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.

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.

Eigen Solutions of Grouped Turbo Blades Solved by the Generalized Differential Quadrature Method

2001 ◽  
Author(s):  
J. H. Kuang ◽  
M. H. Hsu
Keyword(s):  
Eigenvalue Problem ◽  
Natural Frequencies ◽  
Eigenvalue Problems ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Discrete Eigenvalue ◽  
Generalized Differential Quadrature Method ◽  
Generalized Differential ◽  
Eigen Solutions

The eigenvalue problems of grouped turbo blades were numerically formulated by using the generalized differential quadrature method (GDQM). Different boundary approaches accompanying the GDQM to transform the partial differential equations of grouped turbo blades into a discrete eigenvalue problem are discussed. Effects of the number of sample points and the different boundary approaches on the accuracy of the calculated natural frequencies are also studied. Numerical results demonstrated the validity and the efficiency of the GDQM in treating this type of problem.

Eigensolutions of Grouped Turbo Blades Solved by the Generalized Differential Quadrature Method

2002 ◽  
Vol 124 (4) ◽  
pp. 1011-1017 ◽  
Author(s):  
J. H. Kuang ◽  
M. H. Hsu
Keyword(s):  
Partial Differential Equations ◽  
Eigenvalue Problem ◽  
Natural Frequencies ◽  
Eigenvalue Problems ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Discrete Eigenvalue ◽  
Generalized Differential Quadrature Method ◽  
Generalized Differential

The eigenvalue problems of grouped turbo blades were numerically formulated by using the generalized differential quadrature method (GDQM). Different boundary approaches accompanying the GDQM to transform the partial differential equations of grouped turbo blades into a discrete eigenvalue problem are discussed. Effects of the number of sample points and the different boundary approaches on the accuracy of the calculated natural frequencies are also studied. Numerical results demonstrated the validity and the efficiency of the GDQM in treating this type of problem.

Dynamic Behavior of a Plate Under Air Blast Load Using Differential Quadrature Method

2007 ◽  
Author(s):  
Murat Tuna ◽  
Halit S. Turkmen
Keyword(s):  
Dynamic Behavior ◽  
Numerical Solutions ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Differential Quadrature ◽  
Blast Load ◽  
Solution Technique ◽  
Design Decision ◽  
Quadrature Method ◽  
Air Blast

The effect of blast load on the plate and shell structures has an important role on design decision. Blast load experiments are usually difficult and expensive. Therefore, numerical studies have been done on the response of blast loaded structures. However, because of time dependency of the nature of the problem, numerical solutions take long time and need heavy computational effort. The differential quadrature method (DQM) is a numerical solution technique for the rapid solution of linear and non-linear partial differential equations. It has been successfully applied to many engineering problems. The method has especially found application widely in structural analysis such as static and free vibration analysis of beams and plates. The capability of the method to produce highly accurate solutions with minimal computational efforts makes it of current interest. In this paper, the dynamic behavior of isotropic and laminated composite plates under air blast load has been investigated using the differential quadrature method. The results are compared to the numerical and experimental results found in the literature.

Dynamic Characteristics of Composite Helicopter Blade Solved by Using the Differential Quadrature Method

2008 ◽  
Author(s):  
J. H. Kuang ◽  
M. H. Hsu ◽  
T. P. Hung
Keyword(s):  
Dynamic Characteristics ◽  
Differential Quadrature Method ◽  
Numerical Results ◽  
Differential Quadrature ◽  
Dynamic Responses ◽  
Beam Model ◽  
Quadrature Method ◽  
Discrete Eigenvalue ◽  
Composite Blade ◽  
Sample Points

The dynamic characteristics of nonlinear composite helicoper blades are solved by using the differential quadrature method (DQM). The bending-torsion coupled beam model is proposed to characterize the composite blade. The Kelvin-Voigt internal and linear external damping coefficients are also employed. The DQM is used to transform the partial differential equations of a composite rotor blade into a discrete eigenvalue problem. The Chebyshev-Gauss-Lobatto sample point equation is used to select the sample points. Numerical results indicate that even nine sample points can provide the convergent results by employing this DQM for the blade analysis. The difference between the responses derived from the linear and the nonlinear models have been compared to illustrate the significance of the nonlinear effect in this case. The transitional dynamic responses of the derived systems are calculated by using Newmark method. In this study, the effects of the fiber orientation, internal damping, external damping, pre-twisted angle and the rotation speed on the dynamic behavior for a composite beam are studied. The effect of the number of sample points on the accuracy of the calculated natural frequencies is also discussed. The integrity and computational efficiency of the DQM in this problem will be demonstrated through a number of case studies. Numerical results indicated that the DQM is valid and efficient for a composite blade formulation.

Critical buckling load of composite laminates containing delamination using differential quadrature method and ABAQUS finite element

2021 ◽  
pp. 030932472199657
Author(s):  
Hamed Edalati ◽  
Vahid Daghigh ◽  
Kamran Nikbin
Keyword(s):  
Finite Element ◽  
Composite Laminates ◽  
Composite Laminate ◽  
Differential Quadrature Method ◽  
Compressive Load ◽  
Differential Quadrature ◽  
Buckling Load ◽  
Quadrature Method ◽  
Critical Buckling Load ◽  
Finite Element Package

Differential quadrature method (DQM) was used to compute the critical buckling load (CBL) of composite laminates containing complex delamination shapes. The composite laminate was initially flat; however, it buckled under a compressive load due to weak adhesive between the outer ply and the whole composite laminate. Previous data obtained for composite laminates containing circular or elliptical delaminations by finite element and the Rayleigh-Ritz methods as well as DQM available in the literature were used to validate the accuracy of the approach. A good agreement between the results was observed. To show the ability of this approach for calculating the CBL of a composite laminate containing complex delamination shape, a crescent-shaped delamination was considered. The CBLs for various stacking sequences of such a composite laminate were then calculated and discussed. The commercial finite element package, ABAQUS was used to validate the DQM results for crescent delamination.

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