scholarly journals ISOGEOMETRIC – BASED DYNAMIC ANALYSIS OF BERNOULLI – EULER CURVED BEAM SUBJECTED TO MOVING LOAD

2020 ◽  
Vol 14 (1) ◽  
Author(s):  
Miloš M. Jočković ◽  
Marija Nefovska – Danilović
Keyword(s):  
Dynamic Analysis ◽  
Constant Velocity ◽  
Moving Load ◽  
Beam Element ◽  
Basis Functions ◽  
Curved Beam ◽  
Euler Beam ◽  
Velocity Magnitude ◽  
Constant Magnitude ◽  
Single Force

In this paper dynamic analysis of a curved Bernoulli – Euler beam subjected to a moving load ispresented. Moving load is modelled as a single force with constant magnitude and direction, whichmoves along its trajectory. Plane curved Bernoulli – Euler beam element is formulated usingisogeometric approach where both the displacement field and geometry of the beam are describedusing NURBS basis functions. Behavior of the beam element is defined and studied in the case oflinear formulation where displacements and displacement gradients are assumed to be small.Validation of the proposed approach is presented for the plane curved beam subjected to movingload with constant velocity, magnitude and direction.

A New Three-Dimensional Moving Timoshenko Beam Element for Moving Load Problem Analysis

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Yan Xu ◽  
Weidong Zhu ◽  
Wei Fan ◽  
Caijing Yang ◽  
Weihua Zhang
Keyword(s):  
Dynamic Analysis ◽  
Coordinate System ◽  
Timoshenko Beam ◽  
Moving Load ◽  
Three Dimensional ◽  
Beam Element ◽  
Superposition Method ◽  
Reference Coordinate System ◽  
Current Formulation ◽  
Timoshenko Beam Element

Abstract A new three-dimensional moving Timoshenko beam element is developed for dynamic analysis of a moving load problem with a very long beam structure. The beam has small deformations and rotations, and bending, shear, and torsional deformations of the beam are considered. Since the dynamic responses of the beam are concentrated on a small region around the moving load and most of the long beam is at rest, owing to the damping effect, the beam is truncated with a finite length. A control volume that is attached to the moving load is introduced, which encloses the truncated beam, and a reference coordinate system is established on the left end of the truncated beam. The arbitrary Lagrangian–Euler method is used to describe the relationship of the position of a particle on the beam between the reference coordinate system and the global coordinate system. The truncated beam is spatially discretized using the current beam elements. Governing equations of a moving element are derived using Lagrange’s equations. While the whole beam needs to be discretized in the finite element method or modeled in the modal superposition method (MSM), only the truncated beam is discretized in the current formulation, which greatly reduces degrees-of-freedom and increases the efficiency. Furthermore, the efficiency of the present beam element is independent of the moving load speed, and the critical or supercritical speed range of the moving load can be analyzed through the present method. After the validation of the current formulation, a dynamic analysis of three-dimensional train–track interaction with a non-ballasted track is conducted. Results are in excellent agreement with those from the commercial software simpack where the MSM is used, and the calculation time of the current formulation is one-third of that of simpack. The current beam element is accurate and more efficient than the MSM for moving load problems of long three-dimensional beams. The derivation of the current beam element is straightforward, and the beam element can be easily extended for various other moving load problems.

An Efficient Dimension-Adaptive Numerical Integration Method for Stochastic Dynamic Analysis of Structures with Uncertain Parameters

2020 ◽  
pp. 2150035
Author(s):  
Helu Yu ◽  
Bin Wang ◽  
Zongyu Gao ◽  
Yongle Li
Keyword(s):  
Dynamic Analysis ◽  
Numerical Integration ◽  
Structural Model ◽  
Integration Method ◽  
Moving Load ◽  
Quadrature Formulas ◽  
Stochastic Dynamic ◽  
Numerical Integration Method ◽  
Euler Beam ◽  
Stochastic Parameters

This paper presents a novel dimension-adaptive numerical integration method for dynamic analysis of structures with stochastic parameters subjected to deterministic excitations. First, an efficient dimension-adaptive algorithm is proposed to detect the importance of each random parameter involved in the structural model, based on which the quadrature nodes used for numerical integration can be collocated more reasonably. Then, the Gaussian quadrature formulas are used to evaluate the structural response statistics. To further improve the robustness and efficiency of the proposed method, the dimension-adaptive integration is only used to calculate the structural displacement response statistics. The velocity and acceleration response statistics are further evaluated using the finite difference formulas based on the concept of stochastic difference. Such a strategy is especially attractive when evaluating the response statistics of the derivative processes requires more quadrature nodes than that of the original process. Finally, two numerical examples encountered in civil engineering, including a shear frame with stochastic parameters subjected to a seismic ground motion and an Euler beam with unidimensional stochastic field of material properties (discretized via the Karhunen–Loève expansion) subjected to a moving load are studied to illustrate the performance of the proposed method. Via the numerical results, the accuracy and efficiency of the proposed method are verified.

Steady-State Vibrations of a Beam on a Pasternak Foundation for Moving Loads

1980 ◽  
Vol 47 (4) ◽  
pp. 879-883 ◽  
Author(s):  
H. Saito ◽  
T. Terasawa
Keyword(s):  
Steady State ◽  
Constant Velocity ◽  
Moving Load ◽  
Equations Of Motion ◽  
Pasternak Foundation ◽  
Moving Loads ◽  
Euler Beam ◽  
Exponential Fourier Transform ◽  
Steady State Solutions ◽  
Beam Theories

The response of an infinite beam supported by a Pasternak-type foundation and subjected to a moving load is investigated. It is assumed that the load is uniformly distributed over the finite length on a beam and moves with constant velocity. The equations of motion based on the two-dimensional elastic theory are applied to a beam. Steady-state solutions are determined by applying the exponential Fourier transform with respect to the coordinate system attached to the moving load. The results are compared with those obtained from the Timoshenko and the Bernoulli-Euler beam theories, and the differences between the displacement and stress curves obtained from the three theories are clarified.

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