Dynamical response of a rocking rigid block

Area of Science:

• Mechanical Engineering
• Nonlinear Dynamics
• Impulsive Dynamical Systems

Background:

• Investigates rigid block dynamics under harmonic ground excitation, relevant to seismic events and marine wave action.
• Models systems where sliding is prevented by high friction, focusing on impact dynamics and energy loss.

Purpose of the Study:

• To comprehensively analyze the complex dynamical response of a rigid block structure.
• To identify parameter regions that avoid overturning and understand solution properties using basin stability.

Main Methods:

• Formulated and studied an impulsive dynamical systems model.
• Employed direct numerical integration and path-following techniques (COCO platform).
• Utilized the basin stability method for analyzing solution properties and existence ranges.

Main Results:

• Observed diverse phenomena: branching points, fold and period-doubling bifurcations, periodic responses (symmetric/asymmetric), and chaotic motions.
• Characterized solution behavior across phase and parameter spaces.
• Determined conditions to prevent block overturning.

Conclusions:

• The study provides a detailed understanding of rigid block dynamics under harmonic excitation, including stability and chaotic regimes.
• Identified critical parameters and conditions for preventing catastrophic overturning, offering practical insights for structural design and safety.