محمود حشمتی

This work deals with functionally graded piezoelectric energy harvesting from vibrations of functionally graded beam under travelling multi oscillators. To this propose, a function- ally graded piezoelectric harvester is stuck under the beam span. The material properties of the beam and piezoelectric patch are assumed to be graded through the thickness direc- tion according to a functionally graded pattern. The generalized Hamilton’s principle and Euler Bernoulli beam theory are adopted for derivation of governing equations of electro- mechanical materials. The system of equations for is derived by using. This principle leads to the two sets of second order differential equations as the governing equations of motion for both beam and oscillator. These governing equations are coupled by the contact forces between the oscillator and beam. Finally, the finite element formulations of the problem are presented. A comprehensive parameter study is done to find the effects of material distribution, mass ratio, velocity, damping ratio, spring constant of the oscillators as well as time lags between each moving vehicles on the harvested energy. The results reveal the significant effects of the model parameters on the harvested energy from vibrations of the graded beam under travelling multi-moving oscillators.