The Forced Vibration Analysis of Beams Based on a Time-Domain Differential Quadrature Method

2015 ◽  
Vol 741 ◽  
pp. 108-112
Author(s):  
Fan Lin ◽  
Jian She Peng ◽  
Liu Yang
Keyword(s):  
Time Domain ◽  
Differential Quadrature Method ◽  
Boundary Value ◽  
Linear Equations ◽  
Initial Boundary ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Computational Accuracy ◽  
Forced Vibration Analysis ◽  
Initial Boundary Value

Under driving forceF(x,t)=Q*sinwt, a time-domain DQ (differential quadrature) method for dynamic problems of beams with initial-boundary value conditions is presented in this paper. On the basis of governing partial differential equation, the discrete DQ method adopted both in space domain and time domain in this method gives rise to new differential quadrature linear equations with complete initial-boundary value conditions for solving all parameters of the displacement-field. The numerical examples show that the computational accuracy and efficiency of time-domain DQ method is better than finite element method based on time-domain difference.

A Time-Domain DQ Approach for Vibration Analysis of Beams

2013 ◽  
Vol 631-632 ◽  
pp. 957-961
Author(s):  
Jian She Peng ◽  
Gang Xie ◽  
Liu Yang ◽  
Yu Quan Yuan
Keyword(s):  
Time Domain ◽  
Vibration Analysis ◽  
Differential Quadrature Method ◽  
Boundary Value ◽  
Linear Equations ◽  
Initial Boundary ◽  
Differential Quadrature ◽  
Structural Vibration ◽  
Quadrature Method ◽  
Initial Boundary Value

This paper presents a new time-domain DQ (differential quadrature) method for structural vibration analysis. It adopts differential quadrature method both in space domain and in time domain on the basis of governing partial differential equation and initial-boundary value condition of vibration problems of structures, and gets new differential quadrature linear equations with complete initial-boundary value conditions for solving all parameters of the displacement-field. The examples in this paper show the time-domain differential quadrature method is a useful and efficient tool for structural vibration analysis.

scholarly journals Comparative Analysis of Free Optical Vibration of Lamination Composite Optical Beams Using the Boubaker Polynomials Expansion Scheme and the Differential Quadrature Method

ISRN Optics ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-5
Author(s):  
Ugur Yücel ◽  
Emna Gargouri-Ellouze ◽  
Karem Boubaker ◽  
Gökmen Atlihan ◽  
Hasan Çallioglu ◽  
...  
Keyword(s):  
Numerical Solutions ◽  
Differential Quadrature Method ◽  
Initial Boundary ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Initial Boundary Value Problems ◽  
Boubaker Polynomials ◽  
Optical Beams ◽  
Initial Boundary Value ◽  
Expansion Scheme

The effects of stacking sequences of composite laminated optical beams on free vibration frequencies are investigated using two methods: the Boubaker Polynomials Expansion Scheme (pbes) and the Differential Quadrature Method (dqm). In the last decades, these two techniques have been separately performed for obtaining accurate numerical solutions to several initial boundary value problems (Vo et al. 2010, Li et al. 2008, Chen 2003, Hu et al. 2008, Karami et al. 2003, Malekzadeh et al. 2004, Khare et al. 2004, Della and Shu 2005, Ramtekkar et al. 2002, Adam 2003). Conjointly yielded results are compared and discussed.

scholarly journals Characteristics of the Differential Quadrature Method and Its Improvement

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Wang Fangzong ◽  
Liao Xiaobing ◽  
Xie Xiong
Keyword(s):  
Time Domain ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Systematic Analysis ◽  
Runge Kutta Method ◽  
Engineering Computation ◽  
Basic Characteristics ◽  
The Time Domain ◽  
Weighting Coefficients

The differential quadrature method has been widely used in scientific and engineering computation. However, for the basic characteristics of time domain differential quadrature method, such as numerical stability and calculation accuracy or order, it is still lack of systematic analysis conclusions. In this paper, according to the principle of differential quadrature method, it has been derived and proved that the weighting coefficients matrix of differential quadrature method meets the importantV-transformation feature. Through the equivalence of the differential quadrature method and the implicit Runge-Kutta method, it has been proved that the differential quadrature method is A-stable ands-stages-order method. On this basis, in order to further improve the accuracy of the time domain differential quadrature method, a class of improved differential quadrature method ofs-stage 2s-order have been proposed by using undetermined coefficients method and Padé approximations. The numerical results show that the improved differential quadrature method is more precise than the traditional differential quadrature method.

Stability Analysis and Order Improvement for Time Domain Differential Quadrature Method

2015 ◽  
Vol 8 (1) ◽  
pp. 128-144 ◽  
Author(s):  
Fangzong Wang ◽  
Xiaobing Liao ◽  
Xiong Xie
Keyword(s):  
Time Domain ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Systematic Analysis ◽  
Runge Kutta Method ◽  
Engineering Computation ◽  
Basic Characteristics ◽  
The Time Domain ◽  
Weighting Coefficients

AbstractThe differential quadrature method has been widely used in scientific and engineering computation. However, for the basic characteristics of time domain differential quadrature method, such as numerical stability and calculation accuracy or order, it is still lack of systematic analysis conclusions. In this paper, according to the principle of differential quadrature method, it has been derived and proved that the weighting coefficients matrix of differential quadrature method meets the important V-transformation feature. Through the equivalence of the differential quadrature method and the implicit Runge-Kutta method, it has been proved that the differential quadrature method is A-stable and s-stage s-order method. On this basis, in order to further improve the accuracy of the time domain differential quadrature method, a class of improved differential quadrature method of s-stage 2s-order has been proposed by using undetermined coefficients method and Padé approximations. The numerical results show that the proposed differential quadrature method is more precise than the traditional differential quadrature method.

scholarly journals A modified cubic B-spline differential quadrature method for three-dimensional non-linear diffusion equations

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 453-463 ◽  
Author(s):  
Sumita Dahiya ◽  
Ramesh Chandra Mittal
Keyword(s):  
Numerical Solutions ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Initial Boundary ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Linear Diffusion ◽  
B Spline ◽  
Non Linear

AbstractThis paper employs a differential quadrature scheme for solving non-linear partial differential equations. Differential quadrature method (DQM), along with modified cubic B-spline basis, has been adopted to deal with three-dimensional non-linear Brusselator system, enzyme kinetics of Michaelis-Menten type problem and Burgers’ equation. The method has been tested efficiently to three-dimensional equations. Simple algorithm and minimal computational efforts are two of the major achievements of the scheme. Moreover, this methodology produces numerical solutions not only at the knot points but also at every point in the domain under consideration. Stability analysis has been done. The scheme provides convergent approximate solutions and handles different cases and is particularly beneficial to higher dimensional non-linear PDEs with irregularities in initial data or initial-boundary conditions that are discontinuous in nature, because of its capability of damping specious oscillations induced by high frequency components of solutions.

scholarly journals Boundary Value Problems for Fourth-Order Sobolev Type Equations

2001 ◽  
Vol 14 (4) ◽  
pp. 425-432
Author(s):  
Alexander I. Kozhanov ◽  
Keyword(s):  
Boundary Value Problems ◽  
Fourth Order ◽  
Boundary Value ◽  
Linear Equations ◽  
Time Moment ◽  
Initial Boundary ◽  
Initial Time ◽  
Sobolev Type ◽  
Initial Time Moment ◽  
Initial Boundary Value

The goal of the article is the study of solvability in the Sobolev spaces of boundary value problems for some classes of Sobolev-type fourth-order linear equations. We will prove that an initial boundary value problems well problems with data both at the initial time moment and the final time moments can be well-posed for the equations under study

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