scholarly journals Development of a Five-Degree-of-Freedom Seated Human Model and Parametric Studies for Its Vibrational Characteristics

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Jong-Jin Bae ◽  
Namcheol Kang
Keyword(s):  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Human Model ◽  
Whole Body ◽  
Mode Shapes ◽  
Vibrational Characteristics ◽  
Parametric Studies ◽  
Linearized Model ◽  
Nonlinear Equations Of Motion ◽  
Whole Body Vibrations

This study focuses on the biodynamic responses of a seated human model to whole-body vibrations in a vehicle. Five-degree-of-freedom nonlinear equations of motion for a human model were derived, and human parameters such as spring constants and damping coefficients were extracted using a three-step optimization processes that applied the experimental data to the mathematical human model. The natural frequencies and mode shapes of the linearized model were also calculated. In order to examine the effects of the human parameters, parametric studies involving initial segment angles and stiffness values were performed. Interestingly, mode veering was observed between the fourth and fifth human modes when combining two different spring stiffness values. Finally, through the frequency responses of the human model, nonlinear characteristics such as frequency shift and jump phenomena were clearly observed.

Development of Seated Human Model With Uncertain Parameters and Estimation of the Ride Comfort

2018 ◽  
Author(s):  
Jong-Jin Bae ◽  
Namcheol Kang
Keyword(s):  
Ride Comfort ◽  
Probability Distributions ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Human Model ◽  
Whole Body ◽  
Mode Shapes ◽  
Comfort Index ◽  
Parametric Studies ◽  
Nonlinear Equations Of Motion

This study deals with the biodynamic responses of the 5-degree-of-freedom mathematical human model to whole-body vibrations in a vehicle. The nonlinear equations of motion of the human model were derived, and the spring constants and damping coefficients were extracted from the experimental data in the literature using optimization process. The natural frequencies and mode shapes were also calculated using linearized human model. In order to examine the effects of the variations of the human parameters, the parametric studies with respect to the stiffness values were performed. The mode veering phenomenon was observed between fourth and fifth mode of the linearized human model. In addition, the frequency responses of the nonlinear 5-degree-of-freedom model were also obtained, and the frequency shift and jump phenomena were observed. Furthermore, the estimation of the ride comfort was performed using CarSim and Matlab/Simulink with several road profiles according to ISO classification. Besides, we also calculated the ride comfort index using BS 6841 standard. In order to calculate the statistical responses of human model, the Monte-Carlo simulation applied to the nonlinear human model having uncertain stiffness assuming Gaussian distribution. These stochastic approaches enable the proposed human model to estimate probability distributions of the ride comfort index.

Nonlinear Dynamic of Cantilever Functionally Graded Plates Under the Thermalmechanical Loads

2009 ◽  
Author(s):  
Yu-xin Hao ◽  
Wei Zhang ◽  
Jian-hua Wang
Keyword(s):  
Nonlinear System ◽  
Functionally Graded Materials ◽  
Nonlinear Dynamic ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Degree Of Freedom ◽  
Mode Shapes ◽  
Governing Equations ◽  
Graded Materials ◽  
Two Degree Of Freedom

An analysis on nonlinear dynamic of a cantilevered functionally graded materials (FGM) plate which subjected to the transverse excitation in the uniform thermal environment is presented for the first time. Materials properties of the constituents are graded in the thickness direction according to a power-law distribution and assumed to be temperature dependent. In the framework of the Third-order shear deformation plate theory, the nonlinear governing equations of motion for the functionally graded materials plate are derived by using the Hamilton’s principle. For cantilever rectangular plate, the first two vibration mode shapes that satisfy the boundary conditions is given. The Galerkin’s method is utilized to discretize the governing equations of motion to a two-degree-of-freedom nonlinear system under combined thermal and external excitations. By using the numerical method, the two-degree-of-freedom nonlinear system is analyzed to find the nonlinear responses of the cantilever FGMs plate. The influences of the thermal environments on the nonlinear dynamic response of the cantilevered FGM plate are discussed in detail through a parametric study.

Load Transfer Control for a Gantry Crane with Arbitrary Delay Constraints

2002 ◽  
Vol 8 (2) ◽  
pp. 135-158 ◽  
Author(s):  
Paolo Dadone ◽  
Hugh F. Vanlandingham
Keyword(s):  
Load Transfer ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Gantry Crane ◽  
Phase Plane Analysis ◽  
Plane Analysis ◽  
Nonlinear Approach ◽  
Linearized Model ◽  
Nonlinear Equations Of Motion ◽  
Quadratic And Cubic Nonlinearities

This paper describes a method to move the load of a gantry crane to a desired position in the presence of known, but arbitrary, motion-inversion delays as well as cart acceleration constraints. The method idea is based on a phase-plane analysis of the linearized model. In order to limit residual pendulation at the goal position, the method is extended to account for quadratic and cubic nonlinearities. The method of multiple scales is used to determine an approximate solution to the nonlinear equations of motion, thus providing a more accurate measure of the frequency of the oscillations. The nonlinear approach is very successful in limiting residual oscillations to very small values (less than 1 degree of amplitude), offering a reduction, with respect to the linear case, of as much as two orders of magnitude. Finally, this method offers a rationale for the future development of a controller for suppression of load oscillations in ship-mounted cranes in the presence of arbitrary delays.

Multibody Dynamics Approaches for Study on Good and Bad Whole-Body Vibrations

2018 ◽  
Author(s):  
Shanzhong (Shawn) Duan
Keyword(s):  
Multibody Dynamics ◽  
Human Body ◽  
Occupational Diseases ◽  
Equations Of Motion ◽  
Stable Condition ◽  
Rigid Bodies ◽  
Whole Body ◽  
Boundary Line ◽  
Dynamics Models ◽  
Whole Body Vibrations

Whole-body vibrations (WBV) have been used for enhancing muscle strength and bone density of human bodies, training athletes and dancers, and helping people with disabling conditions and rehabilitations. On the other hand, WBV-induced occupational diseases have been reported. Researchers in automotive, farm equipment, and heavy machinery have put forward a few models for studying harmful vibrations on human bodies. This paper will review the effects of frequencies and magnitudes of WBV on a human body. Discussion of effects of frequencies and magnitudes on a human body will provide a preliminary boundary line between good and bad whole-body vibrations. Two multibody dynamics models and associated application cases will be proposed to show how the models may be used to represent whole-body vibrations under both good and bad vibrations. Three basic vibration elements associated with whole-body vibrations of the human body are handled as follows: (1) ligaments are modeled as spring elements; (2) muscles and tendons are modeled as damping elements; (3) bones are modeled as rigid bodies with masses/inertias and connected by idealized massless joints. In such a biomechanical vibration system, the spring elements (ligaments) help hold the human body skeleton structure in a stable condition, pass spring forces and potential energy to rigid bodies (bones) for bone vibrational motions. The damping elements (muscles and tendons) play roles of a damper and absorb energy input from the whole-body vibration resource. Based on the proposed multibody dynamics models, Kane’s method is then used to develop equations of motion. The equations will be further used for development of simulation algorithms to understand frequencies and magnitudes of both good and bad whole-body vibrations. The models may be utilized to understand why frequencies and magnitudes of whole-body vibrations will provide benefits to human health under one situation but cause occupational diseases under another scenario.

Modal Analysis of Ballooning Strings With Small Sag

1999 ◽  
Author(s):  
Rongjun Fan ◽  
Sushil K. Singh ◽  
Christopher D. Rahn
Keyword(s):  
Steady State ◽  
High Speed ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Theoretical Predictions ◽  
Nonlinear Equations Of Motion

Abstract During the manufacture and transport of textile products, yarns are rotated at high speed and form balloons. The dynamic response of the balloon to varying rotation speed, boundary excitation, and disturbance forces governs the quality of the associated process. Resonance, in particular, can cause large tension variations that reduce product quality and may cause yarn breakage. In this paper, the natural frequencies and mode shapes of a single loop balloon are calculated to predict resonance. The three dimensional nonlinear equations of motion are simplified via small steady state displacement (sag) and vibration assumptions. Axial vibration is assumed to propagate instantaneously or in a quasistatic manner. Galerkin’s method is used to calculate the mode shapes and natural frequencies of the linearized equations. Experimental measurements of the steady state balloon shape and the first two natural frequencies and mode shapes are compared with theoretical predictions.

Nonlinear Free Vibration of Hybrid Composite Moving Beams Embedded with Shape Memory Alloy Fibers

2016 ◽  
Vol 16 (07) ◽  
pp. 1550032 ◽  
Author(s):  
M. R. Ebrahimi ◽  
A. Moeinfar ◽  
M. Shakeri
Keyword(s):  
Shape Memory Alloy ◽  
Free Vibration ◽  
Shape Memory ◽  
Hybrid Composite ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Parametric Studies ◽  
The One ◽  
Nonlinear Equations Of Motion

The aim of this paper is to investigate the free vibration of hybrid composite moving beams embedded with shape memory alloy (SMA) fibers. The nonlinear equations of motion are derived based on the Euler–Bernoulli beam theory in conjunction with the von Karman type of nonlinearity in strain–displacement relations via the extended Hamilton principle. Also, the recovery stress induced by the SMA fibers is computed by applying the one-dimensional Brinson model and Reuss scheme. Then, an analytical approach in used to solve the nonlinear equation of motion for the simply supported shape memory alloy hybrid composite (SMAHC) moving beams. Based on the analytical solution, several parametric studies are presented to show the effects of various parameters such as volume fraction, pre-strain in the SMA fibers, temperature rise and velocity on the fundamental frequency of the SMAHC moving beams. Due to the lack of similar results in the specialized literature on the subject of interest, this paper is likely to fill a gap in the state of the art of the related research.

Parametric Stability of a Two-Degree-of-Freedom Machine System: Part I—Equations of Motion and Stability

1987 ◽  
Vol 109 (2) ◽  
pp. 210-215 ◽  
Author(s):  
R. I. Zadoks ◽  
A. Midha
Keyword(s):  
Equations Of Motion ◽  
Monodromy Matrix ◽  
Degree Of Freedom ◽  
Computationally Efficient ◽  
Machine System ◽  
Stable Operating ◽  
System Part ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
Two Degree Of Freedom

An important question facing a designer is whether a certain machine system will have a stable operating condition. To date, the investigations which deal with this question have been scarce. This study treats an elastic two-degree-of-freedom system with position-dependent inertia and external forcing. In Part I, the nonlinear equations of motion are derived and linearized about the system’s steady-state rigid-body response. The stability of the linearized equations is examined using Floquet theory, and a computationally efficient method for approximating the monodromy matrix is presented. A specific example is proposed and the results are presented in Part II of this paper.

Impact Damper With Granular Materials for Multibody System

1996 ◽  
Vol 118 (1) ◽  
pp. 95-103 ◽  
Author(s):  
I. Yokomichi ◽  
Y. Araki ◽  
Y. Jinnouchi ◽  
J. Inoue
Keyword(s):  
Granular Materials ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Mode Shapes ◽  
Maximum Displacement ◽  
Impact Damper ◽  
Particle Bed ◽  
Modal Mass ◽  
Three Degree Of Freedom ◽  
The Impact

An efficient impact damper consists of a bed of granular materials moving in a container mounted on a multibody vibrating system. This paper deals with the damping characteristics of a multidegree-of-freedom (MDOF) system that is provided with the impact damper when the damper may be applied to any point of the system. In the theoretical analysis, the particle bed is assumed to be a mass which moves unidirectionally in a container, and collides plastically with its end. Equations of motion are developed for an equivalent single-degree-of-freedom (SDOF) system and attached damper mass with use made of the normal mode approach. The modal mass is estimated such that it represents the equivalent mass on the point of maximum displacement in each of the vibrating modes. The mass ratio is modified with the modal vector to include the effect of impact interactions. Results of the analysis are applied to the special case of a three-degree-of-freedom (3DOF) system, and the effects of the damper parameteres including mode shapes and damper locations are determined. A digital model is also formulated to simulate the damped motion of the physical system.

Vibrations of a Rotating Beam

1966 ◽  
Vol 11 (4) ◽  
pp. 17-24 ◽  
Author(s):  
Jay L. Lipeles
Keyword(s):  
Boundary Conditions ◽  
Coordinate System ◽  
Equations Of Motion ◽  
Cone Angle ◽  
Elastic Stiffness ◽  
Degree Of Freedom ◽  
Mode Shapes ◽  
Flexible Beam ◽  
Rotor Speed ◽  
Classical Formula

The object of this paper is to analyze the coupled flatwise (out of plane) edgewise (in plane) vibrations of a beam rotating about one if its ends. The hub is assumed motionless and the vibration is considered to occur about a large deflected position. That is, coning and lagging angles are allowed to be large. The equations of motion are derived by a combination of techniques. The kinetic energy of the system is expressed in terms of coordinates lying in the beam. This is done by making use of four coordinate transformations that relate the beam coordinate system to a fixed coordinate system. The inertial load distribution is obtained by application of the first two terms of Lagrange's equation. These loads are used to compute the bending moment distribution which is substituted into Euler's beam bending equation. The equations of motion are solved by assuming a solution in the form of a linear combination of orthogonal modes. These equations are multiplied by the jth mode shape and integrated over the beam length. There are four terms resulting; the mass and elastic stiffness terms form a diagonal array and the Coriolis' and centrifugal spring terms form a full array. These equations may be solved by easily available matrix techniques. The modes chosen for the solution are the normal modes of the nonrotating beam. The advantage of this choice is that each of the modes already satisfies the problem boundary conditions. Since the non‐rotating modes are a good approximation to the rotating modes the series converges rapidly and can be cut off after a few terms. Several sample problems are worked out. First, the beam is assumed rigid and free to flap. The classical formula for flapping frequency is verified with the addition that the terms due to large cone and lag angles are included. Second, the same problem is done except that instead of the flapping degree of freedom the lagging degree of freedom is analyzed. The classical formula for lagging is also verified for the zero cone angle. When the cone angle is large this degree of freedom becomes statically unstable. Third, the above problem is redone for the coupled lagging — flapping degrees of freedom. Fourth, a flexible beam is assumed with zero cone and lag angles. Mode shapes and frequencies are computed as a function of rotor speed. It is shown that as rotor speed increases the beam mode shapes and frequencies approach those of a chain. That is, the elastic stiffness becomes negligible relative to the centrifugal stiffness. The advantages of the formulation developed in this paper (in addition to allowing consideration of large coning and lagging angles) are: 1) that the terms that involve rotor speed (the centrifugal spring and the Coriolis coupling) have that parameter as a factor multiplying the whole matrix so that if frequencies and modes are required over a range of rotor speeds the centrifugal and Coriolis' terms need only be calculated once; 2) at large rotor speeds the Myklestad analysis has difficulty converging but in this procedure, because the non‐rotating modes already satisfy the boundary conditions, there is no difficulty in convergence.

Modal Analysis of Ballooning Strings With Small Curvature

2000 ◽  
Vol 68 (2) ◽  
pp. 332-338 ◽  
Author(s):  
R. Fan ◽  
S. K. Singh ◽  
C. D. Rahn
Keyword(s):  
High Speed ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Small Displacement ◽  
Axial Motion ◽  
Theoretical Predictions ◽  
Nonlinear Equations Of Motion

During the manufacture and transport of textile products, yarns are rotated at high speed. The surface of revolution generated by the rotating yarn is called a balloon. The dynamic response of the balloon to varying rotation speed, boundary excitation, and aerodynamic disturbances affects the quality of the associated textile product. Resonance, in particular, can cause large tension variations that reduce product quality and may cause yarn breakage. In this paper, the natural frequencies and mode shapes of a single loop balloon are calculated to predict resonance. The three-dimensional nonlinear equations of motion are simplified under assumptions of small displacement and quasi-static axial motion. After linearization, Galerkin’s method is used to calculate the mode shapes and natural frequencies. Experimental measurements of the steady-state balloon shape and the first two natural frequencies and mode shapes are compared with theoretical predictions.

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