An innovative inspection of a cantilever beam exposed to principal parametric excitation
Galal M. Moatimid, T. S. Amer, Mona A. A. Mohamed
TL;DR
This paper presents a new method to reduce vibrations in cantilever beams under parametric excitation using a nonlinear feedback law and non-perturbative approach.
Contribution
A novel non-perturbative method is introduced to approximate solutions for nonlinear parametric systems with high precision and reduced complexity.
Findings
The proposed method achieves high numerical accuracy and simplifies solving nonlinear parametric problems.
System stability increases with higher linear and nonlinear damping coefficients.
The Poincaré map, phase portrait, and bifurcation analysis reveal detailed system behavior.
Abstract
The inspection of a cantilever beam subjected to parametric stimulation is essential in engineering structures such as bridges, aircraft wings, and micro electromechanical systems (MEMS). It is demonstrated that nonlinearities restrict the rise in accessibility. The existing issue mitigates vibrations in a structure exposed to primary parametric stimulation. It utilizes knowledge to develop a simple nonlinear feedback law designed to reduce vibrations of the first mode of a cantilever beam. The fundamental methodology relies on the non-perturbative approach (NPA), which is grounded in He’s frequency formula (HFF). This approach simply converts a weakly nonlinear oscillator of a second nonlinear ordinary differential equation (ODE) into a linear one. Consequently, the goal is to depart from traditional perturbation methods and get unrestricted approximation solutions of small amplitude…
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Taxonomy
TopicsBladed Disk Vibration Dynamics · Aeroelasticity and Vibration Control · Structural Health Monitoring Techniques