Forced response of cylindrical shells coupled with nonlinear shape-memory-alloy (SMA) actuators regulated by sinusoidal and saw-tooth temperature profiles

Dynamic responses of cylindrical shells coupled with shape-memory alloy (SMA) ring segments placed at critical locations are investigated. Since the SMA actuators are highly nonlinear and governed by the temperate-dependent stiffness and martensite/austenite fraction, input shaping and phase shift of temperature profiles are incorporated to control the shell vibrations. Open-loop equations of an elastic cylindrical shell panel are defined first and then used with assumed mode-shape functions satisfying specified boundary conditions in the free-vibration analysis. Modal-analysis data are used to determine spatial strain distributions of natural modes. Distributed modal-signal characteristics suggest optimal placements of SMA actuator segment(s) for each given mnth mode. Based on the modal-expansion method, the open-loop control force induced by the SMA ring segments applied to a simply supported cylindrical shell panel is formulated. This formulation indicates that only the odd modes in the circumferential direction can be controlled. Longitudinal modes are controlled via placing specific number, depending on the mode, of actuator segments along the panel length. To predict control effects of the nonlinear SMA ring segments, the modal participation factor response is determined for an external harmonic excitation applied to the shell along with induced SMA control forces, via sinusoidal and saw-tooth temperature profiles to generate desirable control forces and to eliminate the unwanted effects. Analysis results suggest that with proper choice of temperature waveform function to the SMA ring segments and minor modifications to frequency and phase, the SMA ring segments can attenuate unwanted external vibrations of cylindrical shells.