Maximizing wave attenuation in viscoelastic phononic crystals by topology optimization

Area of Science:

• Materials Science
• Acoustics
• Mechanical Engineering

Background:

• Viscoelastic properties significantly influence wave propagation in phononic crystals (PCs).
• Designing viscoelastic PCs for specific wave attenuation and stiffness properties is crucial for advanced applications.

Purpose of the Study:

• To extend the bi-directional evolutionary structure optimization (BESO) method for designing viscoelastic PCs.
• To maximize wave attenuation and stiffness in viscoelastic phononic crystals through inverse design.

Main Methods:

• Utilizing the k(ω)-method to calculate the attenuation factor.
• Employing homogenization theory to determine the effective elasticity matrix of composite PCs.
• Formulating the inverse design as a topology optimization problem solved by the BESO method.

Main Results:

• The BESO method iteratively re-distributes material phases based on sensitivity analysis.
• Optimized viscoelastic PCs with maximum attenuation and desired bulk modulus were achieved.
• Novel topological patterns were discovered for various wave propagation scenarios (in-plane, out-of-plane, combined).

Conclusions:

• The proposed BESO method is effective for the topology optimization of viscoelastic phononic crystals.
• The study demonstrates the ability to design PCs with tailored viscoelastic properties for enhanced wave control.
• The findings offer new possibilities for advanced acoustic and mechanical metamaterials.