On the Existence of Forced Oscillations for the Spherical Pendulum Acted on by a Retarded Periodic Force

2011 ◽  
Vol 23 (3) ◽  
pp. 541-549 ◽  
Author(s):  
Pierluigi Benevieri ◽  
Alessandro Calamai ◽  
Massimo Furi ◽  
Maria Patrizia Pera
2017 ◽  
Vol 151 ◽  
pp. 252-264 ◽  
Author(s):  
Alessandro Calamai ◽  
Maria Patrizia Pera ◽  
Marco Spadini

2019 ◽  
Vol 19 (1) ◽  
pp. 149-163 ◽  
Author(s):  
Alessandro Calamai ◽  
Maria Patrizia Pera ◽  
Marco Spadini

Abstract We study global continuation properties of the set of T-periodic solutions of parameterized second order delay differential equations with constant time lag on smooth manifolds. We apply our results to get multiplicity of T-periodic solutions. Our topological approach is mainly based on the notion of degree of a tangent vector field.


Author(s):  
S. R. Rakhmanov ◽  
V. V. Povorotnii

To form a necessary geometry of a hollow billet to be rolled at a pipe rolling line, stable dynamics of the base equipment of the automatic mill working stand has a practical meaning. Among the forces, acting on its parts and elements, significant by value short-time dynamic loads are the least studied phenomena. These dynamic loads arise during transient interaction of the hollow billet, rollers, mandrel and other mill parts at the forced grip of the hollow billet. Basing of the calculation scheme and dynamic model of the mechanical system of the ТПА 350 automatic mill working stand was accomplished. A mathematical model of dynamics of the system “hollow billet (pipe) – working stand” within accepted calculation scheme and dynamic model of the mechanical system elaborated. Influence of technological load of the rolled hollow billet variation in time was accounted, as well as variation of the mechanical system mass, and rigidity of the ТПА 350 automatic mill working stand. Differential equations of oscillation movement for four-mass model of forked sub-systems of the automatic mill working stand were made up, results of their digital calculation quoted. Dynamic displacement of the stand elements in the inter-roller gap obtained, which enabled to estimate the results of amplitude and frequency characteristics of the branches of the mill rollers setting. It was defined by calculation, that the maximum amplitude of the forced oscillations of elements of the ТПА 350 automatic mill working stand within the inter-roller gap does not exceed 2 mm. It is much higher than the accepted value of adjusting parameters of the deformation center of the ТПА 350 automatic mill. A scheme of comprehensive modernization of the rollers setting in the ТПА 350 automatic mill working stand was proposed. It was shown, that increase of rigidity of rollers setting in the ТПА 350 automatic mill working stand enables to stabilize the amplitude of forced oscillations of the working stand elements within the inter-rollers gap and considerably decrease the induced nonuniform hollow billet wall thickness and increase quality of the rolled pipes at ТПА 350.


Author(s):  
Джугурян Т.Г. ◽  
Марчук В.І. ◽  
Марчук І. В.

During the design of operations of centerless intermittent grinding of surfaces there is a need to identify the natural frequencies of oscillations of the elements of the technological system of grinding. The method of calculation of rigidity, vibration resistance and forced oscillations of the elements of the circular grinding machine is offered in the article. Carrying out of experimental researches of rigidity of elastic system of the SASL 5AD grinding machine. We conducted preliminary experimental studies to measure the oscillations of various elements of the elastic system of the SASL 5AD grinding machine in the horizontal plane by piezoelectric sensors during grinding with continuous and discontinuous circles with different geometric parameters.


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