Vibration analysis of a porous hollow conical rotor with circumferentially distributed piezoceramic strips

Abstract

The present study investigates vibrational behavior of a porous conical hollow rotor. Inner and outer rotor surface, sensor, and actuator strips made of piezoceramic are modeled and positioned, which are symmetrically distributed in the circumferential direction. Kinetic and potential energies were computed considering the effects of Coriolis and centrifugal force. Modeling of the system has been carried out assuming classical theory and using Lagrange approach for simple-supported boundary conditions. Also, the relations of piezoceramic and three types of porosity attend in equilibrium equations. The discretization of kinetic and potential energies using displacement field which is defined as double mixed series based on independent mode shape and time function leads to obtaining the equations in form of ordinary differential. To calculate the natural frequencies, the equations were converted to a special form of state space model. The correctness of the study is examined by comparing it with similar study results. The most consequential parameters affecting the forward and backward natural frequency, such as type and porosity coefficient, size, number, and thickness of piezoceramic, and the rotor angular velocity, are researched. The results demonstrate that the effect of porosity coefficient in various longitudinal modes on natural frequency is different.