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Dynamical flexibility of rod and beam systems in transportation

Żółkiewski S.

Journal of Achievements in Materials and Manufacturing Engineering

2008

Vol. 29, nr 2

171-174

Purpose: Purpose of this paper is to present a mathematical model of rod and beam systems in transportation. The mathematical model is presented in the form of dynamical flexibility of systems. Systems are considered as flexible rotating rods and flexible rotating beams. In solution there was took into account the interaction between the main motion and local vibrations of elements. Design/methodology/approach: The dynamical flexibility was derived by the approximate method, the Galerkin's method. The example dynamical characteristics were presented in form of attenuation-frequency characteristics. The dynamical flexibility was derived on the basis of known equations of motion derived in other publications. Findings: There can be observed so called the transportation effect. This effect consist in that when analyzed system rotates with some angular velocity in the characteristic of dynamical flexibility we can notice additional poles and after increasing angular velocity it is noticeable that created modes are symmetrically propagated from the original mode. It is also palpable fact, instead of the original mode there is created zero. Research limitations/implications: Analyzed systems are simple linear type beams and rods in rotational motion. Motion was restricted to plane motion. Future research ought to consider complex systems, damped models and also nonlinearity. Practical implications: Practical implications of derived mathematical models of beam and rod systems both the free-free ones and fixed ones is a possibility of derivation of the stability zones of analyzed systems and derivation of eigenfrequencies and zeros in the way of changing the value of angular velocity. Originality/value: Presented models apply to rotating flexible rod and beam systems with taking into consideration the transportation effect. It is a new approach of analyzing rod and beam systems and can be put to use in modelling and analyzing machines and mechanisms in rotational transportation.