Chemical Compositions of the Essential Oils of Stems,Leaves, and Roots of <Emphasis Type="Italic">Prangos latiloba</Emphasis>

Hydrodistilled volatile oils from crushed dry stems, leaves, and roots of Prangos latiloba Korov. (Umbelliferae) growing wild in Sabzevar (Iran) were analyzed by GC and GC/MS. Eight compounds constituting 84.72% of stem oil, twelve compounds constituting 95.39% of leaf oil, and nine compounds constituting 88.73% of root oil have been identified. The main components of stem oil were γ-cadinene (30.39%), α-pinene (25.47%), and sabinene (12.55%). The main components of leaf oil were germacrene D (27.79%), α-pinene (17.81%), β-caryophyllene (12.75%), and β-pinene (11.23%). The main components of root oil were spathulenol (29.5%), 1,8-cineol (19.42%), p-cymene (17.03%), and α-bisabolol (15.33%). __________ Published in Kimiya Prirodnikh Soedinenii, No. 5, pp. 443–444, September–October, 2005.     

Dynamic analysis of thick short length FGM cylinders

In this paper a thick short length hollow cylinder made of functionally graded materials (FGMs) under internal impact loading is considered. The inner surface of the cylinder is pure ceramic, the outer surface is pure metal, and the material composition varies continuously along its thickness. Finite Element Method based on Rayleigh-Ritz energy formulation has been applied to study the propagation of elastic waves in FG thick hollow cylinders. The Newmark direct integration method is applied to solve the time dependent equations. The time histories of displacements, stresses, wave propagation in two directions and velocities of radial stress wave propagation for various values of volume fraction exponent have been investigated. Also by using fast Fourier transform, the first natural frequencies for FG cylinders with simply-simply and clamped-clamped ends conditions are illustrated. The model has been compared with result of a plane strain FG thick hollow cylinder which is subjected to an internal impact loading, and it shows very good agreement.     

Transient heat conduction in two-dimensional functionally graded hollow cylinder with finite length

In this paper a thick hollow cylinder with finite length made of two dimensional functionally graded material (2D-FGM) subjected to transient thermal boundary conditions is considered. The volume fraction distribution of materials, geometry and thermal boundary conditions are assumed to be axisymmetric but not uniform along the axial direction. The finite element method with graded material properties within each element is used to model the structure and the Crank–Nicolson finite difference method is implemented to solve time dependent equations of the heat transfer problem. Two-dimensional heat conduction in the cylinder is considered and variation of temperature with time as well as temperature distribution through the cylinder are investigated. Effects of variation of material distribution in two radial and axial directions on the temperature distribution and time response are studied. The achieved results show that using two-dimensional FGM leads to a more flexible design so that transient temperature, maximum amplitude and uniformity of temperature distributions can be modified to achieve required specifications by selecting a suitable material distribution profile in two directions.     

Transient thermal stresses in two-dimensional functionally graded thick hollow cylinder with finite length

In this paper transient thermal stresses in a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) based on classical theory of thermoelasticity are considered. The volume fraction distribution of materials, geometry and thermal load are assumed to be axisymmetric but not uniform along the axial direction. The finite element method with graded material properties within each element is used to model the structure. Temperature, displacements and stress distributions through the cylinder at different times are investigated. Also the effects of variation of material distribution in two radial and axial directions on the thermal stress distribution and time responses are studied. The achieved results show that using 2D-FGM leads to a more flexible design so that time responses of structure, maximum amplitude of stresses and uniformity of stress distributions can be modified to a required manner by selecting suitable material distribution profiles in two directions.     

Viscous fluid damping in a laterally oscillating finger of a comb-drive micro-resonator based on micro-polar fluid theory

Viscous damping is a dominant source of energy dissipation in laterally oscillating micro-structures. In micro-resonators in which the characteristic dimensions are compa-rable to the dimensions of the fluid molecules, the assumption of the continuum fluid theory is no longer justified and the use of micro-polar fluid theory is indispensable. In this paper a mathematical model was presented in order to predict the viscous fluid damping in a laterally oscillating finger of a micro-resonator considering micro-polar fluid theory. The coupled governing partial differential equations of motion for the vibration of the finger and the micro-polar fluid field have been derived. Considering spin and no-spin boundary conditions, the related shape functions for the fluid field were presented. The obtained governing differential equations with time varying boundary conditions have been trans-formed to an enhanced form with homogenous boundary conditions and have been discretized using a Galerkin-based reduced order model. The effects of physical properties of the micro-polar fluid and geometrical parameters of the oscillat-ing structure on the damping ratio of the system have been investigated.     

On the average degree of some irreducible characters of a finite group

Let G be a finite group and N be a non-trivial normal subgroup of G, such that the average degree of irreducible characters in $\mathrm{Irr}(G|N)$ is less than or equal to 16/5. Then, we prove that N is solvable. Also, we prove the solvability of G, by assuming that the average degree of irreducible characters in $\mathrm{Irr}(G|N)$ is strictly less than 16/5. We show that the bounds are sharp.