Vibrational Analysis of Human Femur Bone

2018 ◽  
Author(s):  
Reza Sadeghi ◽  
Firooz Bakhtiari-Nejad ◽  
Taha Goudarzi
Keyword(s):  
Natural Frequencies ◽  
Vibrational Analysis ◽  
Bone Geometry ◽  
The Body ◽  
Mode Shapes ◽  
Pelvic Bone ◽  
Cross Sectional ◽  
Femur Bone ◽  
Bone Structures ◽  
Elderly Falls

Femur bone is the longest and largest bone in the human skeleton. This bone connects the pelvic bone to the knee and carries most of the body weight. The static behavior of femur bone has been a center of investigation for many years while little attention has been given to its dynamic and vibrational behavior, which is of great importance in sports activities, car crashes and elderly falls. Investigation of natural frequencies and mode shapes of bone structures are important to understand the dynamic and vibrating behaviors. Vibrational analysis of femoral bones is presented using finite element method. In the analysis, the bone was modeled with isotropic and orthotropic mechanical properties. The effect of surrounding bone muscles has also been accounted for as a viscoelastic medium embedding the femur bone. Natural frequencies extracted considering the effects of age aggravated by weakening the elastic modulus and density loss. The effects of real complex bone geometry on natural frequencies are studied and are compared with a simple circular cross-sectional model.

scholarly journals Improved Riccati Transfer Matrix Method for Free Vibration of Non-Cylindrical Helical Springs Including Warping

2012 ◽  
Vol 19 (6) ◽  
pp. 1167-1180 ◽  
Author(s):  
A.M. Yu ◽  
Y. Hao
Keyword(s):  
Free Vibration ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Axial Deformation ◽  
Cross Sectional ◽  
Helical Springs

Free vibration equations for non-cylindrical (conical, barrel, and hyperboloidal types) helical springs with noncircular cross-sections, which consist of 14 first-order ordinary differential equations with variable coefficients, are theoretically derived using spatially curved beam theory. In the formulation, the warping effect upon natural frequencies and vibrating mode shapes is first studied in addition to including the rotary inertia, the shear and axial deformation influences. The natural frequencies of the springs are determined by the use of improved Riccati transfer matrix method. The element transfer matrix used in the solution is calculated using the Scaling and Squaring method and Pad'e approximations. Three examples are presented for three types of springs with different cross-sectional shapes under clamped-clamped boundary condition. The accuracy of the proposed method has been compared with the FEM results using three-dimensional solid elements (Solid 45) in ANSYS code. Numerical results reveal that the warping effect is more pronounced in the case of non-cylindrical helical springs than that of cylindrical helical springs, which should be taken into consideration in the free vibration analysis of such springs.

A New Approach to Compute Natural Frequencies and Mode Shapes of Non-Uniform Continuous Bar, Circular Shaft and Beam Vibration

2019 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Natural Frequencies ◽  
Linear Time ◽  
Longitudinal Vibration ◽  
Mode Shapes ◽  
Engineering Structures ◽  
Cross Sectional ◽  
Closed Form Solutions ◽  
Continuous Structure ◽  
Circular Shaft ◽  
Spatial Parameters

Abstract The wave equation governing longitudinal vibration of a bar and torsional vibration of a circular shaft, and the Euler-Bernoulli equation governing transverse vibration of a beam were developed in the eighteenth century. Natural frequencies and mode shapes are easily obtained for uniform or constant spatial parameters (cross sectional area, material property and mass distribution). But, real engineering structures seldom have constant parameters. For non-uniform continuous structure, a large number of papers have been written for more than 100 years since the publication of Kirchhoff’s memoir in 1882. There are analytical solutions only in few cases, and there are approximate numerical methods to deal with other (almost all) cases, most notably Stodola, Holzer and Myklestad methods in addition to Rayleigh-Ritz and finite element methods. This paper presents a novel approach to compute natural frequencies and mode shapes for arbitrary variations of spatial parameters on the basis of linear time-varying system theory. The advantage of this approach is that now it can be claimed that “almost” closed-form solutions are available to find natural frequencies and mode shapes of any non-uniform, linear and one-dimensional continuous structure.

scholarly journals Significance of Sacral Index in Estimation of Sex in Sacra of Cadavers in Bangladesh

2014 ◽  
Vol 11 (1) ◽  
pp. 11-14
Author(s):  
AHM Mostafa Kamal ◽  
Shamim Ara ◽  
Md Mesbahul Hoque ◽  
Khadeza Khatun ◽  
Kazi Afzalur Rahman
Keyword(s):  
Function Analysis ◽  
The Body ◽  
Pelvic Bone ◽  
Digital Slide ◽  
Morphometric Measurements ◽  
Index Method ◽  
Cross Sectional ◽  
Male And Female ◽  
Medical College ◽  
The Mean

Context : The bones of the body are the last to pass away after death, next to enamel of teeth. Hence, in establishing the personal identity with respect to sex, age and stature, medico legal experts, anatomists and anthropologists use the skeletal materials for giving their opinion. Sex-dependent differences have been noted in the pelvic bone anatomy, and so differences exist in male and female sacrum. The aim of this study was to collect data regarding morphometric measurements of maximum length and breadth of sacrum and to find out possible variations of sacral index in different individuals in relation to sex. Material and Methods: A Cross-sectional, analytical type of study was conducted in the department of Anatomy, Dhaka Medical College, on 172 (one hundred seventy two) adult human dry sacra of unknown sex. The study samples were distributed in male and female sex groups by discriminant function analysis. All the samples were studied morphologically. Sacral length and breadth were measured with the help of digital slide calipers. Result : The mean sacral index in male and female were 97.88±6.16 % and 112.69±10.17 % respectively. Female has the greater sacral index than male (P<0.001) Conclusion: Sexing of sacrum, by sacral index method is relevant and significant DOI: http://dx.doi.org/10.3329/bja.v11i1.20502 Bangladesh Journal of Anatomy, January 2013, Vol. 11 No. 1 pp 11-14

Free vibration analysis of a single edge cracked symmetric functionally graded stepped beams

2020 ◽  
Vol 23 (16) ◽  
pp. 3415-3428
Author(s):  
Yusuf Cunedioglu ◽  
Shkelzen Shabani
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Crack Depth ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Single Edge ◽  
Functionally Graded Beam ◽  
Cross Sectional

Free vibration analysis of a single edge cracked multi-layered symmetric sandwich stepped Timoshenko beams, made of functionally graded materials, is studied using finite element method and linear elastic fracture mechanic theory. The cantilever functionally graded beam consists of 50 layers, assumed that the second stage of the beam (step part) is created by machining. Thus, providing the material continuity between the two beam stages. It is assumed that material properties vary continuously, along the thickness direction according to the exponential and power laws. A developed MATLAB code is used to find the natural frequencies of three types of the stepped beam, concluding a good agreement with the known data from the literature, supported also by ANSYS software in data verification. In the study, the effects of the crack location, crack depth, power law gradient index, different material distributions, different stepped length, different cross-sectional geometries on natural frequencies and mode shapes are analysed in detail.

A New Approach to Compute Natural Frequencies and Mode Shapes of One-Dimensional Continuous Structures With Arbitrary Nonuniformities

2020 ◽  
Vol 15 (11) ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Natural Frequencies ◽  
Linear Time ◽  
Longitudinal Vibration ◽  
Numerical Approach ◽  
Mode Shapes ◽  
Cross Sectional ◽  
One Dimensional ◽  
Dirac Delta ◽  
Mass Distributions ◽  
Jump Discontinuities

Abstract One-dimensional continuous structures include longitudinal vibration of bars, torsional vibration of circular shafts, and transverse vibration of beams. Using the linear time-varying system theory, algorithms are developed in this paper to compute natural frequencies and mode shapes of these structures with nonuniform spatial parameters (mass distributions, material properties and cross-sectional areas) which can have jump discontinuities. A general numerical approach has been presented to include Dirac-delta functions and their spatial derivatives due to jump discontinuities. Numerical results are presented to illustrate the application of these techniques to the solution of different types of spatial variations of parameters and boundary conditions.

scholarly journals Free Vibrations of Tapered Horseshoe Circular Arch with Constant Volume

2020 ◽  
Vol 10 (16) ◽  
pp. 5431
Author(s):  
Byoung Koo Lee ◽  
Gweon Sik Kim ◽  
Sang Jin Oh ◽  
Tae Eun Lee
Keyword(s):  
Natural Frequencies ◽  
Quadratic Function ◽  
Free Vibrations ◽  
Constant Volume ◽  
Mode Shapes ◽  
Cross Sectional ◽  
Circular Arch ◽  
Taper Function ◽  
Parametric Studies ◽  
Sectional Shape

This paper presents free vibrations of the tapered horseshoe circular arch with a constant volume. The volume of the arch is constant, and the cross-sectional shape of the arch is square and circular. The taper function of the arch is a quadratic function. Differential equations with the boundary conditions that govern the free vibration of such arches are derived and numerically solved to calculate natural frequencies and mode shapes. The natural frequencies of this study agree well with those of the finite element ADINA. Parametric studies of the geometrical and cross-sectional properties of the arch on frequencies and mode shapes are performed and discussed.

Three-Dimensional Vibration Analysis of a Truncated Quadrangular Pyramid

1987 ◽  
Vol 54 (1) ◽  
pp. 115-120 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
Y. Tagawa
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Three Dimensional ◽  
Frequency Equation ◽  
The Body ◽  
Mode Shapes ◽  
Algebraic Polynomials ◽  
Transformation Of Variables ◽  
Unit Edge

An analysis is presented for the three-dimensional vibration problem of determining the natural frequencies and the mode shapes of a truncated quadrangular pyramid. For this purpose, the body is transformed into a right quadrangular prism with unit edge lengths by a transformation of variables. With the displacements of the transformed prism assumed in the forms of algebraic polynomials, the dynamical energies of the prism are evaluated, and the frequency equation is derived by the Ritz method. This method is applied to quadrangular pyramids in which the base is clamped and the other sides are free, and the natural frequencies (the eigenvalues of vibration) and the mode shapes are calculated numerically, from which the vibration characteristics arising in the pyramids are studied.

Vibrational characterization of a human femur bone and its significance in the designing of artificial implants

2017 ◽  
Vol 14 (3) ◽  
pp. 222-226 ◽  
Author(s):  
Priyadarshi Biplab Kumar ◽  
Dayal R. Parhi
Keyword(s):  
Human Body ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Stress Distributions ◽  
Content Type ◽  
Human Femur ◽  
Femur Bone ◽  
Bone Damage

Purpose Being an interdisciplinary research area, biomechanics has gained interest among researchers. Biomechanics deals with integration of mechanical phenomenon with the structural and functional aspects of biological systems. Biological systems being very much complex provide a very intricate platform for their analysis. In case of damages created by accidents or sport malfunctions, artificial implants are used for the replacement of bones. These implants may cause incompatibility with the human body, depending on their design and characterization. So, this research aims to analyze the vibrational characteristics of a human femur bone and to predict the safe ranges of frequencies of operation. Design/methodology/approach The current research is aimed at vibrational characterization of a human femur bone. The model of the femur bone is prepared using SOLIDWORKS software. The material properties of the femur are collected from the available literature and provided with the CAD model. The model is imported to the ANSYS software. Loading patterns as applied on the human body are also applied to the prepared model. Suitable boundary conditions are chosen for normal sitting and standing positions. The natural frequencies of the femur bone and other vibrational parameters are found out. Findings The first data obtained from the ANSYS software are the natural frequencies and mode shapes of vibration. Other data include the stress distributions, strain distributions, deformation patterns and potential zones of damage. The frequencies and mode shapes enable the safe ranges of human operation and the frequency range to be followed in the designing of implants. The stress distributions enable to know the potential zones of damage so that those areas can be given focus during strength considerations. Research limitations/implications The current investigations take into account only normal sitting and walking conditions. This work can be included under static loadings. This can also be extended toward dynamic loading conditions. In the dynamic loading, walking and running conditions can be taken into account. This work focuses on the safe designing of the artificial implants and their compatibility with the human body. This can also be extended toward role of dynamic forces in the damaged bone formation and the role of implant’s characteristics for healing of bones. Practical implications Bone damage and ligament fracture are common nowadays due to increasing number of accidents, which may be vehicular or sports. In case of any damage to the skeletal parts, some artificial implant is used to support the damaged part and to help in the process of healing. The designing of the implants must be compatible with the human body. The natural frequencies and mode shapes give an idea that the vibrational parameters of the implant material must fall in the same range as the actual bone. The stress distribution and potential zone damage emphasize on strength considerations. Originality/value The current method is a novel approach toward implant designing. Here an analysis of vibrational parameters of the human femur bone is performed. Those parameters include natural frequencies, mode shapes, principal normal stress distributions, principal shear stress distributions, maximum shear elastic strains and total deformation. These parameters reflect an idea about behavior of the femur bone under actual loading conditions. This analysis enables an implant designer to focus on material properties and strength considerations of the implants which are to be used in case of bone damage.

scholarly journals A continuous model of a standing human body in vertical vibration

2019 ◽  
Vol 39 (2) ◽  
pp. 132-140
Author(s):  
Qingwen Zhang ◽  
Yu Zhang ◽  
Tianjian Ji
Keyword(s):  
Natural Frequency ◽  
Mass Distribution ◽  
Human Body ◽  
Natural Frequencies ◽  
Continuous Model ◽  
Vertical Vibration ◽  
The Body ◽  
Discrete Models ◽  
Mode Shapes ◽  
Axial Stiffness

This paper develops a continuous standing human body model in the vertical vibration based on an anthropomorphic model, two measured natural frequencies of a biomechanics model, and structural dynamics methods. The mass distribution of a standing body is formed using the mass distribution of fifteen body segments in the anthropomorphic model. The axial stiffness of the model is determined based on the best matching to the two natural frequencies of the biomechanics model which were obtained using shaking table tests. Four similar models are assessed using finite element parametric analysis. The best of the four models has seven uniform mass segments with two stiffnesses and the same fundamental natural frequency as that of the biomechanics model, but its second natural frequency is 10% higher. The mode shapes of the continuous model are presented to demonstrate the relative magnitude of vibration throughout the height of the body. Finally the modal mass and stiffness of the continuous model are evaluated, which are related to some simple discrete models.

X-ray micro tomography in the scanning electron microscope

1978 ◽  
Vol 36 (1) ◽  
pp. 106-107 ◽  
Author(s):  
W. Brünger
Keyword(s):  
Electron Beam ◽  
Electron Microscope ◽  
Scanning Electron Microscope ◽  
Target Surface ◽  
The Body ◽  
X Rays ◽  
Cross Sectional ◽  
X Ray ◽  
Micro Tomography ◽  
Scanning Electron

Reconstructive tomography is a new technique in diagnostic radiology for imaging cross-sectional planes of the human body /1/. A collimated beam of X-rays is scanned through a thin slice of the body and the transmitted intensity is recorded by a detector giving a linear shadow graph or projection (see fig. 1). Many of these projections at different angles are used to reconstruct the body-layer, usually with the aid of a computer. The picture element size of present tomographic scanners is approximately 1.1 mm2.Micro tomography can be realized using the very fine X-ray source generated by the focused electron beam of a scanning electron microscope (see fig. 2). The translation of the X-ray source is done by a line scan of the electron beam on a polished target surface /2/. Projections at different angles are produced by rotating the object.During the registration of a single scan the electron beam is deflected in one direction only, while both deflections are operating in the display tube.

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