Nonlinear dynamic analysis of dragonfly-inspired piezoelectric unimorph actuated flapping and twisting wing

Abstract

The nonlinear equations for coupled elastic flapping-twisting motion of a dragonfly-inspired smart flapping wing are used for a flapping wing actuated from the root by a PZT unimorph in the piezofan configuration. Excitation by the piezoelectric harmonic force generates only the flap bending motion, which, in turn, induces the elastic twist motion due to interaction between flexural and torsional vibration modes. An unsteady aerodynamic model is used to obtain the aerodynamic forces. Numerical simulations are performed using a wing whose size is the same as the dragonfly Sympetrum frequens wing. It is found that the value of average lift reaches its maximum when the smart flapping wing is excited at a frequency closer to the natural frequency in torsion. Moreover, consideration of the elastic twisting of the flapping wing leads to an increase in the lift force. It is also found that the flapping wing generates sufficient lift to support its own weight and carry a small payload. Therefore, the piezoelectrically actuated smart flapping wing based on the geometry of a Sympetrum frequens wing and undergoing flapping-twisting motions can be considered as a potential candidate for use in micro air vehicle applications.

Active filter driver for piezo-actuators for flapping-wing micro air vehicles

“…This is an all-pole filter. Putting these three Now we compare the transfer function of equation (10) with the transfer function of equation (9). To find out the design of the second-order filter of equation 9, we put R 1 ¼ R 2 ¼ 1, which gives C 1 ¼ 1:998 and C 2 ¼ 0:2258.…”

“…Several researchers have investigated piezoelectric actuatordriven flapping-wing mechanisms. [6][7][8][9] These researchers used piezoelectric bending actuators and emphasized the need for high tip deflection, which is challenging to produce due to low electromechanical coupling coefficient of piezoelectric materials. A high electric field is an elegant approach to increase the tip deflection in such actuators.…”

“…To design the driver, shown in Figure 4(c), first we decide an acceptable gains and the frequency range of operation of the driver for a flapping-wing MAV. This provides the order of the filter equation (6), the pole locations equation (7) and the all pole transfer function equation (9). Finalizing the geometry of the piezoelectric actuator by satisfying the mechanical properties for flapping-wing MAV, the corresponding capacitance is assigned to C 3 , which is shown in Figure 4(c).…”

“…Here also the combination equals C 3 and must satisfy the pre-assigned resistance R 3 . Equations (3) and (4) show that if we increase the capacitance of the actuator to satisfy the transfer function equation (9), the mass of the actuator also increases, which is a crucial parameter in flappingwing MAV design. Therefore, the design approach, illustrated in this section, provides a systematic method to design the driver of a piezoelectric actuator for flappingwing MAV applications.…”

Biomimetic Beetle-Inspired Flapping Air Vehicle Actuated by Ionic Polymer-Metal Composite Actuator

“…The flapping wings of the insects have two kinds of motions: the longitudinal stroke and the rotation of the wings. In this study, we just consider the stroke of wings [ 24 , 25 ]. When the wing flaps, the angular velocity of stroking ω s is not exactly a simple harmonic motion but a complicated nonlinear motion.…”