Eigen Solutions of an Orthotropy Composite Blade Solved by the Differential Quadrature Method

2002 ◽  
Author(s):  
J. H. Kuang ◽  
M. H. Hsu
Keyword(s):  
Eigenvalue Problem ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Beam Model ◽  
Quadrature Method ◽  
Discrete Eigenvalue ◽  
Composite Blade ◽  
Sample Points ◽  
Eigen Solutions ◽  
Inclined Angle

The eigenvalue problem of an orthotropy composite blade is formulated by employing the differential quadrature method (DQM). The Euler-Bernoulli beam model is used to characterize the orthotropy composite blade. The differential quadrature method is used to transform the partial differential equations of an orthotropy composite blade into a discrete eigenvalue problem. The Chebyshev-Gauss-Lobatto sample point equation is used to select the sample points. In this study, the effects of the fiber orientation, internal damping, external damping, inclined angle and the rotation speed on the eigen solutions for an orthotropy composite blade are investigated. 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 differential quadrature method is valid and efficient for an orthotropy composite blade formulation.

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.

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.

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.

Vibration analysis of curved composite sandwich beams with viscoelastic core by using differential quadrature method

2018 ◽  
Vol 22 (3) ◽  
pp. 743-770 ◽  
Author(s):  
Ozgur Demir ◽  
Demet Balkan ◽  
Rahim Can Peker ◽  
Muzaffer Metin ◽  
Aytac Arikoglu
Keyword(s):  
Vibration Analysis ◽  
Virtual Work ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Beam Model ◽  
Sandwich Beams ◽  
Quadrature Method ◽  
Modal Strain Energy ◽  
Viscoelastic Core ◽  
Generalized Differential

This paper focuses on the vibration analysis of three-layered curved sandwich beams with elastic face layers and viscoelastic core. First, the equations of motion that govern the free vibrations of the curved beams together with the boundary conditions are derived by using the principle of virtual work, in the most general form. Then, these equations are solved by using the generalized differential quadrature method in the frequency domain, for the first time to the best of the authors’ knowledge. Verification of the proposed beam model and the generalized differential quadrature solution is carried out via comparison with the results that already exist in literature and the ANSYS finite element solution combined with the modal strain energy method. The effect of system parameters, i.e. layer thicknesses, the lamination angle of layers and the curvature on the vibration and damping characteristics of a curved sandwich beam with laminated composite face layers and a frequency dependent viscoelastic core is investigated in detail.

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