Time integration of rectangular membrane free vibration using spline-based differential quadratu
Journal Title: Journal of Applied and Computational Mechanics - Year 2016, Vol 2, Issue 2
Abstract
In this paper, numerical spline-based differential quadrature is presented for solving the boundary and initial value problems, and its application is used to solve the fixed rectangular membrane vibration equation. For the time integration of the problem, the Runge–Kutta and spline-based differential quadrature methods have been applied. The Runge–Kutta method was unstable for solving the problem, with large errors in its results, but the spline-based differential quadrature method obtained results that agree with the exact solution. The relative errors were calculated and investigated for different values of time and spatial nodes of discretisation. It seems that the spline-based differential quadrature method is proper for the full simulation of membrane vibration in both spatial and temporal solutions. For the time solving of the membrane vibration, conventional methods, such as the Runge–Kutta method, are not useful even if the time steps are considered too small.
Authors and Affiliations
Sara Javidpoor, Nassim Ale Ali, Amer Kabi
Keywords
Related Articles
- EP ID EP178283
- DOI 10.22055/jacm.2016.12365
- Views 112
- Downloads 0
Bending Analysis of Thick Isotropic Plates by Using 5th Order Shear Deformation Theory
A 5th order shear deformation theory considering transverse shear deformation effect as well as transverse normal strain deformation effect is presented for static flexure analysis of simply supported isotropic plate....
Concerning the Effect of a Viscoelastic Foundation on the Dynamic Stability of a Pipeline System Conveying an Incompressible Fluid
In this paper, we present an analytical method for solving a well-posed boundary value problem of mathematical physics governing the vibration characteristics of an internal flow propelled fluid-structure interaction whe...
Uniaxial buckling analysis comparison of nanoplate and nanocomposite plate with central square cut out using domain decomposition method
A comparison of buckling analysis of the nanoplate and nanocomposite plate with central square hole embedded in Winkler foundation is presented in this article. In order to enhance mechanical properties of nanoplate with...
Conjugate and directional chaos control methods for reliability analysis of CNT–reinforced nanocomposite beams under buckling forces; a comparative study
The efficiency and robustness of reliability methods are two important factors in first order reliability method (FORM). The conjugate choice control (CCC) and directional chaos control method (DCC) were developed to imp...
Springbackward Phenomenon of a Transversely Isotropic Functionally Graded Composite Cylindrical Shell
This article gives an approach to predict the springbackward phenomena during post solidification cooling in a functionally graded hybrid composite cylindrical shell with transverse isotropic structure. Here the material...