Harmonic Waves in Fiber-Reinforced Orthotropic Elastic Composites

1981 ◽  
Vol 48 (4) ◽  
pp. 967-971 ◽  
Author(s):  
S. Nemat-Nasser ◽  
M. Yamada
Keyword(s):  
Dispersion Curves ◽  
Orthotropic Materials ◽  
Harmonic Waves ◽  
Fiber Reinforced ◽  
Dispersive Property ◽  
Elastic Composites

The dispersive property of fiber-reinforced elastic composites consisting of orthotropic materials is studied. Based on a new quotient recently proposed by one of the authors, approximate dispersion curves are obtained, and the influence of anisotropy is illustrated.

On Harmonic Waves in Layered Composites

1977 ◽  
Vol 44 (4) ◽  
pp. 689-695 ◽  
Author(s):  
S. Minagawa ◽  
S. Nemat-Nasser
Keyword(s):  
Dispersion Relations ◽  
Harmonic Waves ◽  
Layered Composites ◽  
Fiber Reinforced ◽  
Elastic Composite ◽  
Elastic Composites ◽  
Special Case ◽  
Layer Problem

For harmonic waves propagating in a layered elastic composite, approximate dispersion relations are developed. Both waves propagating in the direction of the layers, and those propagating obliquely to this direction, are considered. The layer problem is treated as a special case of fiber-reinforced elastic composites. For illustration, the approximate results are compared with the exact ones for the special case of homogeneous layers.

On prismatic and bending bifurcations of fiber-reinforced elastic membranes under swelling with application to aortic aneurysms

2021 ◽  
pp. 108128652110587
Author(s):  
Murtadha J. Al-Chlaihawi ◽  
Heiko Topol ◽  
Hasan Demirkoparan ◽  
José Merodio
Keyword(s):  
Axial Loading ◽  
Material Constant ◽  
Exponential Model ◽  
Aortic Aneurysms ◽  
Orthotropic Materials ◽  
Fiber Direction ◽  
Fiber Reinforced ◽  
The Matrix ◽  
Elastic Membranes ◽  
Fiber Winding

The influence of swelling on prismatic and bending bifurcation modes of inflated thin-walled cylinders under axial loading is examined. The bifurcation criteria for a membrane cylinder subjected to combined axial loading, internal pressure, and swelling is provided. We consider orthotropic materials with two preferred directions which are mechanically equivalent and symmetrically disposed. The mechanical behavior of the matrix is described by a swellable isotropic model. The isotropic material is augmented with two functions that are equal, each one of them accounting for the existence of a unidirectional reinforcement. Two reinforcing models that depend only on the stretch in the fiber direction are considered: the so-called standard reinforcing model and an exponential one. The analysis of bifurcation modes for these models under the conditions at hand may establish the connection with modeling of the normal and diseased aorta in arterial wall tissue. The effects of the axial stretch, the strength of the fiber reinforcement and the fiber winding angle on the onset of prismatic and bending bifurcations are investigated. It is shown that for membranes without fibers, prismatic bifurcation is not feasible. On the other hand, bending bifurcation is more likely to occur for swollen cylinders. However, for a particular model of fiber-reinforced membranes, the standard model, there exists a domain of deformation values together with material constant values that may trigger prismatic bifurcation. The exponential model does not allow prismatic bifurcations. Both models allow bending bifurcation and may or may not trigger it depending on the deformation together with material parameters.

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.

Dispersion of waves in two-dimensional layered, fiber-reinforced, and other elastic composites

1984 ◽  
Vol 19 (1-2) ◽  
pp. 119-128 ◽  
Author(s):  
S. Minagawa ◽  
S. Nemat-Nasser ◽  
M. Yamada
Keyword(s):  
Two Dimensional ◽  
Fiber Reinforced ◽  
Elastic Composites

scholarly journals A Recursive Legendre Polynomial Analytical Integral Method for the Fast and Efficient Modelling Guided Wave Propagation in Rectangular Section Bars of Orthotropic Materials

2021 ◽  
Vol 26 (3) ◽  
pp. 221-230
Author(s):  
Xiaoming Zhang ◽  
Shuangshuang Shao ◽  
Shuijun Shao
Keyword(s):  
Numerical Integration ◽  
Legendre Polynomial ◽  
Guided Waves ◽  
Three Dimensional ◽  
Infinite Plate ◽  
Wave Dispersion ◽  
Dispersion Curves ◽  
Guided Wave ◽  
Orthotropic Materials ◽  
Polynomial Method

Ultrasonic guided waves are widely used in non-destructive testing (NDT), and complete guided wave dispersion, including propagating and evanescent modes in a given waveguide, is essential for NDT. Compared with an infinite plate, the finite lateral width of a rectangular bar introduces a greater density of modes, and the dispersion solutions become more complicated. In this study, a recursive Legendre polynomial analytical integral (RLPAI) method is presented to calculate the dispersion behaviours of guided waves in rectangular bars of orthotropic materials. The existing polynomial method involves a large number of numerical integration steps, and it is often computationally costly to compute these integrals. The presented RLPAI method uses analytical integration instead of numerical integration, thus leading to a significant improvement in the computational speed. The results are compared with those published previously to validate our method, and the computational efficiency is discussed. The full three-dimensional dispersion curves are plotted. The dispersion characteristics of propagating and evanescent waves are investigated in various rectangular bars. The influences of different width-to-thickness ratios on the dispersion curves of four types of low-order modes for a rectangular bar of an orthotropic composite are illustrated.

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