Forced guided waves in linearly elastic plates (II) - A modified normal-mode expansion method

Area of Science:

• Solid mechanics
• Acoustics
• Wave propagation

Background:

• The classical normal-mode expansion method (Auld and Kino, 1973) is widely used for guided waves in layered media.
• This method accurately models horizontally polarized shear waves and electromagnetic waves.
• However, it fails to provide correct elastodynamic solutions for Lamb waves.

Purpose of the Study:

• To develop a modified normal-mode expansion method for accurate elastodynamic solutions of forced Lamb waves.
• To ensure the modified method satisfies all governing equations and boundary conditions for Lamb waves in plates.

Main Methods:

• Development of a modified normal-mode expansion technique.
• Validation through comparison with finite element analysis solutions.
• Application to both Lamb waves and horizontally polarized shear waves.

Main Results:

• The modified method yields correct elastodynamic solutions for forced Lamb waves.
• The modified method's solutions align numerically with the classical method for horizontally polarized shear waves.
• The modified normal-mode expansion method demonstrates significantly faster convergence.

Conclusions:

• The modified normal-mode expansion method offers an accurate and efficient approach for analyzing forced Lamb waves.
• This advancement corrects a known limitation of the classical normal-mode expansion method.
• The enhanced convergence offers practical advantages for computational analysis.