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Coaxial magnetic gear is a cutting-edge technology introduced a few years ago. Its middle rotor is a rotating steel cylindrical shell with a variable array of holes that are filled by brass screws, hence it is such a complicated structure due to these holes. At first glance, it seems impossible to apply shear deformation theories to this unusual geometry, but for the first time, this article has introduced a novel mathematical methodology that creatively makes this possible. Consequently, an analytical formulation is presented for free vibration of this complicated structure, with no need to finite element software. The final aim is to extract natural frequencies and critical speeds in terms of different parameters. The formulation begins with the first-order shear deformation theory as the displacement field and continues with the Hamilton approach to gain governing equations of motion. Additionally, the effect of an external radial magnetic field is modeled by Maxwell's relation. In the end, the Galerkin scheme is followed for discretization of the governing equations. This scheme is compared to an older article to guarantee its accuracy. Subsequently, the natural frequencies are estimated in terms of physical parameters of the rotor such as angle and number of holes, hole-thickness to total-thickness ratio, magnetic field and some other parameters. The mode shapes are also depicted for better interoperation of rotor's behavior. The findings show that unlike geometric parameters (e.g., angle and number of holes), the radial magnetic field does not significantly affect the natural frequency. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This article studies dynamic characteristics of a novel porous cylindrical hollow rotor based on the first-order shear deformation theory and Hamilton's principle. The proposed model is made from a core including aluminum with porosity integrated with an arrangement of functionally graded piezoelectric patches placed on its inner and outer surfaces with a customized circumferential orientation. The piezoelectric patches are subjected to applied electric potential as sensor and actuator. The kinematic relations are developed based on the first-order shear deformation theory. Hamilton's principle is used to derive governing equations of motion with calculation of strain and kinetic energies and external work. Solution procedure of the partial differential equations of motion is developed using Galerkin technique for simple boundary conditions. The accuracy and trueness of this work is justified using a comprehensive comparison with previous valid references. A large parametric study is presented to show influence of significant parameters such as dimensionless geometric parameters, porosity coefficient, angular speed, inhomogeneous index, and characteristics of patches on the mode shapes, natural frequencies, and critical speeds of the structure. [ABSTRACT FROM AUTHOR]