Free and forced vibration analysis of Timoshenko composite beam with piezo-electric layers

In this article, Free and forced vibration of Timoshenko composite beam with piezo-electric layers checked. relocation field using First shear deformation beam theory obtained and governor equations on moving beam derivated with using Hamilton,s rule.mechanical boundery conditions of beam bipolar from simple supported is discussed.resolution of moving equations with using programming in matlab software achieved and natural frequencies obtained and compared with [1].in part forced vibration loading, explode load with uniform tensity with harmonic excitation and stepper load is discussed.