Search results for: bone conducted vibration

Authors: Yu Luan

Abstract:

The bone-conducted objective occlusion effect (OE) is characterized by a discomforting sensation of fullness experienced in an occluded ear. This phenomenon arises from various external stimuli, such as human speech, chewing, and walking, which generate vibrations transmitted through the body to the ear canal walls. The bone-conducted OE occurs due to the pressure build-up inside the occluded ear caused by sound radiating into the ear canal cavity from its walls. In the hearing aid industry, artificial ears are utilized as a tool for developing hearing aids. However, the currently available commercial artificial ears primarily focus on pure acoustics measurements, neglecting the bone-conducted vibration aspect. This research endeavors to develop an artificial ear specifically designed for bone-conducted occlusion measurements. Finite Element Analysis (FEA) modeling has been employed to gain insights into the behavior of the artificial ear.

Keywords: Artificial ear, bone conducted vibration, occlusion measurement, Finite Element Modeling.

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Authors: G. M. Ayininuola, A. O. Sogunro

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Most failures of soil have been attributed to poor shear strength. Consequently, the present paper investigated the suitability of cattle bone ash as a possible additive to improve the shear strength of soils. Four soil samples were collected and stabilized with prepared bone ash in proportions of 3%, 5%, 7%, 10%, 15% and 20% by dry weight. Chemical analyses of the bone ash; followed by classification, compaction, and triaxial shear tests of the treated soil samples were conducted. Results obtained showed that bone ash contained high proportion of calcium oxide and phosphate. Addition of bone ash to soil samples led to increase in soil shear strengths within the range of 22.40% to 105.18% over the strengths of the respective control tests. Conversely, all samples attained maximum shear strengths at 7% bone ash stabilization. The use of bone ash as an additive will therefore improve the shear strength of soils; however, using bone ash quantities in excess of 7% may not yield ample results.

Keywords: Bone ash, Shear strength, Stabilization, Soil.

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Authors: Aqoul H. H. Alanezy, Ali M. Abdelsalam, Nouby M. Ghazaly

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In recent years, progress has been made in increasing the renewable energy share in the power sector particularly in the wind. The experimental study conducted in this paper aims to investigate the effects of number of blades and inflow wind speed on vibration signals of a vertical axis Savonius type wind turbine. The operation of the model of Savonius type wind turbine is conducted to compare two, three and four blades wind turbines to show vibration amplitudes related with wind speed. It is found that the increase of the number of blades leads to decrease of the vibration magnitude. Furthermore, inflow wind speed has reduced effect on the vibration level for higher number of blades.

Keywords: Savonius wind turbine, number of blades, vibration amplitude, renewable energy.

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Authors: L. Roseiro, C. Veiga, V. Maranha, A.Neto, N. Laraqi, A. Baïri, N. Alilat

Abstract:

In orthopedic surgery there are various situations in which the surgeon needs to implement methods of cutting and drilling the bone. With this type of procedure the generated friction leads to a localized increase in temperature, which may lead to the bone necrosis. Recognizing the importance of studying this phenomenon, an experimental evaluation of the temperatures developed during the procedure of drilling bone has been done. Additionally the influence of the use of the procedure with / without additional lubrication during drilling of bone has also been done. The obtained results are presented and discussed and suggests an advantage in using additional lubrication as a way to minimize the appearance of bone tissue necrosis during bone drilling procedures.

Keywords: Bone Necrosis, Bone Drilling, Thermography.

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Authors: Donghyun Hwang, Soo-Hun Lee, Moon G. Lee

Abstract:

In the various working field, vibration may cause injurious to human body. Especially, in case of the vibration which is constantly and repeatedly transferred to the human. That gives serious physical problem, so called, Reynaud phenomenon. In this paper, we propose a vibration transmissibility reduction module with flexure mechanism for personal tools. At first, we select a target personal tool, grass cutter, and measure the level of vibration transmissibility on the hand. And then, we develop the concept design of the module that has stiffness for reduction the vibration transmissibility more than 20%, where the vibration transmissibility is measured with an accelerometer. In addition, the vibration reduction can be enhanced when the interior gap between inner and outer body is filled with silicone gel. This will be verified by the further experiment.

Keywords: Flexure spring, tool engineering, vibration damping.

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Authors: Maitham Al-Safwani

Abstract:

Motor vibration issues were analyzed and correlated to poor equipment installation. We had a water injection pump tested in the factory and exceeded the pump vibration limit. Once the pump was brought to the site, its half-size shim plates were replaced with full-size shims plate that drastically reduced the vibration. In this study, vibration data were recorded for several and similar motors run at the same and different speeds. The vibration values were recorded — for two and a half hours — and the vibration readings analyzed to determine when the readings become consistent. This was as well supported by recording the audio noises produced by some machines seeking a relationship between changes in machine noises and machine abnormalities, such as vibration.

Keywords: Vibration, noise, shaft unbalance, shaft misalignment.

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Authors: Yong-Taeg Lee, Jun-Ho Na, Seung-Hun Kim, Seong-Uk Hong

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Damages from noise and vibration are increasing every year, most of which are noises between floors in deteriorated building caused by floor impact sound. In this study, the concrete slab measured vibration impact sound for evaluation floor vibration of deteriorated buildings that fails to satisfy with the minimum thickness. In this experimental study, the vibration scale by impact sound was calibrated and compared with ISO and AIJ standard for vibration. The results show that vibration in slab with thickness used in existing building reach human perception levels.

Keywords: Vibration, Frequency, Accelerometer, Concrete slab.

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Authors: Mostafa Makrahy, Nouby Ghazaly, Ahmad Moaaz

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Brakes are one of the most important safety and performance components in automobiles and airplanes. Development of brakes has mainly focused on increasing braking power and stability. Nowadays, brake noise, vibration and harshness (NVH) together with brake dust emission and pad life are very important to vehicle drivers. The main objective of this research is to define the relationship between compressibility of friction materials and their tendency to generate vibration. An experimental study of the friction-induced vibration obtained by the disc brake system of a passenger car is conducted. Three commercial brake pad materials from different manufacturers are tested and evaluated under various brake conditions against cast iron disc brake. First of all, compressibility test for the brake friction material are measured for each pad. Then, brake dynamometer is used to simulate and reproduce actual vehicle braking conditions. Finally, a comparison between the three pad specimens is conducted. The results showed that compressibility have a very significant effect on reduction the vibration occurrence.

Keywords: Automotive brake, friction material, brake dynamometer, compressibility test.

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Authors: Emad Askar, Eldesoky Elsoaly, Mohamed Kamel, Hisham Kamel

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The objective of this article is to improve the passive vibration damping of solar array (SA) used in space structures, by the effective application of numerical optimization. A case study of a SA is used for demonstration. A finite element (FE) model was created and verified by experimental testing. Optimization was then conducted by implementing the FE model with the genetic algorithm, to find the optimal placement of aluminum circular patches, to suppress the first two bending mode shapes. The results were verified using experimental testing. Finally, a parametric study was conducted using the FE model where patch locations, material type, and shape were varied one at a time, and the results were compared with the optimal ones. The results clearly show that through the proper application of FE modeling and numerical optimization, passive vibration damping of space structures has been successfully achieved.

Keywords: Damping optimization, genetic algorithm optimization, passive vibration damping, solar array vibration damping.

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Authors: Su Yi Ming, Hou Ying, Zou Guang Ping

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Metal-net rubber is a new dry friction damping material, compared with the traditional metal rubber, which has high mechanization degree, and the mechanical performance of metal-net rubber is more stable. Through the sine sweep experiment and random vibration experiment of metal-net rubber vibration isolator, the influence of several important factors such as the lines slope, relative density and wire diameter on the transfer rate, natural frequency and root-mean-square response acceleration of metal-net rubber vibration isolation system, were studied through the method of control variables. Also, several relevant change curves under different vibration levels were derived, and the effects of vibration level on the natural frequency and root-mean-square response acceleration were analyzed through the curves.

Keywords: Metal-net rubber vibration isolator, relative density, vibration level, wire diameter.

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Authors: Vladyslav Povoroznyuk, Oksana Ivanyk, Nataliia Dzerovych

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In the diagnostics of osteoporosis, the gold standard is considered to be bone mineral density; however, X-ray densitometry is not an accurate indicator of osteoporotic fracture risk under all circumstances. In this regard, the search for new methods that could determine the indicators not only of the mineral density, but of the bone tissue quality, is a logical step for diagnostic optimization. One of these methods is the evaluation of trabecular bone quality. The aim of this study was to examine the quality and mineral density of spine bone tissue, femoral neck, and body composition of women depending on the duration of the postmenopausal period, to determine the correlation of body fat with indicators of bone mineral density and quality. The study examined 179 women in premenopausal and postmenopausal periods. The patients were divided into the following groups: Women in the premenopausal period and women in the postmenopausal period at various stages (early, middle, late postmenopause). A general examination and study of the above parameters were conducted with General Electric X-ray densitometer. The results show that bone quality and mineral density probably deteriorate with advancing of postmenopausal period. Total fat and lean mass ratio is not likely to change with age. In the middle and late postmenopausal periods, the bone tissue mineral density of the spine and femoral neck increases along with total fat mass.

Keywords: Osteoporosis, bone tissue mineral density, bone quality, fat mass, lean mass, postmenopausal osteoporosis.

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Authors: Solehuddin Shuib, Koay Boon Aik, Zainul Ahmad Rajion

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There are many types of mechanical failure on the dental implant. In this project, the failure that needs to take into consideration is the bone resorption on the dental implant. Human bone has its ability to remodel after the implantation. As the dental implant is installed into the bone, the bone will detect and change the bone structure to achieve new biomechanical environment. This phenomenon is known as bone remodeling. The objective of the project is to improve the performance of dental implant by using different types of design. These designs are used to analyze and predict the failure of the dental implant by using finite element analysis (FEA) namely ANSYS. The bone is assumed to be fully attached to the implant or cement. Hence, results are then compared with other researchers. The results were presented in the form of Von Mises stress, normal stress, shear stress analysis, and displacement. The selected design will be analyzed further based on a theoretical calculation of bone remodeling on the dental implant. The results have shown that the design constructed passed the failure analysis. Therefore, the selected design is proven to have a stable performance at the recovery stage.

Keywords: Dental implant, FEA, bone remodeling, osseointegration.

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Authors: P. Vosynek, T. Návrat, M. Peč, J. Pořízka, P. Diviš

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Bone properties and response behavior after static or dynamic activation (loading) are still interesting topics in many fields of the science especially in the biomechanical problems such as bone loss of astronauts in space, osteoporosis, bone remodeling after fracture or remodeling after surgery (endoprosthesis and implants) and in osteointegration. This contribution deals with the relation between physiological, demineralized and deproteinized state of the turkey long bone – tibia. Three methods for comparison were used: 1) densitometry, 2) three point bending and 3) frequency analysis. The main goal of this work was to describe the decrease of the protein (collagen) or mineral of the bone with relation to the fracture in three point bending. The comparison is linked to the problem of different bone mechanical behavior in physiological and osteoporotic state.

Keywords: Bone properties, long bone, osteoporosis, response behavior.

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Authors: N. K. Sharma, J. Nayak, D. K. Sehgal, R. K. Pandey

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Bone material is treated as heterogeneous and hierarchical in nature therefore appropriate size of bone specimen is required to analyze its tensile properties at a particular hierarchical level. Tensile properties of cortical bone are important to investigate the effect of drug treatment, disease and aging as well as for development of computational and analytical models. In the present study tensile properties of buffalo as well as goat femoral and tibiae cortical bone are analyzed using sub-size tensile specimens. Femoral cortical bone was found to be stronger in tension as compared to the tibiae cortical bone and the tensile properties obtained using sub-size specimens show close resemblance with the tensile properties of full-size cortical specimens. A two dimensional finite element (FE) modal was also applied to simulate the tensile behavior of sub-size specimens. Good agreement between experimental and FE model was obtained for sub-size tensile specimens of cortical bone.

Keywords: Cortical bone, sub-size specimen, full size specimen, finite element modeling.

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Authors: Young-Dal Kim, Jae-Myung Shim, Woo-Yong Park, Sung-joong Kim, Dong Seok Hyun, Dae-Dong Lee

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The most common cause of power transformer failures is mechanical defect brought about by excessive vibration, which is formed by the combination of multiples of a frequency of 120 Hz. In this paper, the types of mechanical exciting forces applied to the power transformer were classified, and the mechanical damage mechanism of the power transformer was identified using the vibration transfer route to the machine or structure. The general effects of 120 Hz-vibration on the enclosure, bushing, Buchholz relay, pressure release valve and tap changer of the transformer were also examined.

Keywords: Structure-Vibration, Transformer.

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Authors: Long Kim Vu, Ban Dang Nguyen

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In this paper, the finite element method (FEM) is utilized to simulate the comprehensive process including tightening, releasing and self-loosening of a bolt joint under transverse vibration. Following to the accurate geometry of helical threads, an absolutely hexahedral meshing is implemented. The accuracy of simulation process is verified and validated by comparison with the experimental results on clamping force-vibration relationship, which shows the sufficient correlation. Further analysis with different amplitude and frequency of transverse vibration is done to determine the dominant factor inducing the failure.

Keywords: Bolt self-loosening, contact state, FEM, transverse vibration.

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Authors: Abhishek Soni, Bhagat Singh

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In the present study, a methodology has been proposed to treat fracture in the distal part of the femur bone. Initially, bone model has been developed using the computed tomography scan data of the fractured bone. This information has been further used to create polyether ether ketone (PEEK) implant for this fractured bone. Damaged bone and implant models have been assembled. This assembled model has been further analyzed for stress distribution. Moreover, deformation developed was also measured. It has been observed that the stress and deformation developed was not so appreciable. Thus, it proves that the aforementioned procedure can be suitably adopted for the treatment of fractured distal femur bone.

Keywords: Distal femur, fixation plates, PEEK, reverse engineering.

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Authors: Sarina Sulaiman, N. Khairudin, P. Jamal, M. Z. Alam, Zaki Zainudin, S. Azmi

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In this study, fish bone waste was used as a new catalyst for biodiesel production. Instead of discarding the fish bone waste, it will be utilized as a source for catalyst that can provide significant benefit to the environment. Also, it can be substitute as a calcium oxide source instead of using eggshell, crab shell and snail shell. The XRD and SEM analysis proved that calcined fish bone contains calcium oxide, calcium phosphate and hydroxyapatite. The catalyst was characterized using Scanning Electron Microscope (SEM) and X-ray Diffraction (XRD).

Keywords: Calcinations, fish bone, transesterification, waste catalyst.

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Authors: R. Sutjiati, Rubianto, I. B. Narmada, I. K. Sudiana, R. P. Rahayu

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The prevalence of post-treatment relapse in orthodontics in the community is high enough; therefore, relapses in orthodontic treatment must be prevented well. The aim of this study is to experimentally test the inhibition of relapse of orthodontics tooth movement in NaF of expression TGF-β1, Runx2, alkaline phosphatase (ALP) and microscopic of woven bone. The research method used was experimental laboratory research involving 30 rats, which were divided into three groups. Group A: rats were not given orthodontic tooth movement and without NaF. Group B: rats were given orthodontic tooth movement and without 11.5 ppm by topical application. Group C: rats were given orthodontic tooth movement and 11.75 ppm by topical application. Orthodontic tooth movement was conducted by applying ligature wires of 0.02 mm in diameter on the molar-1 (M-1) of left permanent maxilla and left insisivus of maxilla. Immunohistochemical examination was conducted to calculate the number of osteoblast to determine TGF β1, Runx2, ALP and haematoxylin to determine woven bone on day 7 and day 14. Results: It was shown that administrations of Natrium Fluoride topical application proved effective to increase the expression of TGF-β1, Runx2, ALP and to increase woven bone in the tension area greater than administration without natrium fluoride topical application (p < 0.05), except the expression of ALP on day 7 and day 14 which was significant. The results of the study show that NaF significantly increases the expressions of TGF-β1, Runx2, ALP and woven bone. The expression of the variables enhanced on day 7 compared on that on day 14, except ALP. Thus, it can be said that the acceleration of woven bone occurs on day 7.

Keywords: TGF-β1, Runx2, ALP, woven bone, natrium fluoride.

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Authors: Ji Hyung Park, Dong-Hyun Seo, Young-Jin Jung, Han Sung Kim

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The aim of this study is to evaluate the effects of the laser and partial vibration stimulation on the mice tibia with morphological characteristics. Twenty female C57BL/6 mice (12 weeks old) were used for the experiment. The study was carried out on four groups of animals each consisting of five mice. Four groups of mice were ovariectomized. Animals were scanned at 0 and 2 weeks after ovariectomy by using micro computed tomography to estimate morphological characteristics of tibial trabecular bone. Morphological analysis showed that structural parameters of multi-stimuli group appear significantly better phase in BV/TV, BS/BV, Tb.Th, Tb.N, Tb.Sp, and Tb.pf than single stimulation groups. However, single stimulation groups didn’t show significant effect on tibia with Sham group. This study suggests that multi-stimuli may restrain the change as the degenerate phase on osteoporosis in the mice tibia.

Keywords: Laser, Partial Vibration, Osteoporosis, in vivo micro-CT, mice.

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Authors: Ming-Hui Lee, Shou-Jen Hsu

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This study presents an active vibration control technique to reduce the earthquake responses of a retained structural system. The proposed technique is a synthesis of the adaptive input estimation method (AIEM) and linear quadratic Gaussian (LQG) controller. The AIEM can estimate an unknown system input online. The LQG controller offers optimal control forces to suppress wall-structural system vibration. The numerical results show robust performance in the active vibration control technique.

Keywords: Active vibration control, AIEM, LQG, Optimal control

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Authors: Dong Wook Lee, Seung Hyun Kim

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Trial blasting is conducted to identify the characteristics of the blasting of the applicable ground before production blasting and to investigate various problems posed by blasting. The methods and pattern of production blasting are determined based on an analysis of the results of trial blasting. The bedrock in Jeju Island, South Korea is formed through the volcanic activities unlike the inland areas, composed of porous basalt. Trial blasting showed that the blast vibration frequency of sedimentary and metamorphic rocks in the inland areas is in a high frequency band of about 80 Hz while the blast vibration frequency of Jeju Island is in a low frequency band of 10~25 Hz. The frequency band is analyzed to be low due to the large cycle of blasting pattern as blast vibration passes through the layered structured ground layer where the rock formation and clickers irregularly repeat. In addition, the blast vibration equation derived from trial blasting was R: 0.885, S.E: 0.216 when applying the square root scaled distance (SRSD) relatively suitable for long distance, estimated at the confidence level of 95%.

Keywords: Attenuation index, basaltic ground, blasting vibration constant, blast vibration equation, clinker layer.

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Authors: Nimisha R. Shirbhate, Sanjay Bokade

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Bone Scaffolds are fundamental architecture or a support structure that allows the regeneration of lost or damaged tissues and they are developed as a crucial tool in biomedical engineering. The structure of bone scaffolds plays an important role in treating bone defects. The shape of the bone scaffold performs a vital role, specifically pore size and shape, which help understand the behavior and strength of the scaffold. In this article, first, fundamental aspects of bone scaffold design are established. Second, the behavior of each architecture of the bone scaffold with biomaterials is discussed. Finally, for each structure, the stress analysis was carried out. This study aimed to design a porous and mechanically strong bone regeneration scaffold that can be successfully manufactured. Four porous architectures of the bone scaffold were designed using Rhinoceros solid modelling software. The structure model consisted of repeatable unit cells arranged in layers to fill the chosen scaffold volume. The mechanical behavior of used biocompatible material is studied with the help of ANSYS 19.2 software. It is also playing significant role to predict the strength of defined structures or 3 dimensional models.

Keywords: Bone scaffold, stress analysis, porous structure, static loading.

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Authors: Ramirez D. Edgar I., Angeles H. José J., Ruiz C. Osvaldo, Jacobo A. Victor H., Ortiz P. Armando

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Knowledge of bone mechanical properties is important for bone substitutes design and fabrication, and more efficient prostheses development. The aim of this study is to characterize the viscoelastic behavior of bone specimens, through stress relaxation and fatigue tests performed to trabecular bone samples from bovine femoral heads. Relaxation tests consisted on preloading the samples at five different magnitudes and evaluate them for 1020 seconds, adjusting the results to a KWW mathematical model. Fatigue tests consisted of 700 load cycles and analyze their status at the end of the tests. As a conclusion we have that between relaxation stress and each preload there is linear relation and for samples with initial Young´s modulus greater than 1.5 GPa showed no effects due fatigue test loading cycles.

Keywords: Bone viscoelasticity, fatigue test, stress relaxation test, trabecular bone properties.

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Authors: H. K. G. K. D. K. Hapuhinna, R. D. Gunaratne, H. M. J. C. Pitawala

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This study aimed to find out chemical and structural suitability of synthesized eppawala hydroxyapatite composite as bone cement, by comparing and contrasting it with human bone as well as commercially available bone cement, which is currently used in orthopedic surgeries. Therefore, a mixture of commercially available bone cement and its liquid monomer, commercially available methyl methacrylate (MMA) and a mixture of solid state synthesized eppawala hydroxyapatite powder with commercially available MMA were prepared as the direct substitution for bone cement. Then physical and chemical properties including composition, crystallinity, presence of functional groups, thermal stability, surface morphology, and microstructural features were examined compared to human bone. Results show that there is a close similarity between synthesized product and human bone and it has exhibited high thermal stability, good crystalline and porous properties than the commercial product. Finally, the study concluded that synthesized hydroxyapatite composite can be used directly as a substitution for commercial bone cement.

Keywords: Hydroxyapatite, bone cement, methyl methacrylate, orthopedics.

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Authors: Thomas Jin-Chee Liu, Yu-Shen Chen, Hsi-Yang Ho, Jyun-Ting Liu, Chih-Chun Lee

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This paper discusses some notes on the vibration design for the piezoelectric cooling fan. After reviewing the fundamental formulas of the cantilever Euler beam, it is not easy to find the optimal design of the piezoelectric fan. The experiments also show the complicated results of the vibration behavior and air flow.

Keywords: Piezoelectric cooling fan, vibration, cantilever Euler beam, air flow.

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Authors: Sadek Makhlouf, Hassan M. Nouh

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Bone hydatidosis is an infection in worldwide distribution. Although there is no evidence in literature on Bone Hydatid disease in Libya, we tried to present the first Epidemiological study of this disease in Eastern Libya through retrospective study from 1995 to 2013. Our data were collected from 3 hospitals in Eastern Libya particularly the sheep-raising areas with total number of musculoskeletal infection cases of two thousand one hundred ninety four (2,194). There were five (5) five cases of bone infection, four (4) of it have been diagnosed after more than three (3) months.  Our study is comparable to other international study but this type of bone infection need further studies for effective control strategies for all dogs to avoid serious complications that might happened from the delay in diagnosing this type of disease.

Keywords: Bone infection, Hydatidosis, Eastern Libya, Sheep-raising areas.

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Authors: N. Olarte L, A. Rubiano F, A. Mejía F.

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This comparison of valuation techniques for bone age assessment is a work carried out by the Telemedicine Research Group of the Military University - TIGUM, as a preliminary to the Design and development a treatment system of hand and wrist radiological images for children aged 0-6 years to bone age assessment . In this paper the techniques mentioned for decades have been the most widely used and the statistically significant. Althought, initially with the current project, it wants to work with children who have limit age, this comparison and evaluation techniques work will help in the future to expand the study subject in the system to bone age assessment, implementing more techniques, tools and deeper analysis to accomplish this purpose.

Keywords: Atlas, Bone Age Assessment, Hand and Wrist Radiograph, Image Processing

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Authors: H. N. Mehmanparast, J.M. Mac-Thiong., Y. Petit

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Transpedicular screw fixation in spinal fractures, degenerative changes, or deformities is a well-established procedure. However, important rate of fixation failure due to screw bending, loosening, or pullout are still reported particularly in weak bone stock in osteoporosis. To overcome the problem, mechanism of failure has to be fully investigated in vitro. Post-mortem human subjects are less accessible and animal cadavers comprise limitations due to different geometry and mechanical properties. Therefore, the development of a synthetic model mimicking the realistic human vertebra is highly demanded. A bone surrogate, composed of Polyurethane (PU) foam analogous to cancellous bone porous structure, was tested for 3 different densities in this study. The mechanical properties were investigated under uniaxial compression test by minimizing the end artifacts on specimens. The results indicated that PU foam of 0.32 g.cm-3 density has comparable mechanical properties to human cancellous bone in terms of young-s modulus and yield strength. Therefore, the obtained information can be considered as primary step for developing a realistic cancellous bone of human vertebral body. Further evaluations are also recommended for other density groups.

Keywords: Cancellous bone, Pedicle screw, Polyurethane foam, Synthetic bone

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Authors: Mansour Nikkhah-Bahrami, Masih Loghmani, Mostafa Pooyanfar

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In this paper, an analytical approach for free vibration analysis of rectangular and circular membranes is presented. The method is based on wave approach. From wave standpoint vibration propagate, reflect and transmit in a structure. Firstly, the propagation and reflection matrices for rectangular and circular membranes are derived. Then, these matrices are combined to provide a concise and systematic approach to free vibration analysis of membranes. Subsequently, the eigenvalue problem for free vibration of membrane is formulated and the equation of membrane natural frequencies is constructed. Finally, the effectiveness of the approach is shown by comparison of the results with existing classical solution.

Keywords: Rectangular and circular membranes, propagation matrix, reflection matrix, vibration analysis.

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