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3 Vibrations in Physical Systems

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Vibration analysis of a thick ring interacting with the disk treated as an elastic foundation

Noga S., Markowski T.

Vibrations in Physical Systems

2014

Vol. 26

217--222

In this study the in plane flexural vibration of a thick ring interacting with Winkler foundation is analysed on the basis of the analytical and numerical method. The effect of rotary inertia and shear deformation is included. The normal frequencies and natural mode shapes of the system vibration are determined. Achieved results are discussed and compared with an experimental data. FE models are formulated by using ANSYS code.

Free vibrations of column subjected to Euler's load with consideration of Timoshenko's theory

Uzny S., Sokół K.

Vibrations in Physical Systems

2014

Vol. 26

319--326

In this paper the single-rod cantilever column subjected to compressive Euler's load is investigated. The boundary problem has been formulated on the basis of Hamilton's principle and Timoshenko's theory. Numerical simulations of characteristic curves have been plotted on the plane external load-vibration frequency for different magnitudes of slenderness factor of the system. The results of numerical calculations of Timoshenko's beam are compared to the ones obtained from mathematical Bernoulli-Euler's model. The comparison of the results of characteristic curves calculated by means of Timoshenko's theory and Bernoulli-Euler's model are done for first three vibration frequencies.

In plane flexural vibration of a ring interacting with the Winkler foundation

Noga S., Markowski T.

Vibrations in Physical Systems

2012

Vol. 25

305--310

In this study the in plane flexural vibration of a system of circular ring interacting with elastic foundation is presented on the basis of the analytical method and numerical simulation. The elastic foundation is described by the Winkler model. At first the motion of the system is described by partial differential equations. The effect of rotary inertia and shear deformation is included. The general solution of the free vibration is derived by the separation of variable method and the boundary problem is solved. The second model is formulated by using finite element representations. The natural frequencies and natural mode shapes of vibration of the system are determined. The obtained results of calculation are discussed and compared for these two models. FE models are formulated by using ANSYS code. It is important to note that the data presented in the paper brings practical advice to design engineers.