Adomian-modified decomposition method for large-amplitude vibration analysis of stepped beams with elastic boundary conditions

The main objective of this paper is to apply an Adomian modified decomposition method for solving large amplitude vibration analysis of stepped beams with various general and elastic boundary conditions. Damaged or imperfect supports of beams can be modeled by using elastic boundary conditions composing of translational and rotational springs. For the beams subjected to dynamic severe loading, it is important to include the nonlinear term of axial stretching force developed by the large vibration amplitude in the governing equation for more accurate design. By using the method, the convergence studies for linear and nonlinear vibration analyses of stepped beams are shown for determining an appropriate number of terms in the solutions. The accuracy of the present results is validated numerically by comparing with some available results in the literature. New results of nonlinear frequency ratios of stepped beams with different boundary conditions are presented and discussed in detail. Aspects of step ratio, step location, boundary conditions, vibration amplitudes, etc., which have significant impact on linear and nonlinear frequencies of such beams are taken under investigation.     

Chebyshev collocation approach for vibration analysis of functionally graded porous beams based on third-order shear deformation theory

In this paper, vibration analysis of functionally graded porous beams is carried out using the third-order shear deformation theory. The beams have uniform and non-uniform porosity distributions across their thickness and both ends are supported by rotational and translational springs. The material properties of the beams such as elastic moduli and mass density can be related to the porosity and mass coefficient utilizing the typical mechanical features of open-cell metal foams. The Chebyshev collocation method is applied to solve the governing equations derived from Hamilton’s principle, which is used in order to obtain the accurate natural frequencies for the vibration problem of beams with various general and elastic boundary conditions. Based on the numerical experiments, it is revealed that the natural frequencies of the beams with asymmetric and non-uniform porosity distributions are higher than those of other beams with uniform and symmetric porosity distributions.     

The role of target-to-substrate distance on the DC magnetron sputtered zirconia thin films’ bioactivity

Zirconium dioxide thin films were deposited on 316L-stainless steel type substrates using DC unbalanced magnetron sputtering. The process parameter of this work was the target-to-substrate distance (d_t-s), which was varied from 60 to 120 mm. The crystal structure and surface topography of zirconium dioxide thin films were characterized by X-ray diffraction (XRD) and atomic force microscopy (AFM). The results demonstrate that all of the ZrO₂ thin films are composed monoclinic phase. The film sputtered at short d_t-s (60 mm) shows a rather heterogeneous, uneven surface. The grain size, roughness, and thickness of thin films were decreased by increasing d_t-s. The bioactivity was assessed by investigating the formation of hydroxyapatite (Ca₁₀(PO₄)₆(OH)₂) on the thin film surface soaked in simulated body fluids (SBF) for 7 days. XRD and scanning electron microscopy (SEM) were used to verify the formation of apatite layers on the samples. Bone-like apatites were formed on the surface of the ZrO₂ thin film in SBF immersion experiments. A nanocrystalline hydroxyapatite (HA) with a particle size of 2-4 μm was deposited. Higher crystallinity of HA on the surface was observed when the distance d_t-s increased to more than 80 mm. Therefore, it seems that a d_t-s greater than 80 mm is an important sputtering condition for inducing HA on the zirconia film.     

Vicinal dianions of diethyl α-aroylsuccinates: preparation of functionalized-2,3-dihydrofurans and -furans, and diaxial 2,4-diaryl-3,7-dioxabicyclo[3.3.0]octanes

Vicinal dianions of diethyl α-aroylsuccinates react with aromatic aldehydes to provide functionalized 2,3-dihydrofurans as the major products together with γ-butyrolactones after treatment of the adducts obtained with a catalytic amount of p-toluenesulfonic acid in refluxing toluene. cis-2,3-Dihydrofurans are used as precursors for the preparation of tetrasubstituted furans and diaxial 2,4-diaryl-3,7-dioxabicyclo[3.3.0]octanes.