Forced vibration control of Timoshenko’s micro sandwich beam with CNT/GPL/CNR reinforced composites integrated by piezoelectric on Kerr’s elastic foundation using MCST

 In the present article, forced vibration control of Timoshenko’s micro sandwich beam based on modified couple stress theory (MCST) is studied. The face sheets are made of three-phase reinforced nanocomposite including resin, piezoelectric and CNTCNRGPL materials, and top and bottom layers operate as actuator and sensor, respectively. The micro sandwich beam is placed on Kerr’s foundation and subject to harmonic force with resonance excitation frequency. By considering the equations of motion in the state-space form and using LQR, the amplitude of forced vibrations of the micro beam is optimized. Furthermore, the effects of various parameters including the volume fraction of CNT, GPL and CNR, three parameters of Kerr’s elastic foundation and three natural frequency modes on the suppression and settling time and forced vibration response of a micro sandwich beam is investigated. In this research, for various types and volume fractions of nanocomposites, the second and third natural frequency modes increase 3.5 and 6.7 times, respectively, compared to first natural frequency mode. Also, the Kerr foundation increases the first, second and third mode of natural frequency by about 46%, 13.1% and 7.7%, respectively.