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Content available remote New feature of the solution of a Timoshenko beam carrying the moving mass particle
100%
Dyniewicz B. , Bajer C. I.
Archives of Mechanics
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2010
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tom Vol. 62, nr 5
327-341
EN
The paper deals with the problem of vibrations of a Timoshenko beam loaded by a travelling mass particle. Such problems occur in a vehicle/track interaction or a power collector in railways. Increasing speed involves wave phenomena with significant increase of amplitudes. The travelling speed approaches critical values. The moving point mass attached to a structure in some cases can exceed the mass of the structure, i.e. a string or a beam, locally engaged in vibrations. In the literature, the travelling inertial load is often replaced by massless forces or oscillators. Classical solution of the motion equation may involve discussion concerning the contribution of the Dirac delta term, multiplied by the acceleration of the beam in a moving point in the differential equation. Although the solution scheme is classical and successfully applied to numerous problems, in the paper the Lagrange equation of the second kind applied to the problem allows us to obtain the final solution with new features, not reported in the literature. In the case of a string or the Timoshenko beam, the inertial particle trajectory exhibits discontinuity and this phenomenon can be demonstrated or proved mathematically in a particular case. In practice, large jumps of the travelling inertial load is observed.
2
Content available Nonlinear vibration of a beam resting on a nonlinear viscoelastic foundation traversed by a moving mass: a homotopy analysis
100%
Pourseifi M. , Monfared M. M.
Engineering Transactions
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2022
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tom Vol. 70, iss. 4
355--371
EN
In this study, the dynamic response of an Euler-Bernoulli beam resting on the nonlinear viscoelastic foundation under the action of a moving mass by considering the stretching effect of the beam’s neutral axis is investigated. A Dirac-delta function is applied to model the location of the moving mass along the beam as well as its inertial effects. The Galerkin decomposition method is used to transform a partial dimensionless nonlinear differential equation of dynamic motion into an ordinary nonlinear differential equation. Subsequently, the well-known homotopy analysis method (HAM) is employed to obtain an approximate analytical solution of this equation. The validity and accuracy of the solution are examined numerically using the fourth-order Runge-Kutta method. Finally, several examples are provided to show the effects of parameters such as linear and nonlinear stiffness coefficients of a viscoelastic foundation, velocity of the moving mass as well as Coriolis force, centrifugal force and inertia force of the moving mass on the dynamic deflection of the beam.
3
Content available remote Moving inertial load and numerical modelling
75%
Bajer C. , Dyniewicz B.
Vibrations in Physical Systems
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2008
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tom Vol. 23
65--70
EN
The paper presents the numerical approach to the moving mass prob¬lem. We consider the string and beam discrete element carrying a mass particle. In the literature efficient computational methods can not be found. The same disadvantage can be observed in commercial codes for dynamic simulations. Classical finite element solution fails. The space-time finite element approach is the only method which now results in convergent solutions and can be successfully applied in practice. Characteristic matrices and resulting solution scheme are briefly described. Examples prove the efficiency of the approach.
4
Content available remote General numerical description of a mass moving along a structure
75%
Dyniewicz B. , Bajer C.
Vibrations in Physical Systems
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2012
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tom Vol. 25
135--140
EN
The paper deals with vibrations of structures under a moving inertial load. The space-time finite element, approach has been used for a general description of the moving mass particle. Problems occur when we perform computer simulations. In the case of wave problem numerical description of the moving inertial loads requires great mathematical care. Otherwise we get a wrong solution. There is no commercial computing packages that would enable us direct simulation of moving loads, both gravitational and inertial.
5
Content available remote Numerical methods for vibration analysis of Timoshenko beam subjected to inertial moving load
63%
Dyniewicz B. , Bajer C. I.
Vibrations in Physical Systems
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2010
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tom Vol. 24
87--92
EN
The paper deals with the problem of modeling of the moving mass particle in numerical computation by using the finite element method in one dimensional wave problems in which both the displacement and angle of the pure bending are described by linear shape functions. The analysis is based on the Timoshenko beam theory. We consider the simply supported beam, in a range of small deflections with zero initial conditions.
PL
Praca omawia problem modelowania numerycznego poruszającej się cząstki masowej metodą elementów skończonych w zadaniu jednowymiarowym. Przemieszczenia i obroty opisano liniowymi funkcjami kształtu. Analizę oparto na teorii belki Timoshenki.
6
Content available remote String-beam under moving inertial load
63%
Dyniewicz B. , Bajer C.
Vibrations in Physical Systems
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2008
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tom Vol. 23
115--120
EN
The paper deals with the original analytical-numerical approach to the Bernoulli-Euler beam with additional tensile effect under a moving inertial load. The authors applied the 2nd kind Lagrange equation to derive a motion differential equation of the problem. The moving mass can travel through the string-beam with a whole range constant speed, also overcritical. The analytical solution requires a numerical calculation in the last stage and is called a semi-analytical one.
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