Smooth size design for the natural frequencies of curved Timoshenko beams using isogeometric analysis

2018 ◽  
Vol 59 (4) ◽  
pp. 1143-1162 ◽  
Author(s):  
Hongliang Liu ◽  
Dixiong Yang ◽  
Xuan Wang ◽  
Yutian Wang ◽  
Chen Liu ◽  
...  
Keyword(s):  
Isogeometric Analysis ◽  
Natural Frequencies ◽  
Timoshenko Beams

scholarly journals Modal Perturbation Method for the Dynamic Characteristics of Timoshenko Beams

2005 ◽  
Vol 12 (6) ◽  
pp. 425-434 ◽  
Author(s):  
Menglin Lou ◽  
Qiuhua Duan ◽  
Genda Chen
Keyword(s):  
Perturbation Method ◽  
Dynamic Characteristics ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Solution Process ◽  
Equation Of Motion ◽  
Timoshenko Beams ◽  
Algebraic Equations ◽  
Nonlinear Algebraic Equations ◽  
Shear Distortion

Timoshenko beams have been widely used in structural and mechanical systems. Under dynamic loading, the analytical solution of a Timoshenko beam is often difficult to obtain due to the complexity involved in the equation of motion. In this paper, a modal perturbation method is introduced to approximately determine the dynamic characteristics of a Timoshenko beam. In this approach, the differential equation of motion describing the dynamic behavior of the Timoshenko beam can be transformed into a set of nonlinear algebraic equations. Therefore, the solution process can be simplified significantly for the Timoshenko beam with arbitrary boundaries. Several examples are given to illustrate the application of the proposed method. Numerical results have shown that the modal perturbation method is effective in determining the modal characteristics of Timoshenko beams with high accuracy. The effects of shear distortion and moment of inertia on the natural frequencies of Timoshenko beams are discussed in detail.

Free vibration analysis of rotating tapered Timoshenko beams via variational iteration method

2016 ◽  
Vol 23 (2) ◽  
pp. 220-234 ◽  
Author(s):  
Yanfei Chen ◽  
Juan Zhang ◽  
Hong Zhang
Keyword(s):  
Free Vibration ◽  
Iteration Method ◽  
Natural Frequencies ◽  
Eigenvalue Problems ◽  
Accurate Determination ◽  
Variational Iteration Method ◽  
Mode Shapes ◽  
Engineering Practice ◽  
Timoshenko Beams ◽  
Variational Iteration

Accurate determination of natural frequencies and mode shapes of the rotating tapered Timoshenko beam is important in engineering practice. This paper re-examines the free vibration of rotating tapered Timoshenko beams using the technique of variational iteration, which is relatively new and is capable of providing accurate solutions for eigenvalue problems in a quite easy way. Natural frequencies and mode shapes for rotating tapered Timoshenko beams with linearly varying height as well as linearly varying height and width are investigated via two numerical examples, and solutions are compared with results published in literature where available. Since the method constitutes a numerical procedure, the convergence of solutions which is important for practical implementation is evaluated as well, where efficiency and accuracy of variational iteration method in solving high order eigenvalue problems are demonstrated.

Kriging-Based Timoshenko Beam Elements with the Discrete Shear Gap Technique

2018 ◽  
Vol 15 (07) ◽  
pp. 1850064 ◽  
Author(s):  
F. T. Wong ◽  
Adam Sulistio ◽  
Hidayat Syamsoeyadi
Keyword(s):  
Natural Frequencies ◽  
Polynomial Interpolation ◽  
Kriging Interpolation ◽  
Bending Moments ◽  
Shear Locking ◽  
Timoshenko Beams ◽  
Beam Elements ◽  
Numerical Tests ◽  
Gap Technique ◽  
Discrete Shear Gap

Kriging-based finite element method (K-FEM) is an enhancement of the FEM through the use of Kriging interpolation in place of the conventional polynomial interpolation. In this paper, the K-FEM is developed for static, free vibration, and buckling analyses of Timoshenko beams. The discrete shear gap technique is employed to eliminate shear locking. The numerical tests show that a Kriging-Based beam element with cubic basis and three element-layer domain of influencing nodes is free from shear locking. Exceptionally accurate displacements, bending moments, natural frequencies, and buckling loads and reasonably accurate shear force can be achieved using a relatively course mesh.

Forced vibration of delaminated Timoshenko beams subjected to a moving load

2012 ◽  
Vol 19 (2) ◽  
pp. 145-157 ◽  
Author(s):  
Mohammad H. Kargarnovin ◽  
Mohammad T. Ahmadian ◽  
Ramazan Ali Jafari-Talookolaeia
Keyword(s):  
Dynamic Response ◽  
Composite Beam ◽  
Natural Frequencies ◽  
Moving Load ◽  
Ritz Method ◽  
Forced Vibrations ◽  
Mode Shapes ◽  
Timoshenko Beams ◽  
Free And Forced Vibrations ◽  
Spanwise Location

AbstractA composite beam with single delamination under the action of moving load has been modeled accounting for the Poisson’s effect, shear deformation, and rotary inertia. The existence of the delamination changes the stiffness of the structure, and this affects the dynamic response of the structure. We have used a constrained mode to simulate the behavior between the delaminated surfaces. Based on this mode, eigensolution technique is used to obtain the natural frequencies and their corresponding mode shapes for the delaminated beam. Then, the Ritz method is adopted to derive the dynamic response of the beam subjected to a moving load. The obtained results for the free and forced vibrations of beams are verified against reported similar results in the literature. Moreover, the maximum dynamic response of such beam is compared with an intact beam. The effects of different parameters such as the size, depth, and spanwise location of the delamination, the load velocity, the different ply configurations, and the Poisson’s effect on the dynamic response of the beam are studied.

Transverse Free Vibration of Timoshenko Beams Resting on Viscoelastic Foundations

2014 ◽  
Vol 919-921 ◽  
pp. 275-279
Author(s):  
Li Peng ◽  
Ying Wang
Keyword(s):  
Free Vibration ◽  
Modal Analysis ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Numerical Results ◽  
Complex Frequency ◽  
Pasternak Foundation ◽  
Timoshenko Beams ◽  
Numerical Examples ◽  
Complex Modal Analysis

The complex modal analysis is developed to study the transverse vibration of Timoshenko beams resting on viscoelastic Pasternak foundation. Complex frequency equations and modal function expressions are obtained for pinned-pinned ends. In numerical examples, the characteristics of natural frequencies and decrement coefficients of Timoshenko beams are compared with Euler-Bernoulli beams. The numerical results show that with increase in the length, the natural frequencies of Timoshenko beams are slightly less than Euler-Bernoulli beams, and the decrement coefficients of Timoshenko beams are not constant as that of Euler-Bernoulli beams.

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