Free Vibrations and Stability of an Elastically Connected Double-Beam System
Free oscillations and static stability of two elastically connected beams are considered in Chapter 2. At various examples it is shown analytically obtained results and impacts of some mechanical parameters of the system on the natural frequencies and amplitudes. Verification of obtained results is shown by comparison with results of the existed classical models. New scientific contribution in this chapter is formulation of the new double-beam model described with new derived equations of motion with rotational inertia effects and with inertia of rotation with transverse shear (Rayleigh’s model, Timoshenko’s model, Reddy - Bickford’s model). It is formulized the static stability condition of the two elastically connected beams of different types with analytical expressions for the various values of critical forces. Numerical experiments confirmed the validity of the analytical results obtained by comparing the results of the models existing in the literature. From chapter 2 it can be concluded that the effects of rotational inertia and transverse shear must be taken into account in the model of thick beams because errors that occur by ignoring them are increasing with the increasing the mode of vibration.
KeywordsFree Vibration Transverse Shear Rotary Inertia Transverse Motion Axial Compression Force
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