Observability inequalities for wave equations with variable coefficients

2003 ◽  
Author(s):  
Peng-Fei Yao
Keyword(s):  
Wave Equations ◽  
Variable Coefficients

Numerical simulation of higher-order diffusion-wave equations of variable coefficients using the meshless spectral method

2020 ◽  
pp. 2150010
Author(s):  
Manzoor Hussain ◽  
Sirajul Haq
Keyword(s):  
Wave Equations ◽  
Interpolation Method ◽  
Variable Coefficients ◽  
Higher Order ◽  
Implicit Time ◽  
Test Problems ◽  
Time Step ◽  
Diffusion Wave ◽  
Time Step Size ◽  
Time Stepping

In this paper, meshless spectral interpolation technique using implicit time stepping scheme is proposed for the numerical simulations of time-fractional higher-order diffusion wave equations (TFHODWEs) of variable coefficients. Meshless shape functions, obtained from radial basis functions (RBFs) and point interpolation method (PIM), are used for spatial approximation. Central differences coupled with quadrature rule of [Formula: see text] are employed for fractional temporal approximation. For advancement of solution, an implicit time stepping scheme is then invoked. Simulations performed for different benchmark test problems feature good agreement with exact solutions. Stability analysis of the proposed method is theoretically discussed and computationally validated to support the analysis. Accuracy and efficiency of the proposed method are assessed via [Formula: see text], [Formula: see text] and [Formula: see text] error norms as well as number of nodes [Formula: see text] and time step-size [Formula: see text].

Circumferential waves in pre-stressed functionally graded cylindrical curved plates

2014 ◽  
Vol 21 (1) ◽  
pp. 87-97 ◽  
Author(s):  
Jiangong Yu ◽  
Chuanzeng Zhang ◽  
Xiaoming Zhang
Keyword(s):  
Initial Stress ◽  
Wave Equations ◽  
Axial Direction ◽  
Variable Coefficients ◽  
Functionally Graded ◽  
Initial Stresses ◽  
Polynomial Method ◽  
Coupled Wave Equations ◽  
Graded Material ◽  
Polynomial Series

AbstractInitial stress (pre-stress) in functionally graded material (FGM) structures is often inevitable because of the limitation of available manufacturing technology. On the basis of the “mechanics of incremental deformations”, the circumferential wave characteristics in FGM cylindrical curved plates under uniform initial stresses in the radial and axial directions are investigated. The Legendre polynomial series method is used to solve the coupled wave equations with variable coefficients. Through numerical examples, the convergence of the polynomial method is discussed. The influences of the initial stresses on the circumferential Lamb-like and the circumferential SH waves are investigated, respectively. Numerical results show that they are quite distinct. Moreover, the influences of the initial stress in the axial direction are very different from those in the radial direction, both on the dispersion curves and on the displacement and stress distributions.

scholarly journals Periodic solutions of a quasilinear wave equations with variable coefficients.

2014 ◽  
Vol 2014 (3) ◽  
pp. 147-155 ◽  
Author(s):  
Игорь Рудаков ◽  
Igor Rudakov ◽  
Алексей Лукавый ◽  
Aleksey Lukavyy
Keyword(s):  
Boundary Conditions ◽  
Periodic Solutions ◽  
Existence Theorem ◽  
Wave Equations ◽  
Variable Coefficients ◽  
Neumann Condition ◽  
Quasilinear Wave Equations ◽  
Prove Existence Theorem

We prove existence theorem for periodic in time solutions of quasilinear wave level of variable coefficients and homogeneous boundary conditions, one of which is a Neumann condition.

A NOVEL VARIATIONAL PERSPECTIVE TO FRACTAL WAVE EQUATIONS WITH VARIABLE COEFFICIENTS

Fractals ◽  
2021 ◽  
Author(s):  
XUE-FENG HAN ◽  
KANG-LE WANG
Keyword(s):  
Wave Equations ◽  
Variational Principles ◽  
Variable Coefficients ◽  
Transform Method ◽  
Numerical Examples ◽  
Fractal Models ◽  
Inverse Transform ◽  
Fractal Calculus ◽  
Different Types ◽  
Wave Models

This paper aims at establishing two different types of wave models with unsmooth boundaries by the fractal calculus, and their fractal variational principles are successfully designed by employing the fractal semi-inverse transform method. A new approximate technology is proposed to solve the two fractal models based on the variational principle and fractal two-scale transform method. Finally, two numerical examples show that the proposed method is efficient and accurate, which can be extended to solve different types of fractal models.

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