Finite element-based nonlinear dynamic optimization of nanomechanical resonators.

Area of Science:

• Mechanical Engineering
• Computational Mechanics
• Materials Science

Background:

• Nonlinear dynamic simulations of mechanical resonators are crucial for device design.
• Current methods using finite element (FE) based nonlinear reduced order models (ROMs) are computationally intensive.
• Designing devices with specific nonlinear characteristics is inefficient due to manual parameter adjustments and suboptimal outcomes.

Purpose of the Study:

• To develop an integrated methodology for efficient design of nonlinear mechanical resonators.
• To optimize the support design of nanomechanical silicon nitride (Si3N4) string resonators.
• To demonstrate multi-objective optimization for practical nanoresonator design challenges.

Main Methods:

• Integration of FE-based nonlinear ROM technique with a derivative-free optimization algorithm.
• Optimization of high-stress nanomechanical Si3N4 string resonators with conflicting objectives.
• Generation of Pareto frontiers to illustrate trade-offs between Q-factor and nonlinear Duffing constant.
• Simultaneous optimization for power consumption, sensitivity, and response time in resonant sensing.

Main Results:

• Successful optimization of nanomechanical resonator designs for enhanced performance.
• Validation of numerical and experimental results for optimized resonator designs.
• Demonstration of Pareto frontiers highlighting trade-offs in multi-objective optimization.
• Achieved simultaneous optimization of multiple key figure-of-merits for resonant sensing.

Conclusions:

• The presented methodology significantly accelerates the design of nonlinear mechanical resonators.
• The approach enables the creation of resonators with tailored nonlinear characteristics.
• This work facilitates the development of high-performance nanoresonators for diverse applications.