Control of resonating FWMAV structures using repeated eigenvalues

Keywords: FWMAV control, eigensolution sensitivity, repeated eigenvalues, structural modifications, modal basis. Abstract: Several Flapping Wing Micro Air Vehicle (FWMAV) designs use structural resonating properties to increase energy efficiency. For practical use, control of the resonating structure, i.e., the eigensolutions, is required which is complicated by constraints on weight and power consumption. Hence, systematic ways to induce substantial changes in the resonance response are of high interest. Eigensolution sensitivity is used to approximate the change in the resonance vibration, i.e., the eigenmode, due to local structural modifications. Expressing these sensitivities in a modal basis, shows that (nearly) repeated eigenvalues are an indication for effective eigenmode control. The eigenmodes corresponding to repeated eigenvalues are not uniquely defined but any linear combination of these eigenmodes is also an eigenmode. This could lead to substantial changes in the eigenmode, or vibration response, if the eigenmodes become uniquely defined again if the corresponding eigenvalues become distinct due to local structural modifications. A smart structural design could use this idea to exhibit substantial changes in the eigenmodes as introduced by relatively limited control action. The response of a simple symmetric structure, with repeated eigenvalues, shows the response change if the structure becomes asymmetric. Additionally, the influence of structural damping on the effectiveness of the response change is shown.