  Nonlinear dynamic simulations of mechanical resonators have been facilitated
by the advent of computational techniques that generate nonlinear reduced order
models (ROMs) using the finite element (FE) method. However, designing devices
with specific nonlinear characteristics remains inefficient since it requires
manual adjustment of the design parameters and can result in suboptimal
designs. Here, we integrate an FE-based nonlinear ROM technique with a
derivative-free optimization algorithm to enable the design of nonlinear
mechanical resonators. The resulting methodology is used to optimize the
support design of high-stress nanomechanical Si3N4 string resonators, in the
presence of conflicting objectives such as simultaneous enhancement of Q-factor
and nonlinear Duffing constant. To that end, we generate Pareto frontiers that
highlight the trade-offs between optimization objectives and validate the
results both numerically and experimentally. To further demonstrate the
capability of multi-objective optimization for practical design challenges, we
simultaneously optimize the design of nanoresonators for three key
figure-of-merits in resonant sensing: power consumption, sensitivity and
response time. The presented methodology can facilitate and accelerate
designing (nano)mechanical resonators with optimized performance for a wide
variety of applications.
