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3 Vibrations in Physical Systems

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General numerical description of a mass moving along a structure

Dyniewicz B., Bajer C.

Vibrations in Physical Systems

2012

Vol. 25

135--140

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.

String-beam under moving inertial load

Dyniewicz B., Bajer C.

Vibrations in Physical Systems

2008

Vol. 23

115--120

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.

Moving inertial load and numerical modelling

Bajer C., Dyniewicz B.

Vibrations in Physical Systems

2008

Vol. 23

65--70

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.