Potential well escape in a galloping twin-well oscillator

Hussam Alhussein, Mohammad F. Daqaq

Research output: Contribution to journalArticle

Abstract

When a bi-stable oscillator undergoes a supercritical Hopf bifurcation due to a galloping instability, intra-well limit cycle oscillations of small amplitude are born. The amplitude of these oscillations grows as the flow speed is increased to a critical speed at which the dynamic trajectories escape the potential well. The goal of this paper is to obtain a simple yet accurate analytical expression to approximate the escape speed. To this end, three different analytical approaches are implemented: (i) the method of harmonic balance, (ii) the method of multiple scales using harmonic and elliptic basis functions, and (iii) the Melnikov criterion. All methods yielded an identical expression for the escape speed with only one key difference which lies in the value of a constant that changes among the different methods. A comparison between the approximate analytical solutions and a numerical integration of the equation of motion demonstrated that the escape speed obtained via the multiple scales method using the elliptic functions and the Melnikov criterion are in excellent agreement with the numerical simulations. On the other hand, the first-order harmonic balance technique and the multiple scales using harmonic functions provide analytical estimates that significantly underestimate the actual escape speed. Using the Melnikov criterion, the influence of parametric and additive noise on the escape speed was also studied.

Original languageEnglish (US)
JournalNonlinear Dynamics
DOIs
StateAccepted/In press - Jan 1 2019

Fingerprint

Potential Well
Harmonic Balance
Elliptic function
Oscillation
Multiple Scales Method
Scale Function
Harmonic functions
Method of multiple Scales
Hopf bifurcation
Additive noise
Multiple Scales
Additive Noise
Harmonic Functions
Limit Cycle
Hopf Bifurcation
Numerical integration
Equations of motion
Basis Functions
Equations of Motion
Analytical Solution

Keywords

  • Bi-stable
  • Galloping
  • Morphing
  • Noise

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this

Potential well escape in a galloping twin-well oscillator. / Alhussein, Hussam; Daqaq, Mohammad F.

In: Nonlinear Dynamics, 01.01.2019.

Research output: Contribution to journalArticle

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