composite material present distinct frequency ranges where wave propagation is blocked. The steady-state forced analyses are conducted on a structure constructed from a periodic inelasticity material. The material models have a linear dependence for elasticity problems and non-linear for elastoplasticity-damage problems. This paper discusses the pass and stop-band dispersive behavior of material models on temporal and spatial domains. For this purpose, some structural problems are composed of periodic and damping materials for analysis of vibration suppression have been simulated. This work brings a formulation of Galerkin method for one-dimensional elastic-plastic-damage problems. A time-stepping algorithm for non-linear dynamics is also presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spatial discretization the standard finite element method is used. The procedure proposed in this work can be extended to multidimensional problems, analysis of strain localization, and for others material models.

Constitutive Models for Wave Propagation in Soils

2006 ◽  
Vol 59 (3) ◽  
pp. 146-175 ◽  
Author(s):  
Frederick Bloom
Keyword(s):  
Wave Propagation ◽  
Entire Range ◽  
Constitutive Models ◽  
Volume Distribution ◽  
Single Model ◽  
Function Model ◽  
Material Models ◽  
Elastic Plastic ◽  
Variable Modulus ◽  
Loading And Unloading

A survey is provided of the various constitutive models that have been used to study the phenomena of wave propagation in soils. While different material models have been proposed for the response of soils, it is now generally understood that no single model may be used over the entire range of pressures which are typically studied. The constitutive models reviewed in this paper include a number of effective stress and multiphase models, the volume distribution function model, and various versions of the P−α model. Also discussed are classical elastic-plastic models, models possessing different elastic constants in loading and unloading, variable modulus models, and capped elastic-plastic models.

Wave Propagation in Periodic Piezoelectric Elastic Waveguides

2012 ◽  
Author(s):  
D. G. Piliposyan ◽  
K. B. Ghazaryan ◽  
G. T. Piliposian ◽  
A. S. Avetisyan
Keyword(s):  
Wave Propagation ◽  
Stop Band ◽  
Transmission Conditions ◽  
Band Gaps ◽  
Full System ◽  
One Dimensional ◽  
Dynamic Setting ◽  
Floquet Waves ◽  
Wide Range ◽  
Shear Horizontal

The prorogation of electro-magneto-elastic coupled shear-horizontal waves in one dimensional infinite periodic piezoelectric waveguides is considered within a full system of the Maxwell’s equations. Such setting of the problem allows to investigate the Bloch-Floquet waves in a wide range of frequencies. Two different conditions along the guide walls and three kinds of transmission conditions at the interfaces between the laminae of waveguides have been studied. Stop band structures have been identified for Bloch-Floquet waves both at acoustic and optical frequencies. The results demonstrate the significant effect of piezoelectricity on the widths of band gaps at acoustic frequencies and confirm that it does not affect the band structure at optical frequencies. The results show that under electrically shorted transmission conditions Bloch-Floquet waves exist only at acoustic frequencies. For electrically open interfaces the dynamic setting provides solutions only for photonic crystals. In this case the piezoelectricity has no effect on band gaps.

Elastic-Plastic Boundaries in Combined Longitudinal and Torsional Plastic Wave Propagation

1968 ◽  
Vol 35 (4) ◽  
pp. 782-786 ◽  
Author(s):  
R. J. Clifton
Keyword(s):  
Wave Propagation ◽  
Time Derivative ◽  
Plastic Wave ◽  
Wave Speeds ◽  
One Dimensional ◽  
Elastic Plastic ◽  
Simple Waves ◽  
Thin Walled Tube ◽  
Loading And Unloading ◽  
All Speeds

Assuming a one-dimensional rate independent theory of combined longitudinal and torsional plastic wave propagation in a thin-walled tube, restrictions are obtained on the possible speeds of elastic-plastic boundaries. These restrictions are shown to depend on the type of discontinuity at the boundary and on whether loading or unloading is occurring. The range of unloading (loading) wave speeds for the case when the nth time derivative of the solution is the first derivative that is discontinuous across the boundary is the complement of the range of unloading (loading) wave speeds for the case when the first discontinuity is in the (n + 1)th time derivative. Thus all speeds are possible for elastic-plastic boundaries corresponding to either loading or unloading. The general features of the discontinuities associated with loading and unloading boundaries are established, and examples are presented of unloading boundaries overtaking simple waves.

An Investigation of Vibrational Power Flow in One-Dimensional Dissipative Phononic Structures

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
H. Al Ba'ba'a ◽  
M. Nouh
Keyword(s):  
Wave Propagation ◽  
Power Flow ◽  
Vibration Suppression ◽  
Wave Attenuation ◽  
External Disturbance ◽  
Stop Band ◽  
Bragg Scattering ◽  
Spatial Propagation ◽  
The Individual ◽  
Vibrational Power Flow

Owing to their ability to block propagating waves at certain frequencies, phononic materials of self-repeating cells are widely appealing for acoustic mitigation and vibration suppression applications. The stop band behavior achieved via Bragg scattering in phononic media is most commonly evaluated using wave propagation models which predict gaps in the dispersion relations of the individual unit cells for a given frequency range. These models are in many ways limited when analyzing phononic structures with dissipative constituents and need further adjustments to account for viscous damping given by complex elastic moduli and frequency-dependent loss factors. A new approach is presented which relies on evaluating structural intensity parameters, such as the active vibrational power flow in finite phononic structures. It is shown that the steady-state spatial propagation of vibrational power flow initiated by an external disturbance reflects the wave propagation pattern in the phononic medium and can thus be reverse engineered to numerically predict the stop band frequencies for different degrees of damping via a stop band index (SBI). The treatment is shown to be very effective for phononic structures with viscoelastic components and provides a clear distinction between Bragg scattering effects and wave attenuation due to material damping. Since the approach is integrated with finite element methods, the presented analysis can be extended to two-dimensional lattices with complex geometries and multiple material constituents.

Structural Intensity Analysis of Periodic Elastic Structures With Frequency Stop Bands

2016 ◽  
Author(s):  
M. Nouh
Keyword(s):  
Wave Propagation ◽  
Vibration Suppression ◽  
Periodic Structures ◽  
External Disturbance ◽  
Stop Band ◽  
Bloch Wave ◽  
Periodic Medium ◽  
Elastic Structures ◽  
Structural Intensity ◽  
Wide Range

Periodic elastic structures consisting of self-repeating geometric or material arrangements exhibit unique wave propagation characteristics culminating in frequency stop bands, i.e. ranges of frequency where elastic waves can propagate the periodic medium. Such features make periodic structures appealing for a wide range of vibration suppression and noise control applications. Stop bands in periodic media are achieved via Bragg scattering of elastic which is attributed to impedance mismatches between the different constituents of the self-repeating cells. Stop band frequencies can be numerically predicted using mathematical models which generally utilize the Bloch wave theorem and a transfer matrix method to track the spatial and temporal parameters of the propagating waves from one cell to the next. Such analysis generates what is referred to as the band structure (or the dispersion curves) of the periodic medium which can be used to predict the location of the pass and stop bands. Although capable, these models become significantly more involved when analyzing structures with dissipative constituents and/or material damping and need further adjustments to account for complex elastic moduli and frequency dependent loss factors. A new approach is presented which relies on evaluating structural intensity parameters, such as the active vibrational power and energy transmission paths. It is shown that the steady-state spatial propagation of vibrational power caused by an external disturbance accurately reflects the wave propagation pattern in the periodic medium, and can thus be reverse engineered to numerically predict the stop band frequencies for different degrees of damping via a stop band index (SBI). The developed framework is mathematically applied to a one-dimensional periodic rod to validate the proposed method.

The Elastic-Plastic Boundary in One-Dimensional Wave Propagation

1968 ◽  
Vol 35 (4) ◽  
pp. 812-814 ◽  
Author(s):  
R. J. Clifton ◽  
T. C. T. Ting
Keyword(s):  
Wave Propagation ◽  
One Dimensional ◽  
Elastic Plastic ◽  
Dimensional Wave

Determination of the Unloading Boundary in Longitudinal Elastic-Plastic Stress Wave Propagation

1971 ◽  
Vol 38 (4) ◽  
pp. 888-894 ◽  
Author(s):  
P. A. Tuschak ◽  
A. B. Schultz
Keyword(s):  
Wave Propagation ◽  
Moving Boundary ◽  
Stress Waves ◽  
Stress Wave Propagation ◽  
Initial Portion ◽  
One Dimensional ◽  
Elastic Plastic ◽  
In Series ◽  
Plastic Stress

For several types of excitation of one-dimensional elastic-plastic stress waves in a rod, unloading waves propagate which interact with the loading waves. The moving boundary at which this interaction occurs is the unloading boundary. A knowledge of the location of this boundary and the behavior exhibited on it is necessary for the solution of wave-propagation problems of this kind. A technique is presented to obtain an arbitrary number of terms in series expressions describing the response in semi-infinite rods. Several examples, including finite mass impact of the rod, are given to illustrate the use of the technique. The technique will determine the initial portion of the boundary in a finite length rod.

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