ISSN 2542–0380 
Труды Института механики им. Р.Р. Мавлютова
Электронный научный журнал  Electronic Scientific Journal
Proceedings of the Mavlyutov Institute of Mechanics

Research has been performed on natural transverse vibrations of a portion of a constant length in a straight threelayered plate with a filler moving along the neutral line of a nondeformed state. The movement takes place between two rigidly fixed coaxial guides (clamps), the distance between them equalling the length of the vibrating portion. The longitudinal force is assumed to constantly act along the neutral line. It has been found that an increase in the natural frequencies of flexural vibrations of the plate occurs with an increase in the thickness of the filler. Using two frequencies of flexural vibrations, we can determine the velocity of the moving threelayered plate and the thickness of its filler. The results of the research work can find technological use in the problems on dynamics and strength of machines and mechanisms in manufacturing threelayered plate with fillers and can be used to determine the velocity of a plate and the thickness of its filler using two frequencies of flexural vibrations.
plate movement,
threelayered plate,
flexural vibrations,
natural frequencies,
primal and inverse problems
Goal: Determining the velocity parameter of a moving threelayered plate and the thickness of its filler using two natural frequencies of flexural vibrations.
Methods: Research is performed on the natural frequencies of flexural vibrations of a threelayered plate moving between two supports in the form of a sliding connection and affected by the tensile force. The flexural rigidity of the filler is not taken into account. The Kirchhoff's equation of flexural vibrations in a plate is used. In the general case the roots of the characteristic equation are found using the Ferrari's formulae.
In order to determine the velocity parameter and the thickness of the filler, a set of two equations is written down, the solution of which is done using the method of successive approximations in the domain of unique dependence between the velocity parameter and the thickness of the filler from the vibration frequency of the moving threelayered plate.
As a result of the research, it has been found that:
1. An increase in the velocity parameter occurs with a decrease in the natural frequencies of flexural vibrations of the threelayered plate with the filler.
2. An increase in the thickness of the filler occurs with an increase in the natural frequencies of flexural vibrations of the plate. Using two frequencies of flexural vibrations, we can determine the velocity of a moving threelayered plate and the thickness of its filler.
Conclusions: The results of the research work can find technological use in the problems on dynamics and strength of machines and mechanisms: in manufacturing threelayered plates with fillers and can be used to determine the velocity a plate and the thickness of its filler using two frequencies of flexural vibrations.