Timoshenko Beam Structures Research Articles

Vibration Analysis of Multi-Span Timoshenko Beams Due to Moving Loads

The present paper proposes a new dynamic analysis method for multi-span Timoshenko beam structures supported by joints with damping subject to moving loads. An exact dynamic element matrix method is adopted to model Timoshenko beam structures. A generalized modal analysis method is applied to derive response formulae for beam structures subject to moving loads. The proposed method offers an exact and closed form solution. Two numerical examples are provided for validating and illustrating the proposed method. In the first numerical example, a single span beam with multiple moving loads is considered. A dynamic analysis on a multi-span beam under a moving load is considered as the second example, in which the flexibility and damping of supporting joints are taken into account. The numerical study proves that the proposed method is useful for the vibration analysis of multi-span beam-hype structures by moving loads.

Viscous damage model for timoshenko beam structures

A local damage constitutive model based on Kachanov's theory is used within a finite element frame and applied to the case of 2D and 3D Timoshenko beam elements. The model takes into account viscous effects, thus allowing damping to be considered in a rigorous way. A damage index based on potential energy criteria, useful in evaluating the behaviour of structures or of parts of structures, is proposed. The procedure is applied to estimate the damage produced by seismic actions in reinforced concrete building structures, whose response is computed by using a non-linear Newmark-type incremental time integration scheme. Three numerical examples are included; one of them compares results obtained by using the proposed model with results of a laboratory test.

Eigenfrequencies of the three dimensional euler-bernoulli beam system with dissipative joints

In this paper, we will compute the transfer matrices to find the eigenfrequencies for the vibrations of the general non-collinear Euler-Bernoulli or Timoshenko beam structure with dissipative joints. We will allow the structure to be three dimensional, and thus we must consider all types of vibrations simultaneously, including longitudinal and torsional vibrations. The general structure considered will consist of any number of beams joined end to end to form a chain. Many different kinds of dampers are allowed, even within the same structure. We also will allow different materials within the structure as well as different beam widths. We then will show that asymptotic estimates can be used to find the eigenfrequencies approximately.

Nonlinear finite element modeling of a high speed rotating timoshenko beam structure

The demand for designing high speed turbomachinery has led to intensive research in dynamic modeling of rotating elastic mechanisms in recent years. Such a demand in the design arena is usually addressed by better computational schemes. A nonlinear finite element modeling scheme is presented in this paper to address this demand. The proposed modeling scheme incorporates three new features to improve computational accuracy and efficiency. First, the rotating beam is modeled as a Timoshenko beam with the inclusion of gyroscopic inertia and geometric stiffness. The geometric stiffness is modeled with exact tangent matrix as opposed to conventional pseudo-tangent matrix approximation. Second, the time separation concept is introduced to allow time-independent terms being computed separately and assembled with time-dependent terms in each integration time step. This separation concept is applicable to both linear and nonlinear time-independent terms. Third, the computational scheme is formulated in homogeneous coordinates that provide a natural and efficient vector representation for dynamic modeling of a rotating structure. Kane's classic rotating beam problem is used to test the accuracy and efficiency of the proposed computational scheme. The numerical solution of the present formulation agrees well with that of Simo's. Moreover, the computer time required for the present formulation is reduced by a factor of 70%.

Computation of the Eigenvalues of Wave Propagation in Periodic Substructural Systems

The wave propagation constants of periodic structures are computed using the exact dynamic stiffness matrix of a typical substructure. The approach used is to show that wave propagation and the natural vibration eigenproblem are similar to such an extent that methods used to find the natural frequencies of a structure can be applied to find its wave propagation constants. The Wittrick-Williams algorithm has been incorporated into a finite element program, JIGFEX, in conjunction with exact dynamic member stiffnesses, to ensure that no phase propagation eigenvalues are missed during computation. The accuracy of the present approach is then demonstrated by comparing the results that it gives to analytically determined wave propagation curves for a Timoshenko beam on periodic simple supports. Finally, phase propagation curves are given for a complex Timoshenko beam structure of a type that would be very difficult to analyze analytically.