Discontinuous Trajectory of the Mass Particle Moving on a String or a Beam

• Autorzy: Dyniewicz B. , Bajer C. I.
• Konferencja: Polish-German Workshop on Dynamical Problems of Mechanical Systems (10 ; 3-7.09.2007 ; Goslar, Germany)
• Języki publikacji: EN

Abstrakty

EN

The paper deals with a new solution of the string or beam vibrating under a moving mass. Numerous solutions published up to date exhibit incorrect solutions. Moreover, they are not sufficiently simple and can not be applied to a whole range of the mass speed, also in over-critical range. We propose the solution of the problem that allows us to reduce the problem to the second order matrix differential equation. Its solution is characteristic of all features of the critical, sub-critical and over-critical motion. Results exhibit discontinuity of the mass trajectory at the end support point. The closed solution in the case of massless string is analysed and the discontinuity is mathematically proved. Numerical results obtained for inertial string demonstrate similar features. Small vibrations are analysed and that is why the effect discussed in the paper is of pure mathematical interest. However, the phenomenon can increase the complexity in discrete solutions.

Słowa kluczowe

EN

discontinuous trajectory; Fourier solution; Lagrange equation

• Wydawca: Oficyna Wydawnicza Politechniki Warszawskiej
• Czasopismo: Machine Dynamics Problems
• Rocznik: 2007
• Tom: Vol. 31, No. 2
• Strony: 66--79
• Opis fizyczny: Bibliogr. 12 poz., rys., wykr.

Twórcy

autor

Dyniewicz B.

autor

Bajer C. I.

• Polish Academy of Sciences. Institute of Fundamental Research,

Bibliografia

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• Dyniewicz, B., Bajer, C.I., 2007, Inertial load moving on a string-discontinuous solution, in: Theoretical Foundations of Civil Engineering.
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