ABSTRACT
Because of the relatively high flapping frequency associated with hovering insects and flapping wing micro-air vehicles (FWMAVs), dynamic stability analysis typically involves direct averaging of the time-periodic dynamics over a flapping cycle. However, direct application of the averaging theorem may lead to false conclusions about the dynamics and stability of hovering insects and FWMAVs. Higher-order averaging techniques may be needed to understand the dynamics of flapping wing flight and to analyze its stability. We use second-order averaging to analyze the hovering dynamics of five insects in response to high-amplitude, high-frequency, periodic wing motion. We discuss the applicability of direct averaging versus second-order averaging for these insects.
Subject(s)
Biological Clocks/physiology , Flight, Animal/physiology , Insecta/physiology , Models, Biological , Rheology/methods , Wings, Animal/physiology , Animals , Computer Simulation , Linear Models , Orientation/physiology , Oscillometry/methodsABSTRACT
We propose a step-by-step experimental procedure for characterization of the nonlinear contact stiffness on surfaces using contact-mode atomic force microscopy. Our approach directly estimates the first-, second-, and third-order coefficients of the contact stiffness. It neither uses nor requires the underlying assumptions of the Hertzian contact theory. We use a primary resonance excitation of the probe to estimate the linear coefficient of the contact stiffness. We use the method of multiple scales to obtain closed-form expressions approximating the response of the probe to a subharmonic resonance excitation of order one-half. We utilize these expressions and higher-order spectral measurements to independently estimate the quadratic and cubic coefficients of the contact stiffness.
