Papers by Keyword: Timoshenko Beam

Abstract: This article is presents a finite element formulation for the dynamic response of a rotating simply supported shaft subjected to a moving load. The Timoshenko beam theory is used to model the rotating shaft. The assumed modes method and Finite Element method are employed in this study. The equations are solved with numerical method. The influence of parameters moving load speed and rotational speed are discussed for rotating simply supported shaft model. The results show that the maximum displacement occurs in the direction of the load at the midpoint of the simply supported shaft. The gyroscopic effect occurs only in the direction perpendicular to the load and is dependent on rotational speed of the shaft.

Abstract: In this paper, a novel method is proposed to address the non-linear dynamic response of a beam-like structure supported by a tensionless foundation due to moving loads. A lattice spring model (LSM) is developed to describe the structure as a discrete assembly of particles interacting via shear and rotational springs while the tensionless foundation is simulated using a chain of one-way normal springs connecting the particles to the ground. The total time for the travelling load to traverse the beam is divided into a number of steps and the generalised explicit matrix equation can be solved for each time step to obtain the time-history response of the structure. An iterative procedure is adopted to obtain the correct sign of lateral displacement for all particles at each time step, which determines the lift-off regions throughout the beam.

Abstract: The deflection and natural frequency of a 3 – Dimensional Timoshenko Beam (TB) is analyzed using Finite Element (FE) method. Significant improvement in computational time can be obtained when new shape functions are used. The results obtained from existing software packages and the new FE model are compared and good improvement is observed.

Abstract: The design of structures and machineries in present days are based on optimizing of multi-objectives such as maximum strength, maximum life, minimum weight and minimum cost. Due to this flexiblity they allow having a very high level of stresses. This leads to development of cracks in their elements. Due to long-term service many engineering structures may have structural defects such as cracks. So it is very much essential to know the property of structures and response of such structures in various cases. In this article the natural frequencies and mode shapes of an uncracked and cracked cantilever Timoshenko beam is studied by using finite element method (FEM) and MATLAB programme. The effect of crack on the natural frequencies of the uncracked and cracked Timoshenko beam is studied.

Abstract: For the purpose of precise calculation on intrinsic frequency of the deep-hole boring bar in trepanning heavy-duty processing, a new frequency calculation model is proposed, based on the synthetically investigation of the axial press effects, intermediate supported, Coriolis inertia effects induced by cutting fluid and other relevant various factors of boring bar. The boring bar can be decomposed into the two parts, corresponding to the liquid-solid coupling vibration model inside the work part and Timoshenko beam model outside the work part, respectively. Then assume the whole system as continuous equal span beam model to combine these two parts. Through nesting liquid-solid coupled vibration model (considering cutting fluid velocity) and Timoshenko beam model (containing axial pressure and lateral bending) among the continuous beam model (considering equal span), the precise calculation on intrinsic frequency of the boring system can be completed.

Abstract: This paper proposed an efficient method based on theoretical equations to solve the dynamic interaction problem between the Timoshenko beam and maglev vehicles. A systematic PI numerical scheme is developed for the control system of the maglev train. The major advantage is that only one simple equation required in the control calculation, although the original control system is fairly complicated. Numerical simulations indicate that a large time step length can be used in the proposed method to obtain stable and accurate results.

Abstract: Regarding the displacements and internal forces of Timoshenko beams as dual variables, Timoshenko beam problems were included into dual variables system. Corresponding to state transfer solution of Hamiltonian dual equation, transfer form solution of dual variables for Timoshenko beams was presented. Based on transfer form solution, element stiffness equation and the shape functions of Timoshenko beams were deduced, boundary integral equation and the fundamental solution function of Timoshenko beams were obtained, which reveal the intrinsic relationships among the finite element method, the boundary element method and dual variables system of Timoshenko beams. Based on the transfer form solution of Timoshenko beams, transfer matrix method for chain structure of Timoshenko beams was proposed. For chain beam structure problems, transfer matrix method is simple, intuitive, and has the advantages of good boundary adaptability and less calculation in solving the node variables of chain structures with recursive solution. The numerical results demonstrate the feasibility and accuracy of transfer matrix method in complex beam structure problems.

Abstract: The article deals with the actual problem of improving the accuracy of determining the dynamic characteristics of beam structures. To solve such problems the displacement method is used. Defining matrices are calculated with the Godunovs scheme. Numerical solutions in this case can be obtained practically with any accuracy within accepted hypotheses of the mathematical model of the calculated object. This suggests that the resulting solutions are standard. The examples of determining the natural frequencies of vibrations of beam structures that demonstrate an extremely high accuracy of the proposed algorithm are given.

Abstract: Timoshenko beam model and the meshless method based on thin-plate spline radial basis function are used to analyze the free vibration of carbon nanotubes. The natural frequencies of the carbon nanotubes with different length-to-diameter ratios and boudary conditions are compared with the results of published literatures which demonstrate the high accuracy of present method.

Abstract: With its technological development, the CNC embroidery machine rotational speed has increased dramatically. Consequent vibration and noise increase the disconnection rate in the embroidery process and affect the embroidery quality and production efficiency. To solve such problem, by analyzing the vibration causes and comparing the different characteristics of the Timoshenko beam and the Euler-Benouli simply supported beam, the current study indicated the limitation of the traditional vibration analysis method---the widely-used Euler-Bernouli simple beam theory, and constructed a vibration model based on the Timoshenko beam theory. Then a finite element model of the embroidery machine beam was built S and the corresponding experiment were done. Results from the constructed mechanical, mathematical model, and the ANSYS finite element model were compared. It has been verified that the constructed models are consistent with experiment results and that vibration models are constructed reasonably and feasibly. According to these models, the key parameters affecting the beam vibration are identified to work out more accurate and effective structure optimization design and prediction.