Cauchy formalism for Lamb waves in functionally graded plates

2018 ◽  
Vol 25 (6) ◽  
pp. 1227-1232 ◽  
Author(s):  
Sergey V. Kuznetsov
Keyword(s):  
Wave Propagation ◽  
Functionally Graded Materials ◽  
Lamb Wave ◽  
Lamb Waves ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Graded Materials ◽  
Anisotropic Plates ◽  
Transverse Inhomogeneity ◽  
Lamb Wave Propagation

Propagation of harmonic Lamb waves in plates made of functionally graded materials with transverse inhomogeneity is analyzed by applying Cauchy six-dimensional formalism previously developed for the study of Lamb wave propagation in homogeneous or stratified anisotropic plates. For anisotropic plates with arbitrary transverse inhomogeneity a closed form implicit solution for the dispersion equation is derived and analyzed.

scholarly journals Lamb Waves in Anisotropic Functionally Graded Plates: A Closed Form Dispersion Solution

2019 ◽  
Vol 36 (1) ◽  
pp. 1-6
Author(s):  
S. V. Kuznetsov
Keyword(s):  
Closed Form ◽  
Dispersion Equation ◽  
Lamb Waves ◽  
Functionally Graded ◽  
Stratified Media ◽  
Exponential Mapping ◽  
Functionally Graded Plates ◽  
Graded Materials ◽  
Transverse Inhomogeneity ◽  
Dispersion Solution

ABSTRACTPropagation of harmonic Lamb waves in plates made of functionally graded materials (FGM) with transverse inhomogeneity is studied by combination of the Cauchy six-dimensional formalism and matrix exponential mapping. For arbitrary transverse inhomogeneity a closed form implicit solution for dispersion equation is derived and analyzed. Both the dispersion equation and the corresponding solution resemble ones obtained for stratified media. The dispersion equation and the corresponding solution are applicable to media with arbitrary elastic (monoclinic) anisotropy.

P Wave Propagation in the Functionally Graded Materials

2013 ◽  
Vol 706-708 ◽  
pp. 1685-1688
Author(s):  
Li Gang Zhang ◽  
Hong Zhu ◽  
Hong Biao Xie ◽  
Lin Yuan
Keyword(s):  
Differential Equation ◽  
Wave Propagation ◽  
Functionally Graded Materials ◽  
Wave Motion ◽  
Mass Density ◽  
Functionally Graded ◽  
P Wave ◽  
Exponential Form ◽  
Graded Materials ◽  
P Wave Velocity

The P wave propagation in the functionally graded materials (FGM) is studied. The differential equation with varied-coefficient of wave motion in the FGM is established. By using of the WKBJ approximation method, the differential equation with varied-coefficient is solved, and the closed-analytical solutions of displacement in the FGM are obtained. The properties of the FGM whose shear modulus and mass density are gradually varying in exponential form are calculated; the curves of P wave velocity and amplitude, and the general properties of the P wave in the FGM are analyzed.

Lamb Wave Propagation in Anisotropic Laminates

1990 ◽  
Vol 57 (4) ◽  
pp. 923-929 ◽  
Author(s):  
G. R. Liu ◽  
J. Tani ◽  
K. Watanabe ◽  
T. Ohyoshi
Keyword(s):  
Wave Propagation ◽  
Energy Distribution ◽  
Hybrid Composite ◽  
Lamb Wave ◽  
Composite Laminates ◽  
Strain Energy ◽  
Lamb Waves ◽  
Energy Distributions ◽  
Phase Velocities ◽  
Lamb Wave Propagation

The wave propagation in arbitrary anisotropic laminates is investigated on the basis of an exact theory. The dispersion relations of Lamb waves are determined for graphite/epoxy symmetric angle-ply laminates and hybrid composite ones which consist of carbon/epoxy and glass/epoxy layers. The dispersion and anisotropy of phase velocities for fundamental modes are discussed in detail. The energy distributions in the thickness direction of laminates are calculated for each kind of Lamb wave. A hybrid composite laminate is found to have better capability in absorbing impact energy by analyzing the strain energy distribution during the wave propagation. The results of the strain energy distribution are useful in determining the arrangement and the fiber orientation of the layers of hybrid composite laminates.

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