A solution procedure based on the Ateb function for a two-degree-of-freedom oscillator

2015 ◽  
Vol 346 ◽  
pp. 298-313 ◽  
Author(s):  
L. Cveticanin
Keyword(s):  
Solution Procedure ◽  
Degree Of Freedom ◽  
Two Degree Of Freedom

scholarly journals A Solution Procedure Combining Analytical and Numerical Approaches to Investigate a Two-Degree-of-Freedom Vibro-Impact Oscillator

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1374
Author(s):  
Nicolae Herisanu ◽  
Vasile Marinca
Keyword(s):  
Analytical Solutions ◽  
Initial Conditions ◽  
Solution Procedure ◽  
Degree Of Freedom ◽  
Impact Oscillator ◽  
New Approach ◽  
Analytical Technique ◽  
The Stability ◽  
Two Degree Of Freedom ◽  
Numerical Approaches

In this paper, a new approach is proposed to analyze the behavior of a nonlinear two-degree-of-freedom vibro-impact oscillator subject to a harmonic perturbing force, based on a combination of analytical and numerical approaches. The nonlinear governing equations are analytically solved by means of a new analytical technique, namely the Optimal Auxiliary Functions Method (OAFM), which provided highly accurate explicit analytical solutions. Benefiting from these results, the application of Schur principle made it possible to analyze the stability conditions for the considered system. Various types of possible motions were emphasized, taking into account possible initial conditions and different parameters, and the explicit analytical solutions were found to be very useful to analyze the kinetic energy loss, the contact force, and the stability of periodic motions.

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