Lamb waves propagation in functionally graded piezoelectric materials by Peano-series method

Prior research has shown that Lamb waves are used in non-destructive testing and structural health monitoring. It was already known that piezoelectric materials convert mechanical stress into electrical signals. However, functionally graded piezoelectric materials (FGPMs) introduce a new layer of complexity due to their varying properties. No prior work had resolved the precise behavior of Lamb wave modes in FGPMs with exponential gradients. This gap motivated the investigation into how material gradients influence wave propagation characteristics. Existing studies focused on uniform materials, but FGPMs offer tunable properties. That uncertainty drove the need to explore how gradients affect phase velocity and electromechanical coupling. The Peano-series method has been used in similar contexts but not specifically for FGPMs.

The aim of this study is to analyze Lamb wave propagation in FGPM plates using the Peano-series expansion method. The specific problem involves understanding how exponential gradients in material properties influence the S0 and A0 Lamb wave modes. The motivation stems from the potential to design high-performance sensors by adjusting gradient properties. The study seeks to determine how gradients affect phase velocity and coupling factors. The researchers propose that FGPMs can be tailored for specific frequency ranges. The investigation focuses on aluminum nitride as a model material. The goal is to provide numerical results that can guide sensor design. The study also aims to validate the Peano-series method’s effectiveness in FGPM analysis.

The Peano-series expansion method is applied to model Lamb wave propagation in FGPM plates. The material properties of aluminum nitride are assumed to vary exponentially along the thickness direction. The S0 and A0 wave modes are selected for analysis due to their relevance in practical applications. The polarization direction is aligned with the thickness axis for accurate modeling. The method involves expanding the wave equations into a series solution. The exponential gradient is implemented as a continuous variation parameter. The phase velocity and electromechanical coupling factor are calculated for different frequencies. The computations are performed using MATLAB software to ensure accuracy and convergence.

The highest electromechanical coupling factor observed is for the S0 mode, reaching approximately six percent. In contrast, the A0 mode coupling factor remains below 1.5 percent across all tested frequencies. The coupling factor maxima shift toward higher frequencies as the gradient coefficient increases. The phase velocity of Lamb waves is influenced by the exponential variation in material properties. The Peano-series method demonstrates rapid convergence and accurate results. The numerical data obtained can be used to optimize sensor performance at different frequencies. The study confirms that FGPMs allow for tunable wave propagation characteristics. The results provide a foundation for designing high-performance sensors with adjustable gradient properties.

The authors suggest that FGPMs can be engineered to enhance sensor performance through controlled gradient properties. The study confirms that the S0 mode exhibits significantly higher coupling than the A0 mode. The Peano-series method is validated as effective for analyzing FGPM Lamb waves. The shift in coupling factor maxima with increasing gradient coefficient is a key finding. The results indicate that material gradients influence both phase velocity and coupling behavior. The study does not propose new materials but highlights the potential of FGPMs in sensor design. The authors emphasize the importance of frequency tuning in FGPM applications. The findings may guide future sensor development by adjusting gradient parameters.