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

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.

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

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.

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

2000 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Numerical Algorithm ◽  
Equilibrium Equation ◽  
Static Deflection ◽  
Beam Structures ◽  
Prismatic Beam ◽  
Vibration Problems ◽  
Analysis Models ◽  
Element Boundary

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.

DQEM for Buckling Analysis of Nonprismatic Columns with and Without Elastic Foundation

2003 ◽  
Vol 03 (02) ◽  
pp. 183-194 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Boundary Conditions ◽  
Numerical Solution ◽  
Elastic Foundation ◽  
Solution Procedure ◽  
Buckling Analysis ◽  
Numerical Results ◽  
Differential Quadrature ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Element Boundary

The differential quadrature element method is used to solve the buckling problems of nonprismatic column structures with and without elastic foundation. The extended differential quadrature is used to discretize the governing differential eigenvalue 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.

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

2006 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Boundary Conditions ◽  
Axial Force ◽  
Differential Quadrature ◽  
Analysis Model ◽  
Bernoulli Beam ◽  
Beam Structures ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Euler Bernoulli Beam ◽  
Element Boundary

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.

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

2007 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Boundary Conditions ◽  
Numerical Algorithm ◽  
Differential Quadrature ◽  
Analysis Model ◽  
Bernoulli Beam ◽  
Beam Structures ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Euler Bernoulli Beam ◽  
Element Boundary

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.

A 3D BOUNDARY ELEMENT METHOD FOR DETERMINATION OF ACOUSTIC EIGENFREQUENCIES CONSIDERING ADMITTANCE BOUNDARY CONDITIONS

1993 ◽  
Vol 01 (04) ◽  
pp. 455-468 ◽  
Author(s):  
Z. S. CHEN ◽  
G. HOFSTETTER ◽  
H. A. MANG
Keyword(s):  
Boundary Element Method ◽  
Boundary Conditions ◽  
Boundary Element ◽  
Large Scale ◽  
Numerical Study ◽  
Numerical Algorithms ◽  
Numerical Results ◽  
Simple Problem ◽  
Element Method

A 3D boundary element method for the determination of the acoustic eigenfrequencies of car compartments, characterized by a unified treatment of Robin, Dirichlet, and Neumann boundary conditions, is presented. The drawback of frequency-dependent matrices of the eigenvalue problem is overcome by means of the Particular Integral Method. Thus, the standard numerical algorithms for the extraction of eigenvalues can be applied. The numerical study contains both a comparison of numerical results with analytical solutions of a simple problem with different types of boundary conditions and a comparison of numerical results of a large-scale problem with respective numerical results, computed on the basis of the finite element method. In addition, for the latter example, different numerical algorithms for the eigenvalue extraction are examined.

The Timoshenko Beam on an Elastic Foundation and Subject to a Moving Step Load, Part 1: Steady-State Response

1996 ◽  
Vol 118 (3) ◽  
pp. 277-284 ◽  
Author(s):  
S. F. Felszeghy
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Timoshenko Beam ◽  
Equations Of Motion ◽  
Steady State Solution ◽  
State Solution ◽  
Actual Problem ◽  
State Response ◽  
Particular Solution

The response of a simply supported semi-infinite Timoshenko beam on an elastic foundation to a moving step load is determined. The response is found from summing the solutions to two mutually complementary sets of governing equations. The first solution is a particular solution to the forced equations of motion. The second solution is a solution to a set of homogeneous equations of motion and nonhomogeneous boundary conditions so formulated as to satisfy the initial and boundary conditions of the actual problem when the two solutions are summed. As a particular solution, the steady-state solution is used which is the motion that would appear stationary to an observer traveling with the load. Steady-state solutions are developed in Part 1 of this article for all load speeds greater than zero. It is shown that a steady-state solution which is identically zero ahead of the load front exists at every load speed, in the sense of generalized functions, including the critical speeds when the load travels at the minimum phase velocity of propagating harmonic waves and the sonic speeds. The solution to the homogeneous equations of motion is developed in Part 2 where the two solutions in question are summed and numerical results are presented as well.

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

2002 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Boundary Conditions ◽  
Solution Procedure ◽  
Differential Quadrature ◽  
Curved Beam ◽  
Beam Structures ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
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.

DQEM Analysis of In-Plane Deflection of Curved Beam Structures

2003 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Boundary Conditions ◽  
Numerical Algorithm ◽  
Differential Quadrature ◽  
Curved Beam ◽  
Analysis Model ◽  
Beam Structures ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Deflection Analysis ◽  
Element Boundary

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.

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