Dispersion Analysis of Waves in Graphene-Enhanced Conductive Adhesive Piezoelectric Interlayer Structures

This paper presents a study on the dispersion characteristics of waves in graphene-reinforced conductive adhesive piezoelectric sandwich structures, based on nonlocal strain gradient theory. The investigation focuses on how graphene and the viscoelastic matrix influence wave propagation in sandwich plates under hygrothermal–electric multi-field coupling effects. A physical model is developed comprising a piezoelectric ceramic–graphene-reinforced conductive adhesive–piezoelectric ceramic sandwich structure, and the governing dispersion equations are derived using Hamilton’s principle and third-order shear deformation theory. The equations of motion are formulated by incorporating nonlocal strain gradient theory with harmonic solutions. Numerical analyses are conducted to evaluate the effects of graphene content, geometric parameters, nonlocal and strain gradient effects, and environmental conditions, including temperature, humidity and applied voltage, on wave propagation behavior. The results demonstrate that increasing nonlocal parameters and piezoelectric layer thickness leads to a reduction in frequency, whereas the length scale parameter has a frequency-enhancing effect. The stiffness of the sandwich plate is significantly improved with higher graphene content and optimized structural dimensions, resulting in increased wave frequencies. Additionally, frequency variations exhibit linear relationships with humidity coefficient, shear coefficient and excitation voltage, while temperature shows a relatively minor influence. In contrast, the effect of composite layer thickness on frequency is nonlinear. This study offers a theoretical basis for the design and application of piezoelectric smart aggregates in concrete damage monitoring. This paper uncovers the coupled effect between thickness and scale parameters, reveals the regional characteristics of the interaction between wave number and elastic constants and the influence of graphene’s aspect ratio on frequency reflects its agglomeration properties.