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.

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.

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.

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.

Experimental Assessment of the Ride Comfort of Farm Tractors

2013 ◽  
Author(s):  
Stefano Dominoni ◽  
Massimiliano Gobbi ◽  
Giampiero Mastinu ◽  
Giorgio Previati
Keyword(s):  
Ride Comfort ◽  
The Body ◽  
Whole Body ◽  
Huge Number ◽  
Comfort Index ◽  
Proper Comparison ◽  
Vertical Accelerations ◽  
The Time Domain ◽  
Iso 2631 ◽  
Whole Body Vibrations

The paper is focused on the assessment of the ride comfort of that farm tractors. The problem of assessing the ride comfort is crucial due to the fact that operators spend part of their own lives on board of such machines, exposed to whole body vibrations potentially harmful for their health. The paper deals with the experimental measurement of the relevant vibration occurring at the tractor body, at the cabin and at the seat. The focus is on which accelerations are actually relevant and have to be taken into account. A number of farm tractors have been instrumented and run under monitored conditions. The test track was equipped with a number of cleats able to force at resonance the cabin and the seat. The six motions of the tractor body and the six motions of the cabin were measured. The motion of the seat was measured. The signals have been processed in the time domain. Some interesting occurrence have been highlighted referring to the amplification that a badly regulated seat can provide under certain circumstances. The comfort index was computed according with ISO 2631 and other standards. The acceleration of the seated subject was described at different positions on the body. It turned out that the acceleration of the head was particularly relevant for establishing a comparison among different tractors. Synthetic indices have been derived from the measured data able to correlate the subjective drivers’ feeling with the measured level of vibration. The conclusion is that for a proper comparison of the ride performance of different farm tractors a huge number of measurements are needed. There is no possibility to record only the vertical accelerations to assess the ride comfort of farm tractors.

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.

Nonlinear Vibrations Analysis of Overhead Power Lines: A Beam With Mass–Spring–Damper–Mass Systems

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Mohammad A. Bukhari ◽  
Oumar R. Barry
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Nonlinear Frequency ◽  
Response Curves ◽  
Mass System ◽  
Parametric Studies ◽  
Overhead Power Lines ◽  
Nonlinear Equations Of Motion ◽  
Mass Spring ◽  
Stockbridge Damper

This paper examines the nonlinear vibration of a single conductor with Stockbridge dampers. The conductor is modeled as a simply supported beam and the Stockbridge damper is reduced to a mass–spring–damper–mass system. The nonlinearity of the system stems from the midplane stretching of the conductor and the cubic equivalent stiffness of the Stockbridge damper. The derived nonlinear equations of motion are solved by the method of multiple scales. Explicit expressions are presented for the nonlinear frequency, solvability conditions, and detuning parameter. The present results are validated via comparisons with those in the literature. Parametric studies are conducted to investigate the effect of variable control parameters on the nonlinear frequency and the frequency response curves. The findings are promising and open a horizon for future opportunities to optimize the design of nonlinear absorbers.

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