The significance of vibration omission in the engineering structures has led the striking vastness for the applied designing science. The role of vibration omission in materials with emphases on energy-saving and cost reduction is such a topic that has been analyzed and discussed as a challenge in the mechanical engineering. Here, a steel structure with a certain number of piezoelectric pieces with specific dimensions is considered. The aim is to omit vibrations or reduce the vibration range at the minimum time. In this paper, the placement of piezoelectric is carried out in order better to accelerate the suppression of vibration amplitude using the MOPSO, an optimization algorithm. Piezoelectric elements are installed as sensors and actuators on the top and bottom of structures. An early rise is applied to the structure and thus it begins vibration and the amplitude of these vibrations is suppressed by the piezo actuators. Piezoelectric sensors sense the structure’ s vibration motion and control operations are done based on it, and finally to suppress, a control signal is sent to the actuators. The result of this motion is the structural vibration suppression. In this thesis, the studied structure is Timoshenko beam. This beam is considered as a key and basic structure having the vast application in Robotics Science, Engineering, Aerospace Industry and etc. Timoshenko beam is accounted a more accurate model than Euler – Bernoulli beam because it considers the shear effect during deformation. Here, the beam describes its dynamism and constructs the related functions by a numerical method in which each node includes one beam element with 2 degree of freedom(Transitional displacement – Rotational displacement) that is placed under the influence of an external load such as transverse force and bending torque for analyzing the transverse vibration of beam. This external load is a temporal function in the forms of pulse, impulse, step, sine alternatives. Here, PID controller has been used in order to control the structure. In this controller there are three unknown coefficients in Kp, Ki and Kd matrices using multi-objective particle swarm optimization algorithm for or MOPSO, and the unknown coefficients are determined as result of searching this algorithm during the beam in order to determine an optimal point or points of beam to place sensor and piezoelectric actuator in the top and down for the structural suppression at the least possible time.