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Flying insect have evolved over thousands of years and have become efficient flying machines. They served as a source of inspiration for mini and micro unmanned air vehicles. For example, the aerodynamics and kinematic of the flapping wings are well investigated and it is shown that the flapping wings can produce higher lifts than fixed wing alternatives of similar sizes. In most of the insects, the flight muscles are not directly connected to the wings but they cause a deformation of the thorax. The movement of the thorax transfers to the wings through a complex mechanism. Different models are suggested for the wing-muscle interface [1] but its exact function yet still to be explored. The common theme between different models is the nonlinearity in restoring force of the “flight mechanism”. The benefit of such a nonlinear mechanism is attributed to an increase in the kinetic energy of the wings [2,3], modulation of the flapping amplitude [1] and an increase in the flapping speed during half of the flapping cycle [4]. One of the issues that is overlooked in the previous studies is the reactive power requirement which can be attributed to the forces requires for acceleration of masses and deformation of elastic elements of the system from a mechanical point of view. In theory, the energy attributed to the reactive power will return to the source in a cycle. However, it will increase energy loss as most mechanical actuator do not have an energy recovery capability. A larger actuator is also required to compensate the reactive power requirement. A nonlinear flight mechanism is investigated in this study in order to establish the power requirement of a flapping wing micro aerial vehicle.
A lumped parameter model in form of a Duffing oscillator is used in this study as a simplified model of a flapping wing aerial vehicle. The generated lift is modelled by a linear damping term for the simplicity. The performance of the system for a range of parameters is evaluated and it is compared with a linear counterpart. The effect of the damping ratio on the ratio between reactive and active power is demonstrated. The reactive power will disappear at the natural frequency of a linear oscillator but it increases rapidly by any deviation in frequency from the natural frequency. For a nonlinear mechanism, the reactive power is lower at a wider frequency range than a linear mechanism although it never disappears at any frequency.