Papers by Keyword: Differential Quadrature Method

Abstract: This paper investigates free transverse vibrations of finite Euler–Bernoulli beams resting on viscoelastic Pasternak foundations. The differential quadrature methods (DQ) are applied directly to the governing equations of the free vibrations. Under the simple supported boundary condition, the natural frequencies of the transverse vibrations are calculated, and compared with the results of the complex mode analysis method. The numerical results obtained by using the DQ and the complex mode methods are in good agreement for the first seven order natural frequencies, but with the growth of the orders, the small quantitative differences between them increase. The effects of the foundation parameters on the natural frequencies are also studied in numerical examples.

Abstract: In this study, the entropy generation due to the flow of a gravity-driven laminar viscous incompressible fluid through an incline channel is investigated. Fully developed flow field is solved for a Newtonian fluid. Then, the temperature field is numerically resolved using Differential Quadrature Method (DQM) subject to isothermal boundary conditions on the walls and constant rectangular profile at the inlet. The result of DQM is compared to analytical solution and method of lines (MOL) numerical method. Rate of entropy generation is found and its relation with temperature and velocity field is examined.

Abstract: The dynamic characteristics and stability of the thermoelastic coupling moving rectangular plate are investigated. Based on the heat conduction equation involving the thermoelastic coupling term and the differential equation of motion of the plate subjected to the thermal shock, the thermoelastic coupling differential equation of the moving plate is derived. Dimensionless complex frequencies of the thermoelastic coupling moving rectangular plate with two opposite edges simply supported and other two edges clamped are calculated by the differential quadrature method. The results show that the first mode behaves divergent instability firstly, and the critical divergent moving speed of the first mode increase with the increase of the thermoelastic coupling factor for the two kinds of boundary conditions.

Abstract: The vortex structure of lid-driven flow in a cuboid cavity with one or a pair of moving lids is numerated using the differential quadrature method (DQM). According to the characteristics of cavity driven flow, the dimensionless governing equations and its boundary conditions used to describe the flow are established. Based on a non-staggered grid technology, the polynomial-based DQM is combined with the SIMPLE strategy to solve three-dimensional (3D) cavity driven flow. The suitable boundary condition for pressure correction equation on a non-staggered system is implemented and the continuity equation on the boundary is enforced to be satisfied. The 3D vortex structure distributions in a cuboid cavity are obtained for different Reynolds numbers and different driving modes. The analysis shows that the DQM is very suitable for the simulation of 3D vortex structure in a cavity.

Abstract: The Differential Quadrature Method（abbreviated as DQM）is easy to be implemented by computers to solve many problems in engineering mechanics. In the field of pipe vibration methods are mainly finite element method , finite difference calculus and so on. In the formation of coefficient matrix these methods need to calculate a large number of numerical integration , resulting in low efficiency, while we can use matlab to program, taking the advantage of easy programming of DQM, after establishing mathematical model of the pipe conveying fluid .The program designed in this paper can be a very good solution to pipe nature frequency.After obtaining the nature frequency, we have analyzed the relationship between pipe length and nature frequency and have found out the critical value of the pipe length. The method can also be applied to engineering filed related .

Abstract: In this paper, the free vibration of moderately thick annular sector plates made of functionally graded materials is studied using the Differential Quadrature Method (DQM). The material properties of the functionally graded plate are assumed to vary continuously through the thickness, according to a power-law distribution. The governing differential equations of motion are derived based on the First order Shear Deformation plate Theory (FSDT) and then solved numerically using DQM under different boundary conditions. The results for the isotropic plates which are derivable with this approach are presented and compared with the literature and they are in good agreement. The natural frequencies of the functionally graded moderately thick annular sector plates under various combinations of clamped, simple supported and free boundary conditions are presented for the first time. The effects of boundary conditions, sector angle, radius ratio, thickness to outer radius ratio, volume fraction exponent and variation of the Poisson’s ratio on the free vibration behavior of the plate are studied

Abstract: The paper sets up an upwind local differential quadrature-Lagrange interpolation (DQ-Lagrange) method for solving the flow field in the interlocking labyrinth seal. The implementation of the Dirichlet boundary condition and the Neumann boundary condition is improved. The paper analyzes the influence of support domain size, the implementation of boundary condition and the upwind scheme on the accuracy of the calculation. Numerical simulation result shows that the high order Lagrange interpolation may cause numerical oscillation and the local differential quadrature method is recommended. The upwind support domain can improve the accuracy of the calculation. Solution accuracy may be better in case of that the velocity support domain is larger than the pressure support domain.

Abstract: The vibration characteristics of the thermoelastic coupling rectangular plate under the action of uniformly distributed tangential follower force are investigated. The coupled thermoelastic differential equation of the plate under the action of uniformly distributed tangential follower force was derived. Dimensionless complex frequencies of the thermoelastic coupling rectangular plate with one edge clamped and other three edges simply supported, two opposite edges simply supported and other two edges clamped were calculated by the differential quadrature method. The effects of the dimensionless thermoelastic coupling factor on the stability and critical load of the thin plate were analyzed. The results show that the flutter loads of the coupled modes increase with the increase of the dimensionless coupled thermoelastic factor and the aspect ratio.

Abstract: The present paper investigates the dynamic characteristics and stability of moving functionally graded material rectangular thin plate. Based on Voigt model, the material properties are assumed to vary continuously through their thickness according to a power-law distribution of the volume fractions of the plate constituents. By the first order shear deformation theory, the differential equations of motion of the moving FGM rectangular plate are derived. The vibration frequencies are obtained from the solution of a generalized eigenvalue problem. Entire computational work is carried out in a normalized square domain obtained through an appropriate domain mapping technique. Results of the reduced problem revealed excellent agreement with other studies. The dimensionless complex frequencies of the moving FGM rectangular plate with four edges simply supported are calculated by the differential quadrature method. The effects of gradient index, aspect ratio, and dimensionless moving speed on the transverse vibration and stability of the moving FGM rectangular plate are analyzed. Results are furnished in dimensionless amplitude–frequency vs. dimensionless moving speed in the form of curves and pictorial representations of some vibration mode shapes are made.

Abstract: A new differential quadrature element model is presented for the second-order elasto-plastic analysis of frames in this study. The new model is based on the differential quadrature method (DQM) and the finite-cut technique. Firstly the basic equilibrium differential equations of members, the compatibility conditions of joints and the equilibrium equations of joints for the second-order analysis of frames are established. The differential quadrature method is used to discretize the basic equations and then the stiffness equations of the whole structure can be derived. While the corresponding boundary conditions are considered, the mechanical behavior of frames can be obtained. The yielding development along the axis of the member can be taken into consideration by selecting several discrete points and simultaneously the yielding development across the section can be considered using the layered approach. The full historical second-order elasto-plastic analysis is achieved by the incremental iterative algorithm. According to the new model derived in this paper, the interrelated structural calculating program is worked out. The results of numerical examples demonstrate the validity of the differential quadrature element model (DQEM). The new model can be used in the second-order elasto-plastic analysis of arbitrary frames.