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.

scholarly journals Effects of Elliptical Hole on the Correlation of Natural Frequency with Buckling Load of Basalt Laminates Composite Plates

2020 ◽  
Vol 27 (1) ◽  
pp. 216-225
Author(s):  
Buntheng Chhorn ◽  
WooYoung Jung
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Basalt Fiber ◽  
Orientation Angle ◽  
Elliptical Hole ◽  
Composite Plates ◽  
Buckling Load ◽  
Mode Shapes ◽  
Geometric Ratio

AbstractRecently, basalt fiber reinforced polymer (BFRP) is acknowledged as an outstanding material for the strengthening of existing concrete structure, especially it was being used in marine vehicles, aerospace, automotive and nuclear engineering. Most of the structures were subjected to severe dynamic loading during their service life that may induce vibration of the structures. However, free vibration studied on the basalt laminates composite plates with elliptical cut-out and correlation of natural frequency with buckling load has been very limited. Therefore, effects of the elliptical hole on the natural frequency of basalt/epoxy composite plates was performed in this study. Effects of stacking sequence (θ), elliptical hole inclination (ϕ), hole geometric ratio (a/b) and position of the elliptical hole were considered. The numerical modeling of free vibration analysis was based on the mechanical properties of BFRP obtained from the experiment. The natural frequencies as well as mode shapes of basalt laminates composite plates were numerically determined using the commercial program software (ABAQUS). Then, the determination of correlation of natural frequencies with buckling load was carried out. Results showed that elliptical hole inclination and fiber orientation angle induced the inverse proportion between natural frequency and buckling load.

Vibration of Beams with a Single Delamination under Axial Loading

2011 ◽  
Vol 675-677 ◽  
pp. 477-480
Author(s):  
Dong Wei Shu
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Axial Load ◽  
Natural Frequencies ◽  
Axial Loading ◽  
Composite Beams ◽  
Mode Shapes ◽  
Equilibrium Conditions ◽  
Monotonic Relation

In this work analytical solutions are developed to study the free vibration of composite beams under axial loading. The beam with a single delamination is modeled as four interconnected Euler-Bernoulli beams using the delamination as their boundary. The continuity and the equilibrium conditions are satisfied between the adjoining beams. The studies show that the sizes and the locations of the delaminations significantly influence the natural frequencies and mode shapes of the beam. A monotonic relation between the natural frequency and the axial load is predicted.

A Note on the Lowest Natural Frequency of a Square Plate Point-Supported at the Corners

1962 ◽  
Vol 66 (616) ◽  
pp. 240-241 ◽  
Author(s):  
C. L. Kirk
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Present Note ◽  
Flexural Vibration ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Electronic Digital Computer ◽  
Isotropic Plates ◽  
Four Corners ◽  
Square Plate

Recently Cox and Boxer determined natural frequencies and mode shapes of flexural vibration of uniform rectangular isotropic plates, that have free edges and pinpoint supports at the four corners. In their analysis, they obtain approximate solutions of the differential equation through the use of finite difference expressions and an electronic digital computer. In the present note, the frequency expression and mode shape for a square plate, vibrating at the lowest natural frequency, are determined by considerations of energy. The values obtained are compared with those given in reference.

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 Vibrational Analysis on Hemp and Okra Fibres Mixed Glass Fiber Polyester Composite

2021 ◽  
Vol 8 (11) ◽  
pp. 55-62
Author(s):  
Putti Venkata Siva Teja ◽  
Badatala Ooha ◽  
Kondeti Sravanth
Keyword(s):  
Glass Fiber ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Fiber Composite ◽  
Fem Analysis ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Machine Component ◽  
Free System ◽  
Glass Fiber Composite

In transverse vibrations the element moves to and fro in a direction perpendicular to the direction of the advance of the wave. To determine the vibration characteristics i.e., natural frequencies and mode shapes, modal analysis is a process for a structure or a machine component while is being designed. In real life, aero planes, missiles, rockets, space vehicles, satellites, sub marines etc are modeled as free-free mechanical systems. In this paper an attempt was made to compare natural frequency for two composite materials- ladies finger with Glass fiber composite and Hemp with Glass fiber composite by taking as cantilever beams. The cantilever beam which is fixed at one end is vibrated to obtain the natural frequency, mode shapes at four different modes. A simple low cost demonstration experiment is performed in this paper by using common apparatus in order to compare theoretical, numerical (FEM analysis) profiles of two free-free thin two rectangular composite beams of dimensions 305*49.5* 7 in mm. Keywords: Natural frequencies, Mode shapes, Vibration characteristics, Ladies finger fiber, Hemp fiber, Glass fiber, FEM analysis, Free-Free system.

Maximizing the Fundamental Natural Frequency of Triangular Composite Plates

1996 ◽  
Vol 118 (2) ◽  
pp. 141-146 ◽  
Author(s):  
S. Abrate
Keyword(s):  
Natural Frequency ◽  
Material Properties ◽  
Composite Structures ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Laminated Composite ◽  
Composite Plates ◽  
Mode Shapes ◽  
Fundamental Natural Frequency ◽  
Wide Range

While many advances were made in the analysis of composite structures, it is generally recognized that the design of composite structures must be studied further in order to take full advantage of the mechanical properties of these materials. This study is concerned with maximizing the fundamental natural frequency of triangular, symmetrically laminated composite plates. The natural frequencies and mode shapes of composite plates of general triangular planform are determined using the Rayleigh-Ritz method. The plate constitutive equations are written in terms of stiffness invariants and nondimensional lamination parameters. Point supports are introduced in the formulation using the method of Lagrange multipliers. This formulation allows studying the free vibration of a wide range of triangular composite plates with any support condition along the edges and point supports. The boundary conditions are enforced at a number of points along the boundary. The effects of geometry, material properties and lamination on the natural frequencies of the plate are investigated. With this stiffness invariant formulation, the effects of lamination are described by a finite number of parameters regardless of the number of plies in the laminate. We then determine the lay-up that will maximize the fundamental natural frequency of the plate. It is shown that the optimum design is relatively insensitive to the material properties for the commonly used material systems. Results are presented for several cases.

Investigation of stiffness of small wind turbine blade based on vibration analysis technique

2019 ◽  
Vol 44 (1) ◽  
pp. 49-59
Author(s):  
Nilesh Chandgude ◽  
Nitin Gadhave ◽  
Ganesh Taware ◽  
Nitin Patil
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Wind Turbine ◽  
Natural Frequency ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Element Analysis ◽  
Finite Element Software ◽  
Small Wind Turbine

In this article, three small wind turbine blades of different materials were manufactured. Finite element analysis was carried out using finite element software ANSYS 14.5 on modeled blades of National Advisory Committee for Aeronautics 4412 airfoil profile. From finite element analysis, first, two flap-wise natural frequencies and mode shapes of three different blades are obtained. Experimental vibration analysis of manufactured blades was carried out using fast Fourier transform analyzer to find the first two flap-wise natural frequencies. Finally, the results obtained from the finite element analysis and experimental test of three blades are compared. Based on vibration analysis, we found that the natural frequency of glass fiber reinforced plastic blade reinforced with aluminum sheet metal (small) strips increases compared with the remaining blades. An increase in the natural frequency indicates an increase in the stiffness of blade.

Managing Vortex Induced Vibration in Well Jumper Systems

2008 ◽  
Author(s):  
Kenneth Bhalla ◽  
Lixin Gong
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Cross Flow ◽  
Mitigation Measures ◽  
Mode Shapes ◽  
Bottom Current ◽  
Vortex Induced Vibration ◽  
Flow Response ◽  
Out Of Plane ◽  
Lock In

The purpose of this paper is to present a method that has been developed to identify if vortex induced vibration (VIV) occurs in well jumper systems. Moreover, a method has been developed to determine when VIV mitigation measures such as strakes are required. The method involves determining the in-plane and out-of-plane natural frequencies and mode shapes. The natural frequencies are then used, in conjunction with the maximum bottom current expected at a given location to determine if suppression is required. The natural frequency of a jumper system is a function of many variables, e.g. span length, leg height, pipe diameter and thickness, buoyancy placement, buoyancy uplift, buoyancy OD, insulation thickness, and contents of the jumper. The suppression requirement is based upon calculating a lower bound lock-in current speed based upon an assumed velocity bandwidth centered about the lock-in current. The out-of-plane VIV cross-flow response is produced by a current in the plane of the jumper; whereas the in-plane VIV cross-flow response is produced by the out-of-plane current. Typically, the out-of-plane natural frequency is smaller than the in-plane natural frequency. Jumpers with small spans have higher natural frequencies; thus small span jumpers may require no suppression or suppression on the vertical legs. Whereas, larger span jumpers may require no suppression, suppression on the vertical legs or suppression on all the legs. The span of jumper systems (i.e. production, water injection, gas lift/injection ...) may vary in one given field; it has become apparent that not all jumper systems require suppression. This technique has allowed us to recognize when certain legs of a given jumper system may require suppression, thus leading to a jumper design whose safety is not compromised while in the production mode, as well as minimizing downtime and identifying potential savings from probable fatigue failures.

Influence of Axial Boundary Conditions on Free Spanning Pipeline Natural Frequencies

2013 ◽  
Author(s):  
Gareth L. Forbes ◽  
Ahmed M. Reda
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Theoretical Calculation ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Axial Stiffness ◽  
Simple Boundary ◽  
Complex Boundary

The effect of axial restraint (boundary conditions) on the natural frequency of a free spanning pipeline is examined in this paper. Theoretical calculation of the natural frequency of a straight pipeline with simple boundary conditions is a trivial task with exact solutions being available. A pipeline lying on the seabed however is neither completely straight and the interaction with the soil at the span shoulders create more complex boundary conditions. DNV-RP-F105 provides guidance on the calculation of free span boundary conditions with these increased complexities. The DNV recommended practice does not however take into account the effect of the axial restraint on the natural frequency. Results are presented in this paper for a range of axial stiffness combined with span out of straightness for a free spanning pipeline. The results presented show that the effect of axial restraint for moderately out of straight free spans can cause significant deviation in the calculation of the span natural frequency.

Postbuckling and Free Vibrations of Composite Beams

2007 ◽  
Author(s):  
Samir A. Emam ◽  
Ali H. Nayfeh
Keyword(s):  
Natural Frequency ◽  
Axial Load ◽  
Closed Form Solution ◽  
Composite Beams ◽  
Free Vibrations ◽  
Form Solution ◽  
Mode Shapes ◽  
Axial Stiffness ◽  
Fundamental Natural Frequency ◽  
Transverse Vibrations

An exact solution for the postbuckling configurations of composite beams is presented. The equations governing the axial and transverse vibrations of a composite laminated beam accounting for the midplane stretching are presented. The inplane inertia and damping are neglected, and hence the two equations are reduced to a single equation governing the transverse vibrations. This equation is a nonlinear fourth-order partial-integral differential equation. We find that the governing equation for the postbuckling of a symmetric or antisymmetric composite beam has the same form as that of a metallic beam. A closed-form solution for the postbuckling configurations due to a given axial load beyond the critical buckling load is obtained. We followed Nayfeh, Anderson, and Kreider and exactly solved the linear vibration problem around the first buckled configuration to obtain the fundamental natural frequencies and their corresponding mode shapes using different fiber orientations. Characteristic curves showing variations of the maximum static deflection and the fundamental natural frequency of postbuckling vibrations with the applied axial load for a variety of fiber orientations are presented. We find out that the line-up orientation of the laminate strongly affects the static buckled configuration and the fundamental natural frequency. The ratio of the axial stiffness to the bending stiffness is a crucial parameter in the analysis. This parameter can be used to help design and optimize the composite beams behavior in the postbuckling domain.

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