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

Nicolae Herisanu,Vasile Marinca

doi:10.3390/math9121374

Nicolae Herisanu, Vasile Marinca

Open Access

https://doi.org/10.3390/math9121374

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Abstract

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.

Highlights

Vibro-impact processes are widely used in mechanical-engineering applications and devices such as hammer-like devices, rotor-casing dynamical systems, wheel–rail interaction of high-speed railway couches, heat exchangers, fuel elements of nuclear reactors, gears, piping systems [1], stiction and electric short circuits of MEMS [2], noise and wearproducing processes, grinding, foraging, drilling, punching, tamping, pile cutting a variety of objects, and vibrating machinery or structures with stops or clearance [3]
The considered dynamical model of the vibro-impact system under investigation is depicted in Figure 1, which details the two-degree-of-freedom system with gaps
We presented aa study on thethe dynamical model ofaaoftwo-degree-of-freetwo-degree-of-freeIn this paper, we presented study dynamical model

Summary

Introduction

Vibro-impact processes are widely used in mechanical-engineering applications and devices such as hammer-like devices, rotor-casing dynamical systems, wheel–rail interaction of high-speed railway couches, heat exchangers, fuel elements of nuclear reactors, gears, piping systems [1], stiction and electric short circuits of MEMS [2], noise and wearproducing processes, grinding, foraging, drilling, punching, tamping, pile cutting a variety of objects, and vibrating machinery or structures with stops or clearance [3]. Based on Zhuravlev and Ivanov transformations, Grace et al [19] developed an analytical model of a ship’s roll motion interacting with ice. Extensive numerical simulations were carried out for all initial conditions covered by the ship’s grazing orbit for different values of excitation amplitude and frequency of the external wave roll moment. The existing and stability conditions of period-1 motion in a single-degree-of-freedom oscillator with double-side constraints were studied by Wang et al [22]. The present paper analyzes the motion of a horizontal vibro-impact system with two degrees of freedom in the case when the external coercive force and viscous damping force are known and a periodic vibro-impact model is realized in the system. The condition for periodic motion is obtained and the stability of periodic motion is studied

Dynamical Model of the Vibro-Impact System

Analysis of Non-Periodic Motion

The velocity of the mass M1 after the impact will be oscillator

7.Conclusions