Numerical analysis of resonance frequency and stiffness ratio in weak bonded structures

Based on the method of ultrasonic normal incidence, the relationship between reflection coefficients and resonance frequencies under the boundary condition of an adhesive layer with a spring model is analyzed. The stiffness ratio expressions of tangent and normal are derived from the once reflection echo of the adhesive layer. The relationship between the stiffness ratio, resonance frequency and reflection coefficient of adhesive layer under multiple reflection echoes is derived, and the variation rule of reflection coefficients of weak bonded structures with different stiffness ratios is observed. Finally, the influence on the resonance frequency caused by the variation of thickness of a weak bonded structure is analyzed. The theoretical analysis and numerical calculation indicate that the resonance frequency has the trend of shifting to a higher frequency level with the increasing of the stiffness ratio, and the bonded structure has multi-order resonance frequencies with the increasing of the adhesive layer thickness.