Bonnor-Vaidya charged point mass in an external Maxwell field

This work presents an investigation on the free vibration behavior of rotating pre-twisted functionally graded graphene platelets reinforced composite (FG-GPLRC) laminated blades/beams with an attached point mass. The considered beams are constituted of [Formula: see text] layers which are bonded perfectly and made of a mixture of isotropic polymer matrix and graphene platelets (GPLs). The weight fraction of GPLs changes in a layer-wise manner. The effective material properties of FG-GPLRC layers are computed by using the modified Halpin-Tsai model together with rule of mixture. The free vibration eigenvalue equations are developed based on the Reddy’s third-order shear deformation theory (TSDT) using the Chebyshev–Ritz method under different boundary conditions. After validating the approach, the influences of the GPLs distribution pattern, GPLs weight fraction, angular velocity, the variation of the angle of twist along the beam axis, the ratio of attached mass to the beam mass, boundary conditions, position of attached mass, and geometry on the vibration behavior are investigated. The findings demonstrate that the natural frequencies of the rotating pre-twisted FG-GPLRC laminated beams significantly increases by adding a very small amount of GPLs into polymer matrix. It is shown that placing more GPLs near the top and bottom surfaces of the pre-twisted beam is an effective way to strengthen the pre-twisted beam stiffness and increase the natural frequencies.

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Defect structures of sodium and chloride co-substituted hydroxyapatite and its osseointegration capacity

Journal of Materials Science ◽

10.1007/s10853-020-05645-9 ◽

2021 ◽

Vol 56 (9) ◽

pp. 5493-5508

Author(s):

Dong Su Yoo ◽

Jung Sang Cho ◽

Yong-Chae Chung ◽

Sang-Hoon Rhee

Keyword(s):

Binding Energies ◽

Dissolution Behavior ◽

Total System ◽

Carbonate Apatite ◽

In Vivo Test ◽

Co Substitution ◽

Constituent Elements ◽

Low Crystalline ◽

Charged Point

AbstractA defect structure and osseointegration capacity of sodium and chloride co-substituted hydroxyapatite (NaClAp) were newly studied. The NaClAp was prepared by reacting H3PO4 and Ca(OH)2 with NaNO3 and NH4Cl followed by sintering; pure hydroxyapatite (HAp) was synthesized as a control. After sintering, the co-substitution of Ca and OH with Na and Cl, respectively, produced charged point defects at Ca and PO4 sites. Also, OH molecules partially adopted a head-on structure. The calculated total system energy of NaClAp was higher, whereas the binding energies between each constituent elements and system were lower than those of HAp. These results suggest that NaClAp was less stable than HAp, due to the formation of various defects by co-substitution of Na and Cl. Indeed, NaClAp exhibited higher dissolution behavior in simulated body fluid (SBF) compared with HAp. Accordingly, this increased the capability to produce low crystalline hydroxyl carbonate apatite, likely due to the increasing degree of apatite supersaturation in SBF. Besides, the NaClAp granules showed noticeable improvements in osseointegration capacity four weeks after in vivo test compared with HAp. Collectively, these results imply that the defects made by multiple ion substitutions are useful to increase osseointegration capacity of hydroxyapatite.

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