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Dynamical flexibilities of mechanical rotational systems

Żółkiewski S.

Journal of Achievements in Materials and Manufacturing Engineering

2008

Vol. 31, nr 2

602-609

Purpose: of this work is to present dynamical flexibilities of rotational beams and rods systems. The results of mathematical calculations were presented in the form of dynamical flexibility of analyzed systems. In final solution there were took into consideration the interactions between the major motions and local vibrations of subsystems. Design/methodology/approach: The dynamical flexibilities were derived by the Galerkin's method. The dynamical flexibilities for example numerical cases were presented onto charts of attenuation-frequency characteristics. The mathematical models were derived on the basis of known equations of motion derived in previous thesis's. Findings: After analysis of characteristics we can observe the transportation effect. We can notice additional poles on the characteristic of dynamical flexibility characteristics and after increasing angular velocity created modes symmetrically propagate from the origin mode and instead of the original mode there is created a zero's amplitude. Research limitations/implications: Analyzed systems are beams and rods in rotational motion. Motion was limited to plane motion. Future works will be connected with consideration of complex systems. Practical implications: of derived dynamical flexibilities of free-free and fixed beams and rods systems is a possibility of derivation of the stability zones of analyzed systems and derivation of eigenfrequencies and zeros in the function of angular velocity of work motion. Originality/value: Models analyzed in this thesis apply to rotating rod and beam systems with taking into consideration the transportation effect. This new approach of analyzing rod and beam systems can be put to use in modelling, analyzing and designing machines and mechanisms with rotational elements.

Mechanical systems vibrating longitudinally with the transportation effect

Buchacz A., Żółkiewski S.

Journal of Achievements in Materials and Manufacturing Engineering

2007

Vol. 21, nr 1

63-66

Purpose: High work speeds of mechanisms, using materials with high flexibility, high precision of work, etc. are the cause of searching of the new ways of modelling. One of these ways is presented in this thesis. The main purpose of this thesis is the dynamical analysis with taking into consideration the interaction between main motion and local vibrations during the model is loaded by longitudinal forces. Design/methodology/approach: Derived equations of motion were made by classical methods, with generalized coordinates and generalized velocities assumed as orthogonal projections of individual coordinates and velocities of the rod and manipulators to axes of the global inertial frame. Findings: Mathematical model of the longitudinally vibrating systems in terms of plane motion can be put to use to derivation of the dynamical flexibility of these systems, and also those equations are the starting point to the analysis of complex systems, especially we can use those equations to derivation of the substitute dynamical flexibility of n-linked systems in transportation. Research limitations/implications: In the thesis were considered mechanical systems vibrating longitudinally in terms of rotation. Next problem of dynamical analysis is the analysis of systems in non-planar transportation and systems loaded by transversal forces. Practical implications: Results of this thesis can be put to use into machines and mechanisms in transportation such as: wind power plant, high speed turbines, rotors, manipulators and in aerodynamics issues, etc. Originality/value: Up to now there were analyzed beams and rods in a separate way, first main motion of the system and after that the local vibrations. The new approach of modelling were presented by authors of this thesis, a new modelling took into consideration the interaction between those two displacements. There was defined the transportation effect for models vibrating longitudinally in this thesis.