Static Deflection and Free Vibration of Nonprismatic Beam Structures Solved by DQEM Using EDQ

Abstract The development of (DQEM) analysis models of static deformation and free vibration problems of generic non-prismatic beam structures was carried out. The DQEM uses the extended differential quadrature (EDQ) to discretize the buckling equilibrium equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results solved by the developed numerical algorithm are presented. They prove that the DQEM efficient.

Influence of Axially Distributed Force on the Vibration of Euler-Bernoulli Beam Structures Solved by DQEM Using EDQ

Volume 2: Computer Applications/Technology and Bolted Joints ◽

10.1115/pvp2007-26033 ◽

2007 ◽

Author(s):

Chang-New Chen

Keyword(s):

Boundary Conditions ◽

Numerical Algorithm ◽

Differential Quadrature ◽

Analysis Model ◽

Bernoulli Beam ◽

Beam Structures ◽

Euler Bernoulli Beam ◽

The influence of axially distributed force on the vibration of Euler-Bernoulli beam structures is analyzed by differential quadrature element method (DQEM) using extended differential quadrature (EDQ). The DQEM uses the differential quadrature to discretize the governing differential eigenvalue equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results solved by the developed numerical algorithm are presented. The convergence of the developed DQEM analysis model is efficient.

DQEM Analysis of In-Plane Deflection of Curved Beam Structures

Computer Technology and Applications ◽

10.1115/pvp2003-1910 ◽

2003 ◽

Author(s):

Chang-New Chen

Keyword(s):

Boundary Conditions ◽

Numerical Algorithm ◽

Differential Quadrature ◽

Curved Beam ◽

Analysis Model ◽

Beam Structures ◽

Deflection Analysis ◽

The development of differential quadrature element method in-plane deflection analysis model of arbitrarily curved nonprismatic beam structures was carried out. The DQEM uses the extended differential quadrature to discretize the differential eigenvalue equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results solved by the developed numerical algorithm are presented. The convergence of the developed DQEM analysis model is efficient.

Vibration of Timoshenko Beam Structures Resting on a Two-Parameter Elastic Foundation Solved by DQEM Using Chebyshev DQ Model

Volume 2: Computer Applications/Technology and Bolted Joints ◽

10.1115/pvp2008-61901 ◽

2008 ◽

Author(s):

Chang-New Chen

Keyword(s):

Boundary Conditions ◽

Elastic Foundation ◽

Timoshenko Beam ◽

Numerical Algorithms ◽

Numerical Results ◽

Eigenvalue Equation ◽

Beam Structures ◽

Analysis Models ◽

Element Boundary ◽

Two Parameter

The development of DQEM solution of vibration of Timo-shenko beam structures resting on a two-parameter elastic foundation was carried out. The DQEM uses Chebyshev DQ model to discretize the governing differential eigenvalue equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results solved by the developed numerical algorithms are presented. The convergence of the developed DQEM analysis models is efficient.

Volume 1: Offshore Technology; Offshore Wind Energy; Ocean Research Technology; LNG Specialty Symposium ◽

Influence of Axial Force on the Vibration of Euler-Bernoulli Beam Structures Solved by DQEM Using EDQ

10.1115/omae2006-92209 ◽

2006 ◽

Author(s):

Chang-New Chen

Keyword(s):

Boundary Conditions ◽

Axial Force ◽

Differential Quadrature ◽

Analysis Model ◽

Bernoulli Beam ◽

Beam Structures ◽

Euler Bernoulli Beam ◽

The influence of axial force on the vibration of Euler-Bernoulli beam structures is analyzed by differential quadrature element method (DQEM) using extended differential quadrature (EDQ). The DQEM uses the differential quadrature to discretize the governing differential eigenvalue equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results solved by the developed numerical algorithm are presented. The convergence of the developed DQEM analysis model is efficient.

FREE VIBRATION OF KIRCHHOFF PLATES WITH SECTOR SHAPES BY THE METHOD OF DISCRETE SINGULAR CONVOLUTION

International Journal of Computational Methods ◽

10.1142/s0219876210002192 ◽

2010 ◽

Vol 07 (02) ◽

pp. 229-240 ◽

Cited By ~ 3

Author(s):

M. GÜRSES ◽

E. KUZU ◽

Ö. CÍVALEK

Keyword(s):

Free Vibration ◽

Boundary Conditions ◽

Analytical Solutions ◽

Natural Frequencies ◽

Plate Theory ◽

Kirchhoff Plate ◽

Kirchhoff Plates ◽

Vibration Problems ◽

Discrete Singular Convolution ◽

Sector Angle

The free vibration of sector plates based on the classical Kirchhoff plate theory is analyzed by the method of discrete singular convolution using the Regularized Shannon delta (RSD) kernel. This method is applied to sector plates with a combination of boundary conditions, and the natural frequencies are calculated. The effects of the sector angle, boundary conditions and mode numbers on the frequency parameters are investigated. Comparisons are made with existing numerical and analytical solutions in the literature. This method is very effective for the study of vibration problems of sector plates.

DQEM VIBRATION ANALYSES OF NONPRISMATIC BEAMS RESTING ON ELASTIC FOUNDATIONS

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455402000403 ◽

2002 ◽

Vol 02 (01) ◽

pp. 99-115 ◽

Cited By ~ 2

Author(s):

CHANG-NEW CHEN

Keyword(s):

Free Vibration ◽

Numerical Algorithm ◽

Vibration Analysis ◽

Free Vibration Analysis ◽

Differential Quadrature ◽

Analysis Model ◽

Elastic Foundations ◽

The development of differential quadrature element method (DQEM) free vibration analysis model of nonprismatic Bernoulli–Euler beams resting on Winkler elastic foundations was carried out. The DQEM uses the extended differential quadrature (EDQ) to discretize the differential eigenvalue equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results solved by the developed numerical algorithm are presented. They prove that the DQEM is efficient. The developed numerical algorithm can be used to analyze the related pressure vessel and piping structures.

Out-of-Plane Deflections of Nonprismatic Curved Beam Structures Solved by the Differential Quadrature Element Method

Computational Mechanics: Developments and Applications ◽

10.1115/pvp2002-1296 ◽

2002 ◽

Author(s):

Chang-New Chen

Keyword(s):

Boundary Conditions ◽

Solution Procedure ◽

Differential Quadrature ◽

Curved Beam ◽

Beam Structures ◽

Out Of Plane ◽

Element Boundary ◽

Element Method

The differential quadrature element method (DQEM) is used to solve the out-of-plane deflections of nonprismatic curved beam structures. The extended differential quadrature (EDQ) is used to discretize the governing differential equations defined on all elements, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions. Numerical results obtained by DQEM are presented. They demonstrate the developed numerical solution procedure.

24th International Conference on Offshore Mechanics and Arctic Engineering: Volume 3 ◽

Structural Mechanics Problems With Structures on a Two-Parameter Foundation Solved by DQEM

10.1115/omae2005-67124 ◽

2005 ◽

Author(s):

Chang-New Chen

Keyword(s):

Differential Equation ◽

Boundary Conditions ◽

Numerical Algorithms ◽

Structural Mechanics ◽

Numerical Results ◽

Structural Problems ◽

Governing Differential Equation ◽

Analysis Models ◽

Element Boundary ◽

Two Parameter

The development of DQEM solution of structural problems with structures resting on a two-parameter foundation was carried out. The DQEM uses DQ or EDQ to discretize the governing differential equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Some EDQ models can be generated by DQ. They are DQ generated EDQ. Numerical results solved by the developed numerical algorithms are presented. The convergence of the developed DQEM analysis models is efficient.

21st International Conference on Offshore Mechanics and Arctic Engineering, Volume 3 ◽

DQEM Analysis of In-Plane Vibration of Curved Beam Structures

10.1115/omae2002-28488 ◽

2002 ◽

Author(s):

Chang-New Chen

Keyword(s):

Numerical Algorithm ◽

Vibration Analysis ◽

Offshore Structures ◽

Differential Quadrature ◽

Analysis Model ◽

Beam Structures ◽

Plane Vibration ◽

The development of differential quadrature element method (DQEM) in-plane vibration analysis model of arbitrarily curved nonprismatic beam structures was carried out. The DQEM uses the extended differential quadrature (EDQ) to discretize the differential eigenvalue equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results solved by the developed numerical algorithm are presented. The convergence of the developed DQEM analysis model is efficient. This numerical algorithm can be used to analyze the related offshore structures.

Evaluating the Effect of Asymmetric Cross-section in Free Vibration and Bending Analysis Results of FG Sandwich Beam by Proposing Simple Efficient Element

Periodica Polytechnica Civil Engineering ◽

10.3311/ppci.17447 ◽

2021 ◽

Author(s):

Majid Yaghoobi ◽

Mohsen Sedaghatjo ◽

Reyhaneh Alizadeh ◽

Mohammad KARKON

Keyword(s):

Free Vibration ◽

Boundary Conditions ◽

Cross Section ◽

Timoshenko Beam ◽

Equilibrium Equation ◽

Vertical Displacement ◽

Asymmetric Effect ◽

Bending Analysis ◽

Different Boundary Conditions ◽

The Cross

In this paper, the asymmetric effect of the cross-section on the free vibration and bending analysis of FG sandwich beams are evaluated. For this purpose, a simple, efficient element is formulated. The new element is created based on the Timoshenko beam theory. The third- and second-order polynomials will be used for vertical displacement and rotation fields, respectively. The proposed formulation will be written based on satisfying the equilibrium equation. Satisfying the equilibrium equation of the Timoshenko beam, in addition to increasing element efficiency, will reduce the number of nodal unknowns. Several benchmark tests with different boundary conditions are used for thin and thick beams to prove the efficiency of the proposed element. The responses of the good elements of other researchers have been used for comparison. Numerical tests prove the rapid convergence rate and high accuracy of the proposed element in free vibration and bending analysis of the beams with various cross-section types and different boundary conditions. The pinned-sliding support conditions for the beam are used to evaluate the asymmetric effect of the cross-section. The use of asymmetric cross-sections creates additional axial displacements and intensifies the deflection of the beam under the lateral load. By increasing the asymmetry, the additional axial displacement and vertical displacement increase. These additional deflections for thin beams are more than thick ones. Also, asymmetry results in increasing the natural frequencies of beams. In the free vibration analysis, the effect of asymmetry on thick beams is more than thin ones.