Dynamic response and stability of an inclined Euler beam under a moving vertical concentrated load

Yang, D.S.; Wang, Chen

doi:10.1016/j.engstruct.2019.01.140

Cited by 30 publications

(19 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…en, the increment of each unknown quantity of the system in the time step is obtained. e equations of contact surface in three-dimensional are also shown as 8 Mathematical Problems in Engineering…”

Section: Mixed Finite Element Methodologymentioning

confidence: 99%

“…Winkler established the liner relationship between contact forces and deflection deformation, and got the analytical solution of contact problem in beam on elastic foundation [7]. Analytical method is still studied today and is widely used to solve the problem of dynamic load in rail transportation [8,9]. e direct iterative method is numerical.…”

Section: Introductionmentioning

confidence: 99%

“…A series of studies in contact problems of beam on elastic foundation make excellent contributions to long-span engineering programs [8]. It assumes that the reactive force of the foundation carrying a loaded beam at every point is proportional to the corresponding deflection of the beam [7].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Combining Finite Element and Analytical methods to Contact Problems of 3D Structure on Soft Foundation

Zhang

et al. 2020

Mathematical Problems in Engineering

View full text Add to dashboard Cite

The computational efficiency and nonconvergence of the iteration are two main difficulties in contact problems, especially in the creep of the foundation. This paper proposes a method to analyze the structural soft foundation system affected by time. The methodology is an explicit method, combining the finite element method with the analytical method. The creep deformation of soft foundation is obtained based on Laplace transforms. The structural deformation contains the statically determinate structural deformation and rigid body displacement, solved by the finite method. The contact forces are calculated by the deformation coordination equations and equilibrium equations. The methodology is validated through augmented Lagrangian (AL) method. The results can clearly illustrate the local disengagement phenome, greatly overcome the nonconvergence of the iteration, and significantly improve computing efficiency.

show abstract

Section: Mixed Finite Element Methodologymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Combining Finite Element and Analytical methods to Contact Problems of 3D Structure on Soft Foundation

Zhang

et al. 2020

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…This limitation can be overcome by the help of numerical approaches. Among them, the finite element method (FEM) has been widely used because of its powerful flexibility, versatility, and the ability to handle problems with complex geometry and boundary conditions [2,5,12,18,20,21,25,26]. However, the conventional FEM (say the h-version FEM) exhibits slow convergence with mesh refinement.…”

Section: Introductionmentioning

confidence: 99%

An accurate differential quadrature procedure for the numerical solution of the moving load problem

Eftekhari

2020

J Braz. Soc. Mech. Sci. Eng.

View full text Add to dashboard Cite

In moving load-type problems, the moving point load is modeled mathematically by a time-dependent Dirac-delta function. A key and difficult step in solving this type of problems using a point discrete method such as the differential quadrature method is the discretization of the Dirac-delta function in a simple and accurate manner. This paper is conducted to facilitate this step and to present a new way to do this task. In this way, the Dirac-delta function is approximated by orthogonal polynomials such as the Legendre and Chebyshev polynomials. Unlike the original Dirac-delta function, which is a generalized singularity function, the resulting approximation function is a non-singular function which can be discretized simply and efficiently. The proposed procedure is applied herein to solve the moving load problem in beams and rectangular plates. Comparisons with available analytical and numerical solutions prove that the proposed approach is highly accurate and efficient.

show abstract

“…The dynamic problem of beams under moving loads is also a research hot spot. Yang and Wang [16] studied the dynamic response and stability of an inclined beam under a moving vertical concentrated load. They presented the governing equation for transverse motion of the beam.…”

Section: Introductionmentioning

confidence: 99%

Vibration characteristics of Timoshenko stepped beam under moving load considering inertial effect

Wang¹,

Sun²,

Li³

2020

J. vibroeng.

View full text Add to dashboard Cite

The vibration of gun barrels would result in the change of impact point, which would further reduce the firing accuracy of weapons. In the past, the calculation model based on the Euler beam theory could not satisfy the accuracy requirements. Based on the Timoshenko beam theory, the vibration equation of the stepped beam is established by invoking continuum transfer matrix method. The forced vibration of the stepped beam under the inertial moving load is solved. The model has better precision than the Euler beam model. The endpoint of the cantilever beam is analyzed. It is shown that the endpoint response increases with the increasing mass and acceleration of moving load, so does the inertial coefficient. With the increase of moving load speed, the endpoint response decreases, and the inertia coefficient increases. Among the three parameters, the mass of moving load is the main factor affecting the inertia coefficient. Furthermore, both free and forced vibrations of other stepped beam shaped structures with arbitrary segments and boundary conditions can be explored by using the proposed method.

show abstract

Dynamic response and stability of an inclined Euler beam under a moving vertical concentrated load

Cited by 30 publications

References 37 publications

Combining Finite Element and Analytical methods to Contact Problems of 3D Structure on Soft Foundation

Combining Finite Element and Analytical methods to Contact Problems of 3D Structure on Soft Foundation

An accurate differential quadrature procedure for the numerical solution of the moving load problem

Vibration characteristics of Timoshenko stepped beam under moving load considering inertial effect

Contact Info

Product

Resources

About