A New Model of the Fractional Order Dynamics of the Planetary Gears

A theoretical model of planetary gears dynamics is presented. Planetary gears are parametrically excited by the time-varying mesh stiffness that fluctuates as the number of gear tooth pairs in contact changes during gear rotation. In the paper, it has been indicated that even the small disturbance in design realizations of this gear cause nonlinear properties of dynamics which are the source of vibrations and noise in the gear transmission. Dynamic model of the planetary gears with four degrees of freedom is used. Applying the basic principles of analytical mechanics and taking the initial and boundary conditions into consideration, it is possible to obtain the system of equations representing physical meshing process between the two or more gears. This investigation was focused to a new model of the fractional order dynamics of the planetary gear. For this model analytical expressions for the corresponding fractional order modes like one frequency eigen vibrational modes are obtained. For one planetary gear, eigen fractional modes are obtained, and a visualization is presented. By using MathCAD the solution is obtained

Failure criteria of fibre reinforced composites in homogenous temperature field

The present paper examines the failure criteria of layered composites with orthotropic properties in the homogeneous temperature field. The composite has modeled by two mechanically equivalent families of fibres. The paper formulates constitutive equations in terms of intrinsic preferred directions, which are defined by the orientation of fibers at any point of the composite. A uniformly heated, thermoelastic solid undergoes distortion as well as volume change because it experiences differential expansions in different directions. This effect is more complicated if, in addition of being anisotropic, the material is inhomogeneous, as in the case with laminated materials. In order to illustrate the influence of temperature on the failure of this group of materials constitutive equations are derived and adoptedforuse in failure criteria, without the influence of temperatures, and with the influence of increased temperature

Comparative thermal buckling analysis of functionally graded plate

A thermal buckling analysis of functionally graded thick rectangular plates according to von Karman nonlinear theory is presented. The material properties of the functionally graded plate, except for the Poisson's ratio, were assumed to be graded in the thickness direction, according to a power-law distribution, in terms of the volume fractions of the metal and ceramic constituents. Formulations of equilibrium and stability equations are derived using the high order shear deformation theory based on different types of shape functions. Analytical method for determination of the critical buckling temperature for uniform increase of temperature, linear and nonlinear change of temperature across thickness of a plate is developed. Numerical results were obtained in Matlab software using combinations of symbolic and numeric values. The paper presents comparative results of critical buckling temperature for different types of shape functions. The accuracy of the formulation presented is verified by comparing to results available from the literature