Differential quadrature approximation and the Chebyshev collocation method are adopted to convert the partial differential equation that governs heat transfer into a lumped parameter model. The transient responses of a thermostat are calculated using the Runge-Kutta method. Differential quadrature approximation and the Chebyshev collocation method efficiently determinate the heat transfer properties. A control strategy for a fuzzy logic controller in the system is proposed. The fuzzy logic controller is implemented using assembly language and a single chip 89C51.

This paper presents the application of the method of generalized differential quadrature (GDQ) for the analysis of hydrodynamic thrust bearings. GDQ is a simple, efficient, high-order numerical technique and it uses the information on all grid points to approach the derivatives of the unknown function. The effectiveness of the solution technique is verified by comparing the GDQ computed results with the results of analytical solutions, FEM and FDM results from the published literature. It's seen from the results that GDQ method can easily compete with the existing methods of solution of lubrication problems in respect to its analytical simplicity, smaller computer storage requirements and capability of producing accurate results with very high computational efficiency.

In this paper underwater acoustic wave propagation is studied numerically by Differential Quadrature method. Numerical methods are different with respect to accuracy. computer costs and practical flexibility. In this study Differential Quadrature (DQ) method is applied for numerical solution of underwater acoustic wave for first time. Two experimental cases are used to validate the two-dimensional wave model. first the numerical results are verified by analytical solution and the second one showed the applicability of current method in complex domain. Comparisons demonstrate the efficiency. accuracy and robustness of the Differential Quadrature method for acoustic wave simulation.

Kinematic wave equation is a simplification of the fully dynamic wave equation of the fluid flow in open channels. In this equation, the inertia and pressure forces are neglected compared to the gravity force and the friction. Due to the simplicity of kinematic wave, many researchers are still interested in this model in its range of applicability. Until now; various numerical methods such as Finite Difference (FD) and Finite Element (FE) have been used for solution of kinematic wave equation. Differential Quadrature Method (DQM) as an alternative numerical method has attracted the attention of some researchers because of its stability, accuracy and efficiency. In this study, the applicability of DQM for solution of the kinematic wave equation is investigated. For evaluation of this method, the results were compared with analytical solution and observed data. Results of this study show that the type of grid distribution affects the results significantly. The cosine grid distribution is better than uniform grid distribution as it was suggested by previous applications in the literature. DQM for simulating kinematic wave model is not sensitive to choice of the test functions. In general, DQM can be considered as another numerical method for kinematic wave equation using less number of grid points to achieve accurate results. It is also unconditionally stable. The main disadvantage of the kinematic wave equation is its failure to predict wave attenuation. This can be resolved by using diffusion wave model and the same numerical technique.

In this research, in order to investigate the effect of the piezoelectric patch which is used as a sensor or actuator in rotating flexible structures such as a helicopter blade, the free vibrations of the rotating rectangular sheet with and without the piezoelectric patch have been presented. First-order shear deformation theory is considered for plate displacement and piezoelectric field. Considering the effect of Coriolis acceleration, centrifugal acceleration and centrifugal in-plane forces, the equations of motion are derived from Hamilton's principle and the electromechanical couple equation is obtained from Maxwell's equation. For piezoelectric, two electrical conditions, open circuit and closed circuit, which are used in sensors and actuators, respectively, have been considered. The equations are discretized with the help of the numerical method of generalized differential squares and the matrices of inertia mass, eccentricity, Coriolis and stiffness matrix are obtained. Natural frequency values for beam and rotating plate have been compared in Abaqus software. Also, the values obtained from the numerical solution in MATLAB have been verified with articles and ABAQUS, which have high accuracy. The effect of parameters such as hub radius, rotation speed, sheet thickness, aspect ratio, piezoelectric patch thickness and applied voltage on the natural frequency of the system has also been investigated.

In this study, the vibration of cracked plates is investigated using differential quadrature method and experimental modal analysis. The crack, which is assumed to be open, is modeled by the extended rotational spring. With its finite length, the crack divides the plate into six segments.Then, the differential quadrature is applied to the governing differential equations of motion and the corresponding boundary and continuity conditions. An eigenvalue analysis is performed on the resulting system of algebraic equations to obtain the natural frequencies of the cracked plate. To ensure the integrity and robustness of the presented method, experimental modal analysis is carried out on cantilever plates having open cracks with finite length and the results are compared with the proposed method. A numerical study is performed to show the effect of length, depth and location of the crack on natural frequencies of the plates. The results verify the accuracy and efficiency of differential quadrature method.

In this paper, the differential quadrature (DQ) method is employed to solve some nonlinear chaotic systems of ordinary differential equations (ODEs). Here, the method is applied to chaotic Lorenz, Chen, Genesio and Rossler systems. The first three chaotic systems are described by three-dimensional systems of ODEs while the last hyperchaotic system is a four-dimensional system of ODEs. It is found that the DQ method is unconditionally stable in solving first-order ODEs. But, care should be taken to choose a time step when applying the DQ method to nonlinear chaotic systems. Similar to all conventional unconditionally stable time integration schemes, the unconditionally stable DQ time integration scheme may also be possible to produce inaccurate results for nonlinear chaotic systems with an inappropriately too large time step sizes. Numerical comparisons are made between the DQ method and the conventional fourth-order Runge-Kutta method (RK4). It is revealed that the DQ method can produce better accuracy than the RK4 using larger time step sizes.