Optimal profile design for acoustic black holes using Timoshenko beam theory

Area of Science:

• Acoustics
• Mechanical Engineering
• Wave Physics

Background:

• Acoustic black holes (ABHs) are used for wave energy dissipation.
• Euler-Bernoulli beam theory has limitations at higher frequencies.
• Timoshenko beam theory offers a more accurate model for higher frequencies.

Purpose of the Study:

• To construct one-dimensional acoustic black holes using Timoshenko beam theory.
• To minimize the reflection coefficient under a normalized wavenumber variation constraint.
• To determine optimal height profiles for ABHs at various frequencies.

Main Methods:

• Applied calculus of variations to derive the Euler-Lagrange equation.
• Employed numerical methods to solve the derived equation for optimal height profiles.
• Compared results with profiles obtained using Euler-Bernoulli beam theory.

Main Results:

• Derived analytical and numerical solutions for optimal ABH height profiles based on Timoshenko theory.
• Observed near-coincidence of optimal profiles between Timoshenko and Euler-Bernoulli theories at lower dimensionless frequencies (Ω).

Conclusions:

• Timoshenko beam theory provides a more accurate approach for designing acoustic black holes, especially at higher frequencies.
• The study validates the effectiveness of the optimization approach and provides insights into frequency-dependent profile behavior.