DQEM analysis of out-of-plane deflection of non-prismatic curved beam structures considering the effect of shear deformation

2006 ◽  
Vol 24 (7) ◽  
pp. 555-571 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Shear Deformation ◽  
Curved Beam ◽  
Beam Structures ◽  
Out Of Plane

Out-of-Plane Deflection of Nonprismatic Curved Beam Structures Considering the Effect of Shear Deformation Solved by DQEM

2004 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Shear Deformation ◽  
Differential Quadrature ◽  
Analysis Model ◽  
Beam Structures ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Out Of Plane ◽  
Deflection Analysis ◽  
Governing Differential Equation ◽  
Element Boundary

The development of differential quadrature element method out-of-plane deflection analysis model of curved nonprismatic beam structures considering the effect of shear deformation was carried out. The DQEM uses the differential quadrature 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. Numerical results solved by the developed numerical algorithm are presented. The convergence of the developed DQEM analysis model is efficient.

scholarly journals A General Fourier Formulation for In-Plane and Out-of-Plane Vibration Analysis of Curved Beams

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Rui Nie ◽  
Tianyun Li ◽  
Xiang Zhu ◽  
Huihui Zhou
Keyword(s):  
Potential Energy ◽  
Boundary Conditions ◽  
Calculation Model ◽  
Displacement Function ◽  
Curved Beam ◽  
Curved Beams ◽  
Concentrated Mass ◽  
Engineering Structures ◽  
Beam Structures ◽  
Out Of Plane

Based on the principle of energy variation, an improved Fourier series is introduced as an allowable displacement function. This paper constructs a calculation model that can study the in-plane and out-of-plane free and forced vibrations of curved beam structures under different boundary conditions. Firstly, based on the generalized shell theory, considering the shear and inertial effects of curved beam structures, as well as the coupling effects of displacement components, the kinetic energy and strain potential energy of the curved beam are obtained. Subsequently, an artificial spring system is introduced to satisfy the constraint condition of the displacement at the boundary of the curved beam, obtain its elastic potential energy, and add it to the system energy functional. Any concentrated mass point or concentrated external load can also be added to the energy function of the entire system with a corresponding energy term. In various situations including classical boundary conditions, the accuracy and efficiency of the method in this paper are proved by comparing with the calculation results of FEM. Besides, by accurately calculating the vibration characteristics of common engineering structures like slow curvature (whirl line), the wide application prospects of this method are shown.

In-Plane Vibration of Nonprismatic Curved Beam Structures Considering the Effect of Shear Deformation Solved by DQEM

2005 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Shear Deformation ◽  
Vibration Analysis ◽  
Differential Quadrature ◽  
Curved Beam ◽  
Analysis Model ◽  
Beam Structures ◽  
Plane Vibration ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Element Boundary

The development of differential quadrature element method in-plane vibration analysis model of curved nonprismatic beam structures considering the effect of shear deformation was carried out. 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.

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.

Out-of-Plane Vibration of Nonprismatic Curved Beam Structures Considering the Effect of Shear Deformation Solved by DQEM

2004 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Shear Deformation ◽  
Vibration Analysis ◽  
Differential Quadrature ◽  
Analysis Model ◽  
Beam Structures ◽  
Plane Vibration ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Out Of Plane ◽  
Element Boundary

The development of differential quadrature element method out-of-plane vibration analysis model of curved nonprismatic beam structures considering the effect of shear deformation was carried out. 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.

In-Plane Deflection of Nonprismatic Curved Beam Structures Considering the Effect of Shear Deformation Solved by DQEM

2005 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Shear Deformation ◽  
Differential Quadrature ◽  
Curved Beam ◽  
Analysis Model ◽  
Beam Structures ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Deflection Analysis ◽  
Governing Differential Equation ◽  
Element Boundary

The development of differential quadrature element method in-plane deflection analysis model of curved nonprismatic beam structures considering the effect of shear deformation was carried out. The DQEM uses the differential quadrature 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. Numerical results solved by the developed numerical algorithm are presented. The convergence of the developed DQEM analysis model is efficient.

Medium Frequency Vibration Analysis of Beam Structures Modeled by the Timoshenko Beam Theory

2020 ◽  
Author(s):  
Yichi Zhang ◽  
Bingen Yang
Keyword(s):  
Shear Deformation ◽  
Timoshenko Beam ◽  
Vibration Analysis ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Bernoulli Beam ◽  
Beam Structure ◽  
Medium Frequency ◽  
Beam Structures ◽  
Euler Bernoulli Beam

Abstract Vibration analysis of complex structures at medium frequencies plays an important role in automotive engineering. Flexible beam structures modeled by the classical Euler-Bernoulli beam theory have been widely used in many engineering problems. A kinematic hypothesis in the Euler-Bernoulli beam theory is that plane sections of a beam normal to its neutral axis remain normal when the beam experiences bending deformation, which neglects the shear deformation of the beam. However, as observed by researchers, the shear deformation of a beam component becomes noticeable in high-frequency vibrations. In this sense, the Timoshenko beam theory, which describes both bending deformation and shear deformation, may be more suitable for medium-frequency vibration analysis of beam structures. This paper presents an analytical method for medium-frequency vibration analysis of beam structures, with components modeled by the Timoshenko beam theory. The proposed method is developed based on the augmented Distributed Transfer Function Method (DTFM), which has been shown to be useful in various vibration problems. The proposed method models a Timoshenko beam structure by a spatial state-space formulation in the s-domain, without any discretization. With the state-space formulation, the frequency response of a beam structure, in any frequency region (from low to very high frequencies), can be obtained in an exact and analytical form. One advantage of the proposed method is that the local information of a beam structure, such as displacements, bending moment and shear force at any location, can be directly obtained from the space-state formulation, which otherwise would be very difficult with energy-based methods. The medium-frequency analysis by the augmented DTFM is validated with the FEA in numerical examples, where the efficiency and accuracy of the proposed method is present. Also, the effects of shear deformation on the dynamic behaviors of a beam structure at medium frequencies are illustrated through comparison of the Timoshenko beam theory and the Euler-Bernoulli beam theory.

Sign in / Sign up

Export Citation Format

Share Document