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2 Selected Engineering Problems

2 Płaczek M.

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Exact and approximate methods in analysis of one-dimensional mechanical systems

Płaczek M.

Selected Engineering Problems

2016

nr 7

37--42

Paper presents comparison of an exact Fourier method and an approximate Galerkin method in analysis of one-dimensional vibrating mechanical systems. Assumptions of the approximate method are presented. The considered systems are beams with different methods of fixing - different boundary conditions. Values of natural frequencies and dynamic flexibilities of considered systems are designated using the approximate method and compared with results obtained using the exact method.

An example of use of an approximate method to analyse mechanical systems

Płaczek M.

Selected Engineering Problems

2012

nr 3

173--176

Paper presents an example of an approximate method application to the analysis of mechanical systems. The analysed system is a simply supported vibrating beam, excited by an external harmonic force. The approximate Galerkin method is used to analyse it and to designate a dynamic flexibility of the system. The possibility of using the Galerkin method and its verification was a first step to processes of analysis and synthesis of simple and complex mechatronic systems with piezoelectric transducers connected with mechanical subsystems. In this paper the simply supported beam is analysed with the external force applied in a distance η from the one of the beam’s end. It causes the analysis more complicated and exactness of the approximate method must be verified in this case.