Wave Propagation and Parametric Instability in Materials Reinforced by Fibers With Periodically Varying Directions

1975 ◽  
Vol 42 (4) ◽  
pp. 825-831 ◽  
Author(s):  
M. Schoenberg ◽  
Y. Weitsman
Keyword(s):  
Composite Material ◽  
Wave Propagation ◽  
Elastic Medium ◽  
Parametric Instability ◽  
Transversely Isotropic ◽  
Harmonic Waves ◽  
Fiber Reinforced ◽  
Frequency Bands ◽  
Structural Periodicity ◽  
Dominant Direction

This paper concerns the propagation of plane harmonic waves in an infinite fiber-reinforced elastic medium. The composite material is represented by an equivalent homogeneous transversely isotropic matter whose preferred directions coincide with the orientations of the fibers. The fibers are assumed to wobble periodically about a dominant direction, all fibers being parallel to each other. This wobbliness endows the material with a structural periodicity which generates dispersion at all frequencies and instability for various frequency bands. The zones of instability are analyzed in some detail.

Harmonic Wave Propagation in a Periodically Layered, Infinite Elastic Body: Antiplane Strain

1978 ◽  
Vol 45 (2) ◽  
pp. 343-349 ◽  
Author(s):  
T. J. Delph ◽  
G. Herrmann ◽  
R. K. Kaul
Keyword(s):  
Wave Propagation ◽  
Elastic Medium ◽  
Elastic Body ◽  
Dispersion Equation ◽  
Harmonic Wave ◽  
Wave Number ◽  
Harmonic Waves ◽  
Antiplane Strain ◽  
Frequency Wave ◽  
Asymptotic Values

The propagation of horizontally polarized shear waves through a periodically layered elastic medium is analyzed. The dispersion equation is obtained by using Floquet’s theory and is shown to define a surface in frequency-wave number space. The important features of the surface are the passing and stopping bands, where harmonic waves are propagated or attenuated, respectively. Other features of the spectrum, such as uncoupling at the ends of the Brillouin zones, conical points, and asymptotic values at short wavelengths, are also examined.

Finite Element Approximation of Wave Propagation in Composite Material With Asymptotic Homogenization

2014 ◽  
Author(s):  
Bhuiyan Shameem Mahmood Ebna Hai ◽  
Markus Bause
Keyword(s):  
Finite Element ◽  
Composite Material ◽  
Wave Propagation ◽  
Finite Element Approximation ◽  
Ultrasonic Waves ◽  
Element Approximation ◽  
Fiber Reinforced ◽  
Reinforced Plastics ◽  
Advanced Composite Materials ◽  
Time Harmonic

Advanced composite materials such as carbon fiber reinforced plastics are being applied to many aerospace or automotive structures in order to improve material performances and save weight. Most composites have strong, stiff fibres in a matrix which is weaker and less stiff. But these structures can be damaged due to fluid-structure interaction (FSI) oscillations or material fatigue. To design integrated structural health monitoring (SHM) systems in a lightweight structure, it is important to understand wave propagation phenomena in composite material, and the influence of the material properties of the structures. In non-destructive test (NDT), piezoelectric induced ultrasonic waves can be used for damage detection. In this work, we focus on mathematical modeling and numerical approximation of the propagation of time-harmonic elastic waves in a fiber-reinforced composite material. The fibers are assumed to be parallel to each other and statistically uniformly distributed. In this work we study higher order continuous finite element approximation of the elastic wave equation and the implementation is carried out by means of the FEM library deal.II. (Differential Equations Analysis Library)

scholarly journals Effect of the initial stress and rotation on free vibrations in transversely isotropic human long dry bone

2015 ◽  
Vol 23 (1) ◽  
pp. 171-184 ◽  
Author(s):  
S. R. Mahmoud ◽  
M. Marin ◽  
K.S. Al-Basyouni
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Initial Stress ◽  
Isotropic Material ◽  
Transversely Isotropic ◽  
Free Vibrations ◽  
Harmonic Waves ◽  
Transversely Isotropic Material ◽  
Harmonic Vibrations ◽  
Dry Bone

Abstract The object of the present paper is to study the influence of the initial stress and rotation on wave propagation of harmonic waves in a human long dry bone as transversely isotropic material, subject to the boundary conditions that the outer and inner surfaces are traction free. The equations of elastodynamic are solved in terms of displacements. The natural frequency of the plane vibrations in the case of harmonic vibrations has been obtained. The frequencies and the phase velocity are calculated numerically, the effects of the initial stress and rotation are discussed. Comparisons are made with the result in the absence of rotation and initial stress.

Fiber symmetry

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Composite Materials ◽  
Constitutive Equation ◽  
Transversely Isotropic ◽  
Fiber Reinforced ◽  
Fiber Reinforced Materials ◽  
Reinforced Materials

This chapter develops the general constitutive equation for transversely isotropic, fiber-reinforced materials. Applications include composite materials and bio-elasticity.

Transverse surface waves in magneto-elasticity

1966 ◽  
Vol 62 (3) ◽  
pp. 541-545 ◽  
Author(s):  
C. M. Purushothama
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Surface Waves ◽  
Elastic Medium ◽  
Uniform Magnetic Field ◽  
Shear Waves ◽  
Plane Shear ◽  
Electrically Conducting ◽  
Velocity Of Propagation

AbstractIt has been shown that uncoupled surface waves of SH type can be propagated without any dispersion in an electrically conducting semi-infinite elastic medium provided a uniform magnetic field acts non-aligned to the direction of wave propagation. In general, the velocity of propagation will be slightly greater than that of plane shear waves in the medium.

scholarly journals Tunable Mechanical Filter for Longitudinal Vibrations

2007 ◽  
Vol 14 (5) ◽  
pp. 377-391 ◽  
Author(s):  
S. Asiri
Keyword(s):  
Wave Propagation ◽  
Spectral Width ◽  
Design Parameters ◽  
Vibration Source ◽  
Vibration Isolator ◽  
Force Transmission ◽  
Longitudinal Vibrations ◽  
Frequency Bands ◽  
Mechanical Filter ◽  
Vibration And Sound Radiation

This paper presents both theoretically and experimentally a new kind of vibration isolator called tunable mechanical filter which consists of four parallel hybrid periodic rods connected between two plates. The rods consist of an assembly of periodic cells, each cell being composed of a short rod and piezoelectric inserts. By actively controlling the piezoelectric elements, it is shown that the periodic rods can efficiently attenuate the propagation of vibration from the upper plate to the lower one within critical frequency bands and consequently minimize the effects of transmission of undesirable vibration and sound radiation. In such a filter, longitudinal waves can propagate from the vibration source in the upper plate to the lower one along the rods only within specific frequency bands called the “Pass Bands” and wave propagation is efficiently attenuated within other frequency bands called the “Stop Bands”. The spectral width of these bands can be tuned according to the nature of the external excitation. The theory governing the operation of this class of vibration isolator is presented and their tunable filtering characteristics are demonstrated experimentally as functions of their design parameters. The concept of this mechanical filter as presented can be employed in many applications to control the wave propagation and the force transmission of longitudinal vibrations both in the spectral and spatial domains in an attempt to stop/attenuate the propagation of undesirable disturbances.

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