Abstract
Nonlinear oscillations of single-mass system at force excitation of vibration connected with fixed base by weightless viscoelastic spring are considered. To take into account the rheological properties of the spring material, the Boltzmann-Volterr principle was used. Mathematical models of the problem in question are obtained, which are described by nonlinear integro-differential equations. A solution method based on the use of quadrature formulas has been developed and a computer program has been compiled on its basis, the results of which are reflected in the form of graphs. Influence of nonlinear and rheological properties of spring on amplitude and phase of mass oscillations is investigated.
Highlights
IntroductionTo solve the problems of radiation protection in the design and operation of machines, equipment and structures, it is necessary to have dependences of the vibration parameters of their structures, excited by deterministic and random dynamic influences
Vibrating machines, structures or their components are vibrating systems
One of the most important features of an oscillatory system is the number of degrees of freedom, i.e. the number of independent numerical parameters that uniquely determine the position of all points of the system in space at any fixed time moment t [1, 2]
Summary
To solve the problems of radiation protection in the design and operation of machines, equipment and structures, it is necessary to have dependences of the vibration parameters of their structures, excited by deterministic and random dynamic influences. In this case, the design model of structures can be taken as discrete or distributed (continuous), linear or nonlinear [3, 4]. The discrete model is characterized by the fact that all the masses of the structure are replaced by several lumped masses, the distributed and dissipative properties of the structure are replaced by lumped elements of stiffness and inelastic resistance. The dynamics of discrete models is described by ordinary differential equations [5, 6]
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