H_∞ Optimization of Three-Element-Type Dynamic Vibration Absorber with Inerter and Negative Stiffness Based on the...

Area of Science:

• Mechanical Engineering
• Vibration Control
• Optimization Algorithms

Background:

• Dynamic Vibration Absorbers (DVAs) are crucial for mitigating vibrations in structures and vehicles.
• Optimizing DVA parameters is essential for maximizing their damping effectiveness.
• Novel DVA designs incorporating inerters and negative stiffness springs offer potential for enhanced performance.

Purpose of the Study:

• To investigate an H∞ optimization problem for a novel three-element DVA model.
• To combine traditional fixed-point theory with particle swarm optimization (PSO) for DVA parameter tuning.
• To evaluate the vibration absorption efficacy of the proposed DVA model.

Main Methods:

• Analytical determination of optimal tuning frequency, stiffness, and damping ratios using fixed-point theory.
• Application of the particle swarm optimization (PSO) algorithm for simultaneous optimization of four DVA parameters.
• Comparative analysis of fixed-point theory, PSO, and their combined approach.

Main Results:

• Fixed-point theory provided analytical expressions and an iterative range for optimization.
• The combined traditional theory and PSO approach achieved near-equal resonance peaks, outperforming fixed-point theory alone.
• The proposed DVA model demonstrated superior vibration absorption under harmonic and random excitations.

Conclusions:

• The integration of traditional theory and intelligent algorithms (PSO) enhances DVA performance.
• The novel three-element DVA with inerter and negative stiffness shows significant vibration reduction capabilities.
• This research offers valuable theoretical and algorithmic support for designing advanced DVAs in engineering.