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.

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.

Effect of Functionally Graded Materials on Resonances of Bending Shafts Under Time-Dependent Axial Loading

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Arnaldo J. Mazzei ◽  
Richard A. Scott
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Functionally Graded Materials ◽  
Parametric Resonance ◽  
Axial Load ◽  
Volume Fraction ◽  
Axial Loading ◽  
Functionally Graded ◽  
Time Dependent ◽  
Graded Materials

The effect of functionally graded materials (FGMs) on resonances of bending shafts under time-dependent axial loading is investigated. The axial load is taken to be a sinusoidal function of time and the shaft is modeled via an Euler–Bernoulli beam approach (pin-pin boundary conditions). The axial load enters the formulation via a “buckling load type” approach. For generality, two distinct particulate models for the FGM are considered, namely, one involving power law variations and another based on a volume fraction approach, for both Young’s modulus and material density. The spatial dependence in the partial differential equation of motion is suppressed by utilizing Galerkin’s method with homogeneous beam mode shapes. To check the accuracy of this approximation, numerical solutions for the boundary value problem represented by the original partial differential equation are obtained using MAPLE®’s PDE solver. Good agreement (within 5%) was found between the PDE results and the one-mode approximation. The approximation leads to ordinary differential equations that have time-dependent coefficients and are prone to parametric and forced motions instabilities. Hill’s infinite determinant approach is used to study stability. The main focus is on the primary parametric resonance. It was found that in most cases the FGM shafts increase the parametric resonance frequencies substantially, while decreasing the zone thicknesses, both desirable trends. For instance, for an axial load about one-third of the buckling value, an aluminum/silicon carbide shaft, when compared to a pure aluminum shaft, increases the primary parametric resonance by 21% and decreases instabilities by 23%. For one model of FGM, the sensitivity of the results to volume fraction variations is examined and it was found that increasing the volume fraction is not uniformly beneficial. Results for other parametric zones are also presented. Forced resonances are also briefly treated.

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