scholarly journals Least Squares Differential Quadrature Method for the Generalized Bagley–Torvik Fractional Differential Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Constantin Bota ◽  
Bogdan Căruntu ◽  
Mădălina Sofia Paşca ◽  
Dumitru Ţucu ◽  
Marioara Lăpădat
Keyword(s):  
Differential Equation ◽  
Least Squares ◽  
Fractional Differential Equation ◽  
Analytical Solutions ◽  
Differential Quadrature Method ◽  
Accurate Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Approximate Analytical Solutions ◽  
Fractional Differential

In this paper, the least squares differential quadrature method for computing approximate analytical solutions for the generalized Bagley–Torvik fractional differential equation is presented. This new method is introduced as a straightforward and accurate method, fact proved by the examples included, containing a comparison with previous results obtained by using other methods.

scholarly journals On Analytical Solutions of the Fractional Differential Equation with Uncertainty: Application to the Basset Problem

Entropy ◽  
2015 ◽  
Vol 17 (2) ◽  
pp. 885-902 ◽  
Author(s):  
Soheil Salahshour ◽  
Ali Ahmadian ◽  
Norazak Senu ◽  
Dumitru Baleanu ◽  
Praveen Agarwal
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Analytical Solutions ◽  
Fractional Differential ◽  
Basset Problem

scholarly journals Dynamic Analysis of Electrostatic Microactuators Using the Differential Quadrature Method

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Ming-Hung Hsu
Keyword(s):  
Differential Equation ◽  
Dynamic Behavior ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Electrostatic Actuator ◽  
Discrete Eigenvalue ◽  
Electrostatic Actuators ◽  
Finite Element Package ◽  
Length Width

This work studies the dynamic behavior of electrostatic actuators using finite-element package software (FEMLAB) and differential quadrature method. The differential quadrature technique is used to transform partial differential equations into a discrete eigenvalue problem. Numerical results indicate that length, width, and thickness significantly impact the frequencies of the electrostatic actuators. The thickness could not affect markedly the electrostatic actuator capacities. The effects of varying actuator length, width, and thickness on the dynamic behavior and actuator capacities in electrostatic actuator systems are investigated. The differential quadrature method is an efficient differential equation solver.

scholarly journals A Least Squares Differential Quadrature Method for a Class of Nonlinear Partial Differential Equations of Fractional Order

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1336
Author(s):  
Constantin Bota ◽  
Bogdan Căruntu ◽  
Dumitru Ţucu ◽  
Marioara Lăpădat ◽  
Mădălina Sofia Paşca
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Least Squares ◽  
Least Squares Method ◽  
Differential Quadrature Method ◽  
Nonlinear Partial Differential Equations ◽  
Differential Quadrature ◽  
Test Problems ◽  
Quadrature Method ◽  
Partial Differential

In this paper a new method called the least squares differential quadrature method (LSDQM) is introduced as a straightforward and efficient method to compute analytical approximate polynomial solutions for nonlinear partial differential equations with fractional time derivatives. LSDQM is a combination of the differential quadrature method and the least squares method and in this paper it is employed to find approximate solutions for a very general class of nonlinear partial differential equations, wherein the fractional derivatives are described in the Caputo sense. The paper contains a clear, step-by-step presentation of the method and a convergence theorem. In order to emphasize the accuracy of LSDQM we included two test problems previously solved by means of other, well-known methods, and observed that our solutions present not only a smaller error but also a much simpler expression. We also included a problem with no known exact solution and the solutions computed by LSDQM are in good agreement with previous ones.

Free vibration analysis of a rotating double tapered beam with flexible root via differential quadrature method

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mustafa Tolga Tolga Yavuz ◽  
İbrahim Özkol
Keyword(s):  
Differential Equation ◽  
Free Vibration ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Operating Conditions ◽  
Design Parameters ◽  
Quadrature Method ◽  
Content Type ◽  
Uniform Beam ◽  
Governing Differential Equation

Purpose This study aims to develop the governing differential equation and to analyze the free vibration of a rotating non-uniform beam having a flexible root and setting angle for variations in operating conditions and structural design parameters. Design/methodology/approach Hamiltonian principle is used to derive the flapwise bending motion of the structure, and the governing differential equations are solved numerically by using differential quadrature with satisfactory accuracy and computation time. Findings The results obtained by using the differential quadrature method (DQM) are compared to results of previous studies in the open literature to show the power of the used method. Important results affecting the dynamics characteristics of a rotating beam are tabulated and illustrated in concerned figures to show the effect of investigated design parameters and operating conditions. Originality/value The principal novelty of this paper arises from the application of the DQM to a rotating non-uniform beam with flexible root and deriving new governing differential equation including various parameters such as rotary inertia, setting angle, taper ratios, root flexibility, hub radius and rotational speed. Also, the application of the used numerical method is expressed clearly step by step with the algorithm scheme.

Dynamic Stability Analysis of Functionally Graded Plates Subjected to Complex Loads

2014 ◽  
Vol 578-579 ◽  
pp. 679-686 ◽  
Author(s):  
Sheng Fei Yang ◽  
Hao Chen ◽  
Chun Ran
Keyword(s):  
Least Squares ◽  
Dynamic Stability ◽  
Differential Quadrature Method ◽  
Instability Region ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Moving Least Squares ◽  
Quadrature Method ◽  
Thickness Direction ◽  
Functionally Graded Plates

The paper investigates the dynamic stability of thick functionally graded plates subjected to aero-thermo-mechanical loads, using the moving least squares differential quadrature method. Temperature field is assumed to be a uniform distribution over the plate plane, and varied in the thickness direction only. Material properties are assumed to be temperature dependent and graded in the thickness direction in the simple power law manner. The equilibrium equations governing the dynamic stability of the plate are derived by the Hamilton’s principle, then these equations are discretized by the moving least squares differential quadrature method. The boundaries of the instability region are obtained using the principle of Bolotin’s method and are conveniently represented in the non-dimensional excitation frequency to load amplitude plane. The influence of various factors such as gradient index, temperature, mechanical and aerodynamic loads, thickness and aspect ratios, as well as the boundary conditions on the dynamic instability region are carefully studied.

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