Xiaojun Huang¹, Liaojun Zhang^2,*, Hanbo Cui¹, Gaoxing Hu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.140, No.2, pp. 1647-1668, 2024, DOI:10.32604/cmes.2024.049124

Abstract This study proposes an effective method to enhance the accuracy of the Differential Quadrature Method (DQM) for calculating the dynamic characteristics of functionally graded beams by improving the form of discrete node distribution. Firstly, based on the first-order shear deformation theory, the governing equation of free vibration of a functionally graded beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam axial displacement, transverse displacement, and cross-sectional rotation angle by considering the effects of shear deformation and rotational inertia of the beam cross-section. Then, ignoring the shear deformation of the… More >

T.-L. Zhu¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.7, No.3, pp. 107-112, 2008, DOI:10.3970/icces.2008.007.107

Abstract A modeling method for flapwise and chordwise bending vibration analysis for rotating Timoshenko beams is introduced. For the modeling method shear and the rotary inertia effects are correctly judged based on \textit {Timoshenko beam theory}. Equations of motion of continuous models are derived from a modeling method which employs hybrid deformation variables. The equations thus derived are transmitted into dimensionless forms. The effects of dimensionless parameters on the modal characteristics of the Timoshenko beams are successfully examined through numerical study. In particular, eigenvalue loci veering phenomena and integrated mode shape critical deviations are contemplated and More >

A.E. Kampitsis¹, E.J. Sapountzakis²

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.6, pp. 367-409, 2014, DOI:10.3970/cmes.2014.103.367

Abstract In this paper a Boundary Element Method (BEM) is developed for the geometrically nonlinear inelastic analysis of Timoshenko beams of arbitrary doubly symmetric simply or multiply connected constant cross-section, resting on inelastic tensionless Winkler foundation. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as to axial loading, while its edges are subjected to the most general boundary conditions. To account for shear deformations, the concept of shear deformation coefficients is used. A displacement based formulation is developed and inelastic redistribution More >

A.S Vinod Kumar, Ranjan Ganguli²

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.6, pp. 443-474, 2012, DOI:10.3970/cmes.2012.088.443

Abstract The governing differential equation of a rotating beam becomes the stiff-string equation if we assume uniform tension. We find the tension in the stiff string which yields the same frequency as a rotating cantilever beam with a prescribed rotating speed and identical uniform mass and stiffness. This tension varies for different modes and are found by solving a transcendental equation using bisection method. We also find the location along the rotating beam where equivalent constant tension for the stiff string acts for a given mode. Both Euler-Bernoulli and Timoshenko beams are considered for numerical results. More >

Sen Yung Lee¹, Jyh Shyang Wu²

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.2, pp. 133-154, 2009, DOI:10.3970/cmes.2009.040.133

Abstract The three coupled governing differential equations for the in-plane vibrations of curved non-uniform Timoshenko beams are derived via the Hamilton's principle. Three physical parameters are introduced to simplify the analysis. By eliminating all the terms with the axial displacement parameter, then reducing the order of differential operator acting on the flexural displacement parameter, one uncouples the three governing characteristic differential equations with variable coefficients and reduces them into a sixth-order ordinary differential equation with variable coefficients in term of the angle of the rotation due to bending for the first time. The explicit relations between More >

Sen Yung Lee¹, Shin Yi Lu², Yen Tse Liu², Hui Chen Huang²

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.3, pp. 293-312, 2008, DOI:10.3970/cmes.2008.033.293

Abstract A new analytic solution method is developed to find the exact static deflection of a Timoshenko beam with nonlinear elastic boundary conditions for the first time. The associated mathematic system is shifted and decomposed into six linear differential equations and at most four algebra equations. After finding the roots of the algebra equations, the exact solution of the nonlinear beam system can be reconstructed. It is shown that the proposed method is valid for the problem with strong nonlinearity. Examples, limiting studies and numerical analysis are given to illustrate the analysis. The exact solutions are More >