Active control for higher order micro sandwich beam with various cores integrated by piezoelectric layers based on MSGT on the Pasternak foundation

Abstract

In the present article, the vibration suppression of higher order micro sandwich beams based on modified strain gradient beam theory (MSGT) and Reddy/Timoshenko beam theories is developed. Three types of core, including honeycomb, foam, and porous for a micro sandwich beam, are considered. The core’s top and bottom are integrated by piezoelectric layers as actuator and sensor, respectively. Displacement fields are defined via third-order shear deformation beam theory (TSDBT) (or Reddy beam theory (RBT)) and first-order shear deformation beam theory (FSDBT) (or Timoshenko beam theory (TBT)). The governing equations of motion are derived using MSGT to consider the small-scale effect. To optimal approaches for the controller, state feedback is designed based on a linear quadratic regulator (LQR) in the state-space form. Moreover, the effect of various parameters, including small-scale parameters, three types of core, temperature changes, Pasternak foundation, density of core, dimensionless cell thickness ((Formula presented.)), and internal aspect ratio ((Formula presented.)), angles ((Formula presented.)) of honeycomb, and the porosity parameter is performed on the active control of the smart micro sandwich beam. The numerical results indicate that the parameters mentioned significantly affect the optimal vibration control of the smart micro sandwich beam. It is found that the lightweight cores have more attenuation of the transient response and faster settling time. By analyzing the effect of temperature changes on active vibration control of lighter core, it was found that the frequency decreases as the temperature increases. Also, by considering the Pasternak foundation, it is found that the time period without considering the elastic foundation is longer than when considering the elastic foundation, and the natural frequency is vice versa. Also, the settling time by considering the elastic foundation occurs earlier. In the active control field of smart micro beams, this theoretical investigation developed widely as a benchmark for experimental research and the manufacturing process.