Dynamic and sensitivity analysis of V-shaped cross section piezoelectric beam as mass sensor for high-order vibration modes

Resonators represent a new generation of sensors with superior performance and high sensitivity, making them well-suited for mass sensing applications. While V-shaped cross-section beams have demonstrated enhanced particle absorption and improved performance over conventional rectangular beams in the first bending mode, their behavior in higher-order vibration modes including lateral bending, torsion, and in-plane bending remains unexplored. This study presents a dynamic model of the vibratory motion of V-shaped beams after particle adsorption, employing both modal analysis and finite element methods. A sensitivity analysis based on Sobol’s method is conducted to evaluate the influence of beam geometry on resonance frequency shifts post-adsorption and to quantify the extent of this effect. Simulation results reveal that V-shaped cross-section beams exhibit superior performance compared to rectangular beams not only in the fundamental bending mode but also in higher-order vibration modes, including lateral bending, torsion, and in-plane bending. These findings highlight the potential of V-shaped resonators for advanced mass sensing applications requiring multi-mode vibrational sensitivity.