Grazing instabilities and post-bifurcation behavior in an impacting string

Area of Science:

• Mechanical Engineering
• Nonlinear Dynamics
• Vibrational Analysis

Background:

• Strings with amplitude restraints exhibit complex dynamic behaviors under periodic excitation.
• Impact conditions arise when response amplitudes approach the restraint, leading to nonlinear phenomena.
• Grazing instability, a specific zero-velocity impact, is a key factor in complex post-bifurcation dynamics.

Purpose of the Study:

• To theoretically and experimentally investigate the nonlinear dynamic response of a periodically excited string with a knife-edge amplitude restraint.
• To analyze the influence of grazing instability on the system's behavior.
• To identify parameter combinations that lead to grazing incidence.

Main Methods:

• Nonlinear dynamic response analysis using theoretical modeling and experimental investigation.
• Multiple scales perturbation analysis to identify parameter spaces for grazing.
• Numerical simulations to study multifrequency periodic motion and chaotic responses.

Main Results:

• The study demonstrates that grazing instability can lead to complex post-bifurcation behaviors, including multifrequency periodic motion and chaos.
• Parameter combinations leading to grazing incidence were clearly identified in the excitation force-excitation frequency space.
• The research provides insights into the transition from simple periodic responses to chaotic dynamics.

Conclusions:

• Grazing instability significantly influences the nonlinear dynamic response of the investigated string system.
• Understanding the identified parameter space is crucial for predicting and controlling the system's behavior.
• The findings contribute to the understanding of impact dynamics in mechanical systems and have implications for engineering design.