Mixing Wave Generated by the Interaction of Two-way Collinear Waves with Arbitrary Frequency under Quadratic Nonlinearity

Materials, such as vehicle lightweighting, intelligent materials, and aviation damping material, are frequently subjected to prolonged loading conditions. During the service life of materials, micro-damage will inevitably occur. The ultrasonic wave-mixing method is an emerging technique in detecting subtle damage in materials. Investigating the interaction between two waves in nonlinear materials guides the non-destructive detection of defects. In the ultrasonic wave-mixing technique, the resonance condition is commonly employed for the selection of the two primary wave frequencies. However, resonance conditions are often not strictly satisfied in practical applications. The mixing wave still contains important information that requires attention in detection. The theoretical solution of the mixing wave interacted by two-way collinear waves with arbitrary frequencies is derived. The results advance us to understand the intrinsic properties of wave interaction.