A computational method for wave propagation from a point load in an anisotropic material

Area of Science:

• Mechanical Engineering
• Applied Mathematics
• Materials Science

Background:

• Dynamic point load problems in plates and laminates are often solved using integral transforms.
• This method reduces governing equations to ordinary differential equations, allowing for transient response recovery via transform inversion.
• Previous applications to composite laminates resulted in non-causal signals.

Purpose of the Study:

• To investigate a proposed integral transform method for dynamic point load problems.
• To analyze wave propagation in a two-dimensional anisotropic medium as a model problem.
• To identify and understand the origins of non-causal signals in the numerical approach.

Main Methods:

• Application of integral transforms to simplify governing equations.
• Solving ordinary differential equations with respect to depth.
• Numerical inversion of multiple transforms, including a change of variable to simplify integrals.
• Analysis of wave propagation for delta function and sine function time histories.
• Comparison with analytic solutions for validation.

Main Results:

• The method was applied to wave propagation in a 2D anisotropic medium.
• Results were obtained for delta function and single-period sine function point loads.
• A comparison with the analytic solution for the delta function source highlighted numerical errors.
• Non-causal contributions to the response were identified at specific line source orientations.

Conclusions:

• The integral transform method, while powerful, can yield non-causal signals in dynamic point load analysis.
• Understanding these non-causal components is crucial for accurate interpretation of results.
• Further investigation is needed to refine the method and mitigate spurious signals in complex materials.