Modeling and active vibration control of lattice grid beam with piezoelectric fiber composite using fractional order PD^μ algorithm

One of challenging issues in structural dynamics is to accurately and rapidly control the vibration levels. It is even important to minimize the occurrence of structural failure in lightweight design. As smart sensors or actuators, the new piezoelectric fiber composite are able to coat onto large area in flexible smart structures, and also has large actuating force. But little is known about the performance of the piezoelectric fiber composite on active vibration control of lattice sandwich structure. In this paper, a novel fractional order PD^μ control of lattice grid beam with piezoelectric fiber composite face sheets is proposed. Firstly, the dynamic model and the vibration responses of the smart sandwich structure are obtained on the basis of the third order shear deformation theory. The ply pattern of piezoelectric fiber composite and structural damping are taken into account for more accurately predict the dynamic behavior. Then, a new active control method by using the fractional order PD^μ algorithm is presented, and simulations of vibration control of the lattice grid beam subjected to various dynamic loadings are conducted, such as initial disturbance, harmonic excitation, step excitation and explosive impact excitation. Consequently, it is proved that the fractional order PD^μ control can reduce the vibration amplitude of lattice grid beam more significantly and more rapidly, by comparing its numerical results with those of the integer order PD algorithm and uncontrolled results.