A Refined Model of Dynamic Deformation of a Rod-Strip with a Fixed Section of a Finite Length on One of the Facial Surfaces
V. N. Paimushin1,2, V. M. Shishkin3
1Kazan National Research Technical University, Kazan, Russia
2Kazan (Volga Region) Federal University, Kazan, Russia
3Vyatka State University, Kirov, Russia
Keywords: oscillations, rod-strip, fixed section of final length, Timoshenko shear model, transverse compression
Abstract
The problem of forced bending vibrations of a rod-strip with two consoles and a fixed section of finite length on one of the front surfaces is solved. To describe the processes of deformation of consoles, the Timoshenko model is used without taking into account transverse compression and a fixed section - the same deformation model taking into account transverse compression, modified by taking into account the presence of a fixed fixed section. The conditions for the kinematic coupling of the consoles and the fixed section are formulated. Based on the Hamilton-Ostrogradsky variational principle, the equations of motion and boundary conditions, as well as the force conditions for the coupling of sections of the rod, are formulated. Exact analytical solutions of the equations of motion under the influence of a harmonic transverse force at the end of one of the rod consoles are obtained. Numerical experiments were carried out in which the passage of resonant vibrations through a fixed section of finite length in rods made of duralumin and fiber composite was studied, with and without taking into account the transverse compression of the fixed section. A significant increase in the vibration amplitude of the end of the unloaded cantilever of a duralumin rod was discovered due to transverse compression of the fixed section. For a composite rod, the vibration amplitude increased slightly.
|
