Analytical modeling for the bending resonant frequency of multilayered microresonators with variable cross-section

Area of Science:

• Mechanical Engineering
• Materials Science
• Nanotechnology

Background:

• Multilayered microresonators are crucial for mass and gas detection, often employing sensitive coatings or piezoelectric layers.
• Predicting the fundamental resonant frequency of microresonators with variable cross-sections is challenging with conventional analytical methods.

Purpose of the Study:

• To develop an analytical model for estimating the first resonant frequency and deflection curve of single-clamped multilayered microresonators with variable cross-sections.
• To provide a tool for designing microresonators with specific operational resonant frequencies.

Main Methods:

• The analytical model utilizes the Rayleigh and Macaulay methods combined with the Euler-Bernoulli beam theory.
• The model was applied to two multilayered microresonators featuring piezoelectric excitation and seven distinct material layers.

Main Results:

• The developed analytical model shows excellent agreement with results from finite element models (FEMs) and experimental data.
• The model successfully estimates the first resonant frequency and deflection curve for the analyzed microresonators.

Conclusions:

• The presented analytical model offers a reliable method for analyzing multilayered microresonators with variable cross-sections.
• This model facilitates the precise design of microresonators for targeted applications by enabling the optimization of layer dimensions for desired resonant frequencies.