scholarly journals Properties of Love Waves in Functional Graded Saturated Material

Materials ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 2165 ◽  
Author(s):  
Zhen Qu ◽  
Xiaoshan Cao ◽  
Xiaoqin Shen
Keyword(s):  
Power Series ◽  
Transversely Isotropic ◽  
Variable Coefficients ◽  
Love Waves ◽  
Series Method ◽  
Power Series Method ◽  
Material Parameters ◽  
Non Destructive Evaluation ◽  
Saturated Layer ◽  
Non Destructive

In the present study, the propagation of Love waves is investigated in a layered structure with two different homogeneity saturated materials based on Biot’s theory. The upper layer is a transversely isotropic functional graded saturated layer, and the substrate is a saturated semi-space. The inhomogeneity of the functional graded layer is taken into account. Furthermore, the gradient coefficient is employed as the representation of the relation with the layer thickness and the material parameters, and the power series method is applied to solve the variable coefficients governing the equations. In this regard, the influence of the gradient coefficients of saturated material on the dispersion relations, and the attenuation of Love waves in this structure are explored, and the results of the present study can provide theoretical guidance for the non-destructive evaluation of functional graded saturated material.

scholarly journals Applications of General Residual Power Series Method to Differential Equations with Variable Coefficients

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Bochao Chen ◽  
Li Qin ◽  
Fei Xu ◽  
Jian Zu
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Variable Coefficients ◽  
Series Solutions ◽  
Series Method ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Residual Power Series ◽  
Analytical Series ◽  
Residual Power

This paper is devoted to studying the analytical series solutions for the differential equations with variable coefficients. By a general residual power series method, we construct the approximate analytical series solutions for differential equations with variable coefficients, including nonhomogeneous parabolic equations, fractional heat equations in 2D, and fractional wave equations in 3D. These applications show that residual power series method is a simple, effective, and powerful method for seeking analytical series solutions of differential equations (especially for fractional differential equations) with variable coefficients.

scholarly journals An analytical solution for a fractional heat-like equation with variable coefficients

2017 ◽  
Vol 21 (4) ◽  
pp. 1759-1764 ◽  
Author(s):  
Run-qing Cui ◽  
Tao Ban
Keyword(s):  
Analytical Solution ◽  
Power Series ◽  
Solution Process ◽  
Fractional Power ◽  
Variable Coefficients ◽  
Series Method ◽  
Power Series Method ◽  
Fractional Power Series

The fractional power series method is used to solve a fractional heat-like equations with variable coefficients. The solution process is elucidated, and the results show that the method is simple but effective.

STRESS ANALYSIS OF TRANSVERSELY ISOTROPIC CYLINDER UNDER ARBITRARY AXISYMMETRIC LOAD

2008 ◽  
Vol 22 (09n11) ◽  
pp. 1431-1436
Author(s):  
BIN LIU ◽  
QUAN-SHENG LIU
Keyword(s):  
Normal Load ◽  
Axial Stress ◽  
Transversely Isotropic ◽  
Series Method ◽  
Unknown Parameters ◽  
Power Series Method ◽  
Isotropic Cylinder ◽  
Material Parameters ◽  
Distribution Of Stresses ◽  
Transversely Isotropic Cylinder

Power series method is used to analyze the distribution of stresses of the transversely isotropic cylinder under arbitrary axisymmetrical normal load. The stress function and normal load are expanded as the form of Fourier series. Unknown parameters in equations are determined using boundary conditions and final solutions of stress and displacement are obtained accordingly. The analysis of stresses obtained from different material parameters shows that the axial stress is significantly affected by Young's modulus and the circumference stress is sensitive to the variation of Poisson's ratio.

scholarly journals Symmetry Analysis and Exact Solutions to the Space-Dependent Coefficient PDEs in Finance

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Hanze Liu
Keyword(s):  
Power Series ◽  
Exact Solutions ◽  
Variable Coefficients ◽  
Similarity Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Series Method ◽  
Lie Symmetry Analysis ◽  
Power Series Method ◽  
Generalized Power Series

The variable-coefficients partial differential equations (vc-PDEs) in finance are investigated by Lie symmetry analysis and the generalized power series method. All of the geometric vector fields of the equations are obtained; the symmetry reductions and exact solutions to the equations are presented, including the exponentiated solutions and the similarity solutions. Furthermore, the exact analytic solutions are provided by the transformation technique and generalized power series method, which has shown that the combination of Lie symmetry analysis and the generalized power series method is a feasible approach to dealing with exact solutions to the variable-coefficients PDEs.

scholarly journals Approximate analytic solution for multi-dimensional fractional wave-like equation

2020 ◽  
Vol 24 (4) ◽  
pp. 2645-2652
Author(s):  
Jian-She Sun
Keyword(s):  
Power Series ◽  
Fractional Derivatives ◽  
Analytic Solution ◽  
Fractional Power ◽  
Variable Coefficients ◽  
Approximate Analytic Solution ◽  
Series Method ◽  
Power Series Method ◽  
Fractional Power Series

The fractional power series method is used to solve 2- and 3-D fractional wave-like models with variable coefficients. The fractional derivatives are described in the Caputo sense. Two examples are considered to show the effectiveness and convenience of the method.

The Scope of the Power Series Method

2013 ◽  
Vol 86 (1) ◽  
pp. 56-62
Author(s):  
Richard Beals
Keyword(s):  
Power Series ◽  
Series Method ◽  
Power Series Method
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