  Insect flight motors are extraordinary natural structures that operate
efficiently at high frequencies. Structural resonance is thought to play a role
in ensuring efficient motor operation, but the details of this role are
elusive. While the efficiency benefits associated with resonance may be
significant, a range of counterintuitive behaviours are observed. In
particular, the relationship between insect wingbeat frequencies and thoracic
natural frequencies are uncertain, with insects showing wingbeat frequency
modulation over both short and long timescales. Here, we offer new explanations
for this modulation. We show how, in linear and nonlinear models of an indirect
flight motor, resonance is not a unitary state at a single frequency; but a
complex cluster of distinct and mutually-exclusive states, each representing a
different form of resonant optimality. Additionally, by characterising the
relationship between resonance and the state of negative work absorption within
the motor, we demonstrate how near-perfect negative work absorption can be
maintained over significant wingbeat frequency ranges. Our analysis leads to a
new conceptual model of flight motor operation: one in which insects are
indifferent to their precise wingbeat frequency, and robust to changes in
thoracic and environmental properties - illustrating the extraordinary
robustness of these natural motors.
