Abstract
The consistently conducted analytical, numerical and experimental studies of nonlinear damped vibrations of planar discrete systems are presented in the paper. The combined methodology is applied to a horizontal vibrating system, consisting of two translational moving bodies connected by three springs. The non-linear nature of the damping is due to the dry friction forces accompanying the vibrating process. The mathematical model of the vibrating system is composed in a matrix form by the second order Lagrange equations. Numerical studies are realized in two ways. Firstly, in the Simulink environment, a simulation model was composed. Then, in the MATLAB environment, an animation model was developed using the third animation method offered by the programming system. The experimental studies were conducted by stand for study the small vibrations of discrete planar systems. The stand is part of the experimental equipment of the Lab for numerical and experimental dynamic modelling, UACEG, Sofia, Bulgaria. (www.dlab-uacg-bg.eu). All models - the dynamic model and its corresponding mathematical, simulation, animation and experimental model are open to additional bodies to obtain discrete vibrating systems with a larger number of degrees of freedom.
Highlights
The logical sequence of work, in studying any dynamic problem in the area of mechanical vibrations, is to conduct analytical, numerical and experimental research
The analytical studies are related to clarification of the dynamic model of the vibrating system, inference of the differential equations (DE), describing its motion and integration of the DE, when a precise analytical solution is possible
This is possible in linear DE, or linear systems with a small number of degrees of freedom (DOF)
Summary
The logical sequence of work, in studying any dynamic problem in the area of mechanical vibrations, is to conduct analytical, numerical and experimental research. The analytical studies are related to clarification of the dynamic model of the vibrating system, inference of the differential equations (DE), describing its motion and integration of the DE, when a precise analytical solution is possible. This is possible in linear DE, or linear systems with a small number of degrees of freedom (DOF). To determine how the friction forces affect the vibrations of the material objects, a combined study of a discrete vibrating system with two degrees of freedom was conducted. Unlike the logical sequence of work, noted at the beginning of the Introduction, in the present study the dynamic model is based on an already constructed experimental model and corresponds not to a certain real system, but rather to the experimental model
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