scholarly journals Elastic guide rail oscillation due to moving concentrated load

2019 ◽  
pp. 62-66
Author(s):  
Vladimir P. Savchuk ◽  
Pavel A. Savenkov
Keyword(s):  
Differential Equation ◽  
Moving Load ◽  
Oscillatory System ◽  
Material Point ◽  
Elastic Cylindrical Shell ◽  
Dimensionless Form ◽  
Guide Rail ◽  
Concentrated Load ◽  
Deviating Argument ◽  
Internal Forces

This article illustrates the solution of a differential equation describing oscillations of an elastic tensioned guide rail, which consist of string bundle enclosed in an elastic cylindrical shell, while concentrated load, simulated by a material point, moves along it. The oscillatory system is considered in such way that the guide rail supports freely. The existing external and internal forces of resistance to movement of the guide rail are also taken into account. Initial and boundary conditions are zero. In article «A string bend under a moving load», published in the journal «Vestnik BGU. Seriya 1, Fizika. Matematika. Informatika» (2004, No. 1), the deflection of a flexible guide rail under load was obtained by solving an equation with deviating argument. In this article, an algorithm is constructed for finding deflection of an elastic tensioned guide rail in the form of a cubic splines. All the results of calculations are presented in a dimensionless form.

scholarly journals Modal Analysis of Vibration of Euler-Bernoulli Beam Subjected to Concentrated Moving Load

2020 ◽  
pp. 2324-2334
Author(s):  
Usman M. A ◽  
Makinde T. A. ◽  
Daniel D. O.
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Methods ◽  
Modal Analysis ◽  
Series Solution ◽  
Moving Load ◽  
Bernoulli Beam ◽  
Partial Differential ◽  
Concentrated Load ◽  
Euler Bernoulli Beam

This paper investigates the modal analysis of vibration of Euler-Bernoulli beam subjected to concentrated load. The governing partial differential equation was analysed to determine the behaviour of the system under consideration. The series solution and numerical methods were used to solve the governing partial differential equation. The results revealed that the amplitude increases as the length of the beam increases. It was also found that the response amplitude increases as the foundation increases at fixed length of the beam.

Numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument

2017 ◽  
Vol 23 (2) ◽  
Author(s):  
Muhad H. Abregov ◽  
Vladimir Z. Kanchukoev ◽  
Maryana A. Shardanova
Keyword(s):  
Differential Equation ◽  
Numerical Methods ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
Deviating Argument ◽  
Second Order Differential Equation

AbstractThis work is devoted to the numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument in minor terms. The sufficient conditions of the one-valued solvability are established, and the a priori estimate of the solution is obtained. For the numerical solution, the problem studied is reduced to the equivalent boundary value problem for an ordinary linear differential equation of fourth order, for which the finite-difference scheme of second-order approximation was built. The convergence of this scheme to the exact solution is shown under certain conditions of the solvability of the initial problem. To solve the finite-difference problem, the method of five-point marching of schemes is used.

scholarly journals ON OSCILLATIONS DESCRIBING A GENERALIZED DIFFERENTIAL RELAY EQUATION

2020 ◽  
pp. 53-60
Author(s):  
Vasiliy Olshansky ◽  
Stanislav Olshansky ◽  
Oleksіі Tokarchuk
Keyword(s):  
Differential Equation ◽  
Initial Conditions ◽  
Oscillatory System ◽  
Equation Of Motion ◽  
Resistance Force ◽  
Oscillatory Process ◽  
Initial Deviation ◽  
Approximate Analytical Solutions ◽  
Positive Exponent ◽  
Generalized Differential

The motion of an oscillatory system with one degree of freedom, described by the generalized Rayleigh differential equation, is considered. The generalization is achieved by replacing the cubic term, which expresses the dissipative strength of the equation of motion, by a power term with an arbitrary positive exponent. To study the oscillatory process involved the method of energy balance. Using it, an approximate differential equation of the envelope of the graph of the oscillatory process is compiled and its analytical solution is constructed from which it follows that quasilinear frictional self-oscillations are possible only when the exponent is greater than unity. The value of the amplitude of the self-oscillations in the steady state also depends on the value of the indicator. A compact formula for calculating this amplitude is derived. In the general case, the calculation involves the use of a gamma function table. In the case when the exponent is three, the amplitude turned out to be the same as in the asymptotic solution of the Rayleigh equation that Stoker constructed. The amplitude is independent of the initial conditions. Self-oscillations are impossible if the exponent is less than or equal to unity, since depending on the initial deviation of the system, oscillations either sway (instability of the movement is manifested) or the range decreases to zero with a limited number of cycles, which is usually observed with free oscillations of the oscillator with dry friction. These properties of the oscillatory system are also confirmed by numerical computer integration of the differential equation of motion for specific initial data. In the Maple environment, the oscillator trajectories are constructed for various values of the nonlinearity index in the expression of the viscous resistance force and a corresponding comparative analysis is carried out, which confirms the adequacy of approximate analytical solutions.

Calculation of State Transfer of Curved Bridge

2011 ◽  
Vol 243-249 ◽  
pp. 1701-1706 ◽  
Author(s):  
Jing Jing Xi ◽  
Qing Ning Li ◽  
Tian Li Wang
Keyword(s):  
Differential Equation ◽  
Structural Analysis ◽  
Cross Section ◽  
Transfer Matrix Method ◽  
Transfer Equation ◽  
Matrix Method ◽  
Curved Bridge ◽  
State Transfer ◽  
Torsional Coupling ◽  
Internal Forces

The field transfer matrixs and the point transfer matrixs can be established by the transfer matrix method, which can solve the internal forces and deformations problems of each cross-section, based on the solutions of deflection differential equation of the curved bridge. The bending-torsional coupling, horizontal bending and axial deformations should be considered into the structural analysis of the curved bridge, under the influence of curvature. To establish the general transfer equation requires the field transfer matrixs and the point transfer matrixs of the curved bridge in horizontal and vertical directions. The state vectors of each cross-section can be obtained depending on the general transfer equation.

Green's function for a differential equation with a deviating argument

1975 ◽  
Vol 17 (3) ◽  
pp. 259-262
Author(s):  
I. N. Inozemtseva ◽  
Yu. V. Komlenko ◽  
S. A. Pak
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Deviating Argument

scholarly journals On nonlinear boundary value problems with deviating arguments and discontinuous right hand side

1993 ◽  
Vol 6 (1) ◽  
pp. 83-91
Author(s):  
B. C. Dhage ◽  
S. Heikkilä
Keyword(s):  
Differential Equation ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Deviating Arguments ◽  
Deviating Argument ◽  
Right Hand ◽  
Nonlinear Boundary Value ◽  
The Right ◽  
Generalized Iteration

In this paper we shall study the existence of the extremal solutions of a nonlinear boundary value problem of a second order differential equation with general Dirichlet/Neumann form boundary conditions. The right hand side of the differential equation is assumed to contain a deviating argument, and it is allowed to possess discontinuities in all the variables. The proof is based on a generalized iteration method.

Sign in / Sign up

Export Citation Format

Share Document