Radial vibration analysis of heterogeneous and non-uniform disks via complementary functions method

Free vibration analysis of heterogeneous (functionally graded) and non-uniform (variable thickness) disks using plane elasticity results in a two-point boundary value problem. Spatially varying mechanical and thickness properties yield variable coefficient governing differential equations where obtaining closed-form solutions are not possible except for certain simple grading and thickness functions. This article uses complementary functions method as a novel approach to determine natural frequencies of functionally graded non-uniform disks. The validation and observation of converges are done using analytical and ANSYS results for a simple power law model uniform disk. The proposed solution method can be applied for disks with any continuous thickness and material grading functions.

The brachistochronic motion of a vertical disk rolling on a horizontal plane without slip

This paper deals with the brachistochronic motion of a thin uniform disk rolling on a horizontal plane without slip. The problem is formulated and solved within the frame of the optimal control theory. The brachistochronic motion of the disk is controlled by three torques. The possibility of the realization of the brachistochronic motion found in presence of Coulomb dry friction forces is inspected. Also, the influence of values of the coefficient of dry friction on the structure of the extremal trajectory is analyzed. Two illustrative numerical examples are provided.

Application of the Complementary Functions Method to an Accurate Elasticity Solution for the Radially Functionally Graded (FG) Rotating Disks with Continuously Variable Thickness and Density

In this work, elastic stress and deformation distribution through the radial direction of FG rotating disks are accurately calculated by employing the complementary functions method. A parabolic variation of the thickness is used for the concave, linear and convex thickness profiles. The inner and outer surfaces of the FG disk are assumed to be ceramic-rich and metal-rich, respectively. Between these two surfaces material properties vary radially according to Mori-Tanaka grading rule. After confirming the present results with the analytical results for the uniform disk with power-law graded rule, the effect due to many parameters such as angular velocity, metal-ceramic pairs, and material grading index on the stresses and displacements is investigated.

Distance and Size of the Red Hypergiant NML Cyg

We present astrometric results of phase-referencing VLBI observations of 22 GHz H2O maser and 43 GHz SiO maser emission towards the red hypergiant NML Cyg using VLBA. We obtained an annual parallax of 0.62 ± 0.04 mas, corresponding to a distance of 1.61+0.13−0.11 kpc. With a VLA observation in its largest (A) configuration at 43 GHz, we barely resolve the radio photosphere of NML Cyg, and find a uniform-disk diameter of 44 ± 16 mas.

Equilibrium neck shapes for initial stages of solid-state sintering due to surface diffusion in a disk model of clays

We study equilibrium neck shapes corresponding to initial stages of solid-state sintering, using a microscopic model of clays in which particles have a uniform disk shape with a microscale diameter R and a nanoscale thickness ? = R/100. Particles are stacked on top of each other, forming vertical piles of various heights ranging from h = ? to h = 10?. Pores are formed in the spaces between any three touching piles of the same height. Assuming that surface diffusion is the dominant sintering mechanism and considering a simplified form of the neck configuration, we derive equilibrium neck shapes by minimizing a neck surface free energy when a neck volume V fixed. We allow for the anisotropy of the surface free energy, using a single anisotropy parameter q. We discuss the dependence of the obtained neck shapes on the neck volume V, pore height h, and anisotropy parameter q.

Cool Giant Stars are Bigger at 712 nm than at 754 nm

We used the Mark III Optical Interferometer on Mt. Wilson in 1991 and 1992 to measure the diameters of 42 stars with 10 nm wide filters centered at 712 nm and at 754 nm. These filters probe the stellar atmosphere in a strong TiO band (712 nm) and in a “continuum” band relatively free of TiO absorption (754 nm). The data were taken on a North-South baseline that could be configured to lengths between 3.0 m and 31.5 m. Observations of the target stars were interleaved with frequent measurements of calibrator stars. The square of the calibrated visibility amplitude V2 was determined as a function of baseline length, and a uniform disk model fitted to these data (for details see Mozurkewich et al. 1991). The average formal error of the diameter measurements - derived from the χ2 of the model fits - is 2.5%. Data for a subset of 12 stars have already been published (Quirrenbach et al. 1993).