Vehicle Moving Along an Infinite Beam With Random Surface Irregularities on a Kelvin Foundation

2001 ◽  
Vol 69 (1) ◽  
pp. 69-75 ◽  
Author(s):  
L. Andersen ◽  
S. R. K. Nielsen ◽  
R. Iwankiewicz
Keyword(s):  
Equations Of Motion ◽  
Response Functions ◽  
Spring Stiffness ◽  
Euler Beam ◽  
Random Surface ◽  
Single Degree Of Freedom ◽  
Surface Irregularities ◽  
Stiffness And Damping Coefficient ◽  
Mass Spring ◽  
Stiffness And Damping

The paper deals with the stochastic analysis of a single-degree-of-freedom vehicle moving at a constant velocity along an infinite Bernoulli-Euler beam with surface irregularities supported by a Kelvin foundation. Both the Bernoulli-Euler beam and the Kelvin foundation are assumed to be constant and deterministic. This also applies to the mass, spring stiffness, and damping coefficient of the vehicle. At first the equations of motion for the vehicle and beam are formulated in a coordinate system following the vehicle. The frequency response functions for the displacement of the vehicle and beam are determined for harmonically varying surface irregularities. Next, the surface irregularities are modeled as a random process. The variance response of the mass of the vehicle as well as the displacement variance of the beam under the oscillator are determined in terms of the autospectrum of the surface irregularities.

Fast Simulation of a Single Degree-of-Freedom System Consisting of An Iwan Element Using the Method of Averaging

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Drithi Shetty ◽  
Matthew Allen
Keyword(s):  
Equations Of Motion ◽  
Element Model ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Weakly Nonlinear ◽  
Single Degree ◽  
Integration Schemes ◽  
Current Implementation ◽  
Modal Model ◽  
Stiffness And Damping

Abstract While Iwan elements have been used to effectively model the stiffness and energy dissipation in bolted joints, integrating the equations of motion of these elements is fairly expensive since implicit schemes, such as Newmark’s methods, need to be used. This paper presents a method of simulating dynamic systems containing nonlinear Iwan elements that significantly reduce the computation cost by using closed-form expressions for stiffness and damping in the microslip regime and an averaging method for regions of time in which no external force is applied. The proposed algorithm is demonstrated on a single degree-of-freedom (SDOF) system to evaluate the range over which it retains accuracy and the improvement in performance it offers. Although the current implementation is limited to SDOF systems, it can be used to simulate the response of each mode in structures exhibiting weak nonlinearity that can be modeled using the modal Iwan approach. To verify this, the dynamic response of a finite element model of a beam assembly, integrated using the Newmark-β method, has been compared with its equivalent modal model integrated using the proposed algorithm. The results show that the algorithm accurately predicts the response in a fraction of the time taken by implicit integration schemes, so long as the modes remain uncoupled and weakly nonlinear.

Reduction of Jerk Through Optimization of a Knee Assistive Device Designed Using Four-Bar Controlled Compliance Actuator

2018 ◽  
Author(s):  
Saikat Sahoo ◽  
Aditya Jain ◽  
Dilip Kumar Pratihar
Keyword(s):  
Knee Joint ◽  
Stance Phase ◽  
Reaction Force ◽  
Swing Phase ◽  
Damping Coefficient ◽  
Assistive Device ◽  
Spring Stiffness ◽  
Design Variables ◽  
Stiffness And Damping Coefficient ◽  
Stiffness And Damping

Two major responsibilities are taken by a knee joint during level ground walking of a human being. At stance phase, knee joint is locked in order to provide stability against ground reaction force, and in swing phase, knee flexes for ground clearance of the foot. In this study, a four-bar controlled compliance actuator (FCCA) has been configured for assisting the knee joint during walking. The main focus of FCCA design is the reduction of required mechanical power through a compliance actuation strategy and amplification of motor power. The proposed design consists of two linear spring-damper systems, out of which, one controls the locking of knee during stance phase and another takes care of knee flexion at swing phase. Without a proper selection of stiffness and damping coefficient for both the springs, the knee may be subjected to jerk during flexion, which may give rise to discomfort to the user and consequently, he/she may fall during walking. This study aims to ensure smooth knee operation in both stance phase as well as swing phase by assigning the proper spring stiffness and damping coefficient for both the springs. The responsibility is given to a non-traditional optimization tool, namely particle swarm optimization (PSO). The optimization is carried out using a co-simulation approach between Matlab and ADAMS. The aim of PSO (run in Matlab) is to minimize both the frequency as well as amplitude of the jerk by finding a suitable set of design variables, that is, spring stiffness and damping coefficient of two spring-damper systems.

INTEGRATING BIOMECHANICAL PARAMETERS IN MODELING OF LIVER WITH AND WITHOUT TUMOR IN VIRTUAL ENVIRONMENT

2015 ◽  
Vol 75 (4) ◽  
Author(s):  
Salina Sulaiman ◽  
Liew Kar Thye ◽  
Abdullah Bade ◽  
Rechard Lee ◽  
Siti Hasnah Tanalol
Keyword(s):  
Real Time ◽  
Surgical Simulation ◽  
Computational Cost ◽  
Damping Coefficient ◽  
Model Parameters ◽  
Spring Stiffness ◽  
Time Step ◽  
Biomechanical Parameters ◽  
Mass Spring ◽  
Stiffness And Damping

One of the fundamental components of a surgical simulator is a deformable object. Two main approaches used in surgical simulation to model deformable objects are Finite Element Model (FEM) and Mass Spring Model (MSM). MSM is often preferred due to its simplicity and low computational cost. However, setting of appropriate model parameters such as mass, spring stiffness and damping coefficients in order to reproduce mechanical responses remains an issue. In this paper, biomechanical parameters (Poisson’s values, density) are integrated into MSM based on a tetrahedral structured network in modeling of liver with and without tumor. For the identification of parameters in a real time surgical simulation, Barycentric mass lumping, Lloyd’s approach, Rayleigh formula and Fourth order Runge-Kutta integration method are used to determine the node mass, spring stiffness, damping coefficient and suitable time step respectively. The resulted node mass, spring stiffness and damping coefficient for liver without tumor and with tumor are 1.9825kg, 5.4225 kPa, 7.4525 N/m2 and 5.9256kg, 7.0484 kPa, 11.9012 N/m2 respectively. These values are substituted into MSM, which is then visualized in CHAI 3D ensuring the performance required by a real time simulation. Finally, comparison between the liver with and without tumor in terms of mass, spring stiffness, and damping constant is highlighted.

Mass–spring–damper modelling of the human body to study running and hopping – an overview

2011 ◽  
Vol 225 (12) ◽  
pp. 1121-1135 ◽  
Author(s):  
A A Nikooyan ◽  
A A Zadpoor
Keyword(s):  
Mechanical Properties ◽  
Human Body ◽  
Soft Tissues ◽  
Equations Of Motion ◽  
Future Research ◽  
Advantages And Disadvantages ◽  
The Masses ◽  
Mass Spring ◽  
Stiffness And Damping ◽  
Multi Body

Several mass–spring–damper models have been developed to study the response of the human body to the collision with the ground during hopping, trotting, or running. The mass, spring, and damper elements represent the masses, stiffness properties, and damping properties of hard and soft tissues. The masses that models are composed of are connected to each other via springs and dampers. The present paper reviews the various types of mass–spring–damper models including one-body and multi-body models. The models are further categorized as being either passive or active. In passive models, the mechanical properties (stiffness and damping) of soft tissues remain constant regardless of the type of footwear, ground stiffness, etc. In active models, the mechanical properties adapt to external loads. The governing equations of motion of all models as well as their parameters are presented. The specific ways that the models take account of the shoe–ground interactions are discussed as well. The methods used for determination of different modelling parameters are briefly surveyed. The advantages and disadvantages of the different types of mass–spring–damper models are also discussed. The paper concludes with a brief discussion of possible future research trends in the area of mass–spring–damper modelling.

scholarly journals Identification of Dynamic Parameters of Pedestrian Walking Model Based on a Coupled Pedestrian–Structure System

2021 ◽  
Vol 11 (14) ◽  
pp. 6407
Author(s):  
Huiqi Liang ◽  
Wenbo Xie ◽  
Peizi Wei ◽  
Dehao Ai ◽  
Zhiqiang Zhang
Keyword(s):  
Negative Correlation ◽  
Dynamic Properties ◽  
Damping Ratio ◽  
Field Testing ◽  
The Body ◽  
Structural Vibration ◽  
Pedestrian Dynamics ◽  
Structure Interaction ◽  
Mass Spring ◽  
Stiffness And Damping

As human occupancy has an enormous effect on the dynamics of light, flexible, large-span, low-damping structures, which are sensitive to human-induced vibrations, it is essential to investigate the effects of pedestrian–structure interaction. The single-degree-of-freedom (SDOF) mass–spring–damping (MSD) model, the simplest dynamical model that considers how pedestrian mass, stiffness and damping impact the dynamic properties of structures, is widely used in civil engineering. With field testing methods and the SDOF MSD model, this study obtained pedestrian dynamics parameters from measured data of the properties of both empty structures and structures with pedestrian occupancy. The parameters identification procedure involved individuals at four walking frequencies. Body frequency is positively correlated to the walking frequency, while a negative correlation is observed between the body damping ratio and the walking frequency. The test results further show a negative correlation between the pedestrian’s frequency and his/her weight, but no significant correlation exists between one’s damping ratio and weight. The findings provide a reference for structural vibration serviceability assessments that would consider pedestrian–structure interaction effects.

A Method for Fatigue Analysis of Pipelines on Topsides of FPSO Systems

2005 ◽  
Author(s):  
Pol Spanos ◽  
Alba Sofi ◽  
Juan Wang ◽  
Berry Peng
Keyword(s):  
Fatigue Life ◽  
Random Vibration ◽  
Equations Of Motion ◽  
Plug Flow ◽  
Fatigue Curve ◽  
Sea Waves ◽  
Random Loading ◽  
Euler Beam ◽  
Stress Spectrum ◽  
The Galerkin Method

Pipelines located on the decks of FPSO systems are exposed to damage due to sea waves induced random loading. In this context, a methodology for estimating the fatigue life of conveying-fluid pipelines is presented. The pipeline is subjected to a random support motion which simulates the effect of the FPSO heaving. The equation of motion of the fluid-carrying pipeline is derived by assuming small amplitude displacements, modeling the empty pipeline as a Bernoulli-Euler beam, and adopting the so-called “plug-flow” approximation for the fluid (Pai¨doussis, 1998). Random vibration analysis is carried out by the Galerkin method selecting as basis functions the natural modes of a beam with the same boundary conditions as the pipeline. The discretized equations of motion are used in conjunction with linear random vibration theory to compute the stress spectrum for a generic section of the pipeline. For this purpose, the power spectrum of the acceleration at the deck level is determined by using the Response Amplitude Operator of the FPSO hull. Finally, the computed stress spectrum is used to estimate the pipeline fatigue life employing an appropriate S-N fatigue curve of the material. An illustrative example concerning a pipeline simply-supported at both ends is included in the paper.

scholarly journals Scaling of Dynamics in the Earliest Stages of Walking

2007 ◽  
Vol 87 (11) ◽  
pp. 1458-1467 ◽  
Author(s):  
Kenneth G Holt ◽  
Elliot Saltzman ◽  
Chia-Ling Ho ◽  
Beverly D Ulrich
Keyword(s):  
Developmental Delays ◽  
Physical Therapist ◽  
Equations Of Motion ◽  
Fine Tuning ◽  
Spring Stiffness ◽  
Kinematic Data ◽  
Ground Testing ◽  
Stage Process ◽  
Study Participants ◽  
Isometric Muscle

Background and Purpose Although the description of mature walking is fairly well established, less is known about what is being learned in the process. Such knowledge is critical to the physical therapist who wants to teach children with developmental delays. The purpose of this experiment was to test the notion that learning to walk efficiently involves fine-tuning the body’s controllable stiffness (by co-contraction and isometric muscle contractions against gravity) to match (at a 1:1 scaling) the gravitational (pendular) stiffness of the swing leg. Subjects The study participants were 7 children with typical development and the newly emerged ability to walk 6 steps without falling (ages 11 months to 1 year 5 months at the onset of walking). Methods Pendular stiffness and spring stiffness were estimated from the equations of motion for a hybrid model with kinematic data as children walked over ground. Testing occurred once per month for the first 7 months of walking. Results After the first month of walking, children walked with greater spring stiffness than would be predicted by the model. The ratio began to approach the predicted value (1:1) as the months progressed. Discussion and Conclusion The results of this and a previous study of the pendular dynamics of gait suggest that learning to walk is a 2-stage process. The first stage involves the child’s discovery of how to conserve energy by inputting a particular muscular force at the correct moment in the cycle. The second stage involves the fine-tuning of the soft-tissue stiffness that takes advantage of the resonance characteristics of tissues. In order to address developmental delays, investigators must discover the dynamic resources used for the activity and attempt to foster their development. A number of interventions that probe this approach are discussed.

A Comparison of the Effects of Nonlinear Damping on the Free Vibration of a Single-Degree-of-Freedom System

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Bin Tang ◽  
M. J. Brennan
Keyword(s):  
Free Vibration ◽  
Equations Of Motion ◽  
Nonlinear Damping ◽  
Degree Of Freedom ◽  
Damping Force ◽  
Single Degree Of Freedom ◽  
Sdof System ◽  
Single Degree ◽  
Dependent Term ◽  
Quadratic Damping

This article concerns the free vibration of a single-degree-of-freedom (SDOF) system with three types of nonlinear damping. One system considered is where the spring and the damper are connected to the mass so that they are orthogonal, and the vibration is in the direction of the spring. It is shown that, provided the displacement is small, this system behaves in a similar way to the conventional SDOF system with cubic damping, in which the spring and the damper are connected so they act in the same direction. For completeness, these systems are compared with a conventional SDOF system with quadratic damping. By transforming all the equations of motion of the systems so that the damping force is proportional to the product of a displacement dependent term and velocity, then all the systems can be directly compared. It is seen that the system with cubic damping is worse than that with quadratic damping for the attenuation of free vibration.

Numerical analysis of the dynamic performance of aerostatic thrust bearings with different restrictors

2018 ◽  
Vol 233 (3) ◽  
pp. 406-423 ◽  
Author(s):  
Hailong Cui ◽  
Yang Wang ◽  
Xiaobin Yue ◽  
Yifei Li ◽  
Zhengyi Jiang
Keyword(s):  
Load Capacity ◽  
Dynamic Stiffness ◽  
Dynamic Performance ◽  
Dynamic Mesh ◽  
Eccentricity Ratio ◽  
Thrust Bearings ◽  
Stiffness And Damping Coefficient ◽  
Stiffness And Damping ◽  
The Impact ◽  
The Relationship

This study utilizes a dynamic mesh technology to investigate the dynamic performance of aerostatic thrust bearings with orifice restrictor, multiple restrictors, and porous restrictor. An experiment, which investigates the bearing static load capacity, was carried out to verify the calculation accuracy of dynamic mesh technology. Further, the impact of incentive amplitude, incentive frequency, axial eccentricity ratio, and non-flatness on the bearing dynamic performance was also studied. The results show incentive amplitude effect can be ignored at the condition of amplitude less than 5% film thickness, while the relationship between dynamic characteristics and incentive frequency presented a strong nonlinear relationship in the whole frequency range. The change law of dynamic stiffness and damping coefficient for porous restrictor was quite different from orifice restrictor and multiple restrictors. The bearing dynamic performance increased significantly with the growth of axial eccentricity ratio, and the surface non-flatness enhanced dynamic performance of aerostatic thrust bearings.

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