Four degree-of-freedom lumped parameter model of the foot-ankle system exposed to vertical vibration from 10 to 60 Hz with varying centre of pressure conditions

Whole body vibration (WBV) can induce a host of pathologies, including muscle fatigue and neck and low back pain [1,2]. A new model of WBV in the rat has been developed to define relationships between WBV exposures, kinematics, and behavioral sensitivity (i.e. pain) [3]. Although in vivo studies provide valuable associations between biomechanics and physiology, they are not able to fully define the mechanical loading of specific spinal regions and/or the tissues that may undergo injurious loading or deformation. Mathematical models of seated humans and primates have been used to estimate spinal loads and design measures that mitigate them during WBV [4–6]. Although such models provide estimates of relative spinal motions, they have limited utility for relating potentially pathological effects of vibration-induced kinematics and kinetics since those models do not enable simultaneous evaluation of relevant spinal tissues with the potential for injury and pain generation. As such, the goal of this work was to develop and validate a three degree of freedom (3DOF) lumped-parameter model of the prone rat undergoing WBV directed along the long-axis of the spine. The model was constructed with dimensions of a generalized rat and model parameters optimized using kinematics over a range of frequencies. It was validated by comparing predicted and measured transmissibility and further used to predict spinal extension and compression, as well as acceleration, during WBV for frequencies known to produce resonance in the seated human and pain in the rat [3,7].

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Influence of Friction Dampers on Torsional Blade Flutter

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.3239905 ◽

1986 ◽

Vol 108 (2) ◽

pp. 313-318 ◽

Cited By ~ 7

Author(s):

A. Sinha ◽

J. H. Griffin ◽

R. E. Kielb

Keyword(s):

Dry Friction ◽

Fluid Velocity ◽

Supersonic Flows ◽

Degree Of Freedom ◽

Lumped Parameter Model ◽

Single Degree Of Freedom ◽

Friction Dampers ◽

Single Degree ◽

Lumped Parameter ◽

Blade Flutter

This paper deals with the stabilizing effects of dry friction on torsional blade flutter. A lumped parameter model with single degree of freedom per blade has been used to represent the rotor stage. The well-known cascade theories for incompressible and supersonic flows have been used to determine the allowable increase in fluid velocity relative to the blade. It has been found that the effectiveness of friction dampers in controlling flutter can be substantial.

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Mathematical Model of Suspension Seat-Person Exposed to Vertical Vibration for Off-Road Vehicles

International Journal of Automotive and Mechanical Engineering ◽

10.15282/ijame.16.2.2019.22.0509 ◽

2019 ◽

Vol 16 (2) ◽

pp. 6773-6782

Author(s):

S. Aisyah Adam ◽

N. A. A. Jalil ◽

K. A. Md Razali ◽

Y. G. Ng ◽

M. F. Aladdin

Keyword(s):

Human Body ◽

Degrees Of Freedom ◽

Low Frequency ◽

Coupled System ◽

Vertical Vibration ◽

Lumped Parameter Model ◽

Model Parameters ◽

Road Vehicles ◽

Lumped Parameter ◽

Variable Function

Off-road drivers are exposed to a high magnitude of vibration at low frequency (0.5-25Hz), that can cause harm and possibly attribute to musculoskeletal disorder, particularly low-back pain. The suspension seat is commonly used on an off-road condition to isolate the vibration transmitted to the human body. Nevertheless, the suspension seat modelling that incorporates the human body is still scarce. The objective of this study is to develop a mathematical modelling to represent the suspension seat-person for off-road vehicles. This paper presents a three degrees-of-freedom lumped parameter model. A curve-fitting method is used for parameter identification, which includes the constraint variable function (fmincon()) from the optimisation toolbox of MATLAB(R2017a). The model parameters are optimised using experimentally measured of suspension seat transmissibility. It was found that the model provides a reasonable fit to the measured suspension seat transmissibility at the first peak of resonance frequency, around 2-3 Hz. The results of the study suggested that the human body forms a coupled system with the suspension seat and thus affects the overall performance of the suspension system. As a conclusion, the influence of the human body should not be ignored in the modelling, and a three-degrees degree-of-freedom lumped parameter model provides a better prediction of suspension seat transmissibility. This proposed model is recommended to predict vibration transmissibility for off-road suspension seat.

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PREDICTING THE TRANSMISSIBILITY OF A GLOVE MATERIAL TO THE PALM USING A SIMPLE LUMPED PARAMETER MODEL OF THE HAND AND THE GLOVE

Jurnal Teknologi ◽

10.11113/jt.v78.9180 ◽

2016 ◽

Vol 78 (6-10) ◽

Author(s):

K.A.M. Rezali ◽

A. As’arry ◽

Z.A. Zulkefli ◽

R. Samin ◽

N.A.A. Jalil

Keyword(s):

Degree Of Freedom ◽

Lumped Parameter Model ◽

Main Body ◽

Body Segments ◽

Lumped Parameter ◽

Translational Spring ◽

Reasonable Prediction ◽

Three Degree Of Freedom

Assessing a glove for its ability to reduce vibration transmitted to the hand can be improved if the transmissibility of the glove to the hand can be predicted. This study proposes a simple lumped parameter model of the hand and the glove for predicting the transmissibility of a glove to the hand. The model of the hand consists of three main body segments: the palm, the fingers, and the palm tissues, connected via translational and rotational springs and dampers. The glove material was represented by translational spring and damper. The results showed that the glove transmissibility predicted using the model overestimated the glove transmissibility measured experimentally at frequencies greater than 62 Hz, implying that a simple three degree-of-freedom model of the hand and the glove may not be able to provide a reasonable prediction of glove transmissibility.

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Nonlinear Dynamic Modelling of a Suspension Seat for Predicting the Vertical Seat Transmissibility

Mathematical Problems in Engineering ◽

10.1155/2021/3026108 ◽

2021 ◽

Vol 2021 ◽

pp. 1-10

Author(s):

Weitan Yin ◽

Juyue Ding ◽

Yi Qiu

Keyword(s):

Nonlinear Dynamic ◽

Ride Comfort ◽

Dynamic Modelling ◽

Vertical Vibration ◽

Lumped Parameter Model ◽

Nonlinear Behaviour ◽

Seat Suspension ◽

Lumped Parameter ◽

Seat Cushion ◽

Inert Mass

Suspension seats are widely used in heavy vehicles to reduce vibration transmitted to human body and promote ride comfort. Previous studies have shown that the dynamics of the suspension seat exhibits nonlinear behaviour with changed vibration magnitudes. Despite various linear seat models developed in the past, a nonlinear model of the suspension seat capturing the nonlinear dynamic behaviour of the seat suspension and cushion has not been developed for the prediction of the seat transmissibility. This paper proposes a nonlinear lumped parameter model of the suspension seat to predict the nonlinear dynamic response of the seat. The suspension seat model comprises of a nonlinear suspension submodel integrated with a nonlinear cushion submodel. The parameters of the submodels are determined by minimizing the error between the simulated and the measured transmissibility of the suspension mechanism and the force-deflection curve of the seat cushion, respectively. The model of the complete seat is then validated using the seat transmissibility measured with inert mass under vertical vibration excitation. The results show that the proposed suspension seat model can be used to predict the seat transmissibility with various excitation magnitudes.

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MoorDyn V2: New Capabilities in Mooring System Components and Load Cases

Volume 9: Ocean Renewable Energy ◽

10.1115/omae2020-19341 ◽

2020 ◽

Author(s):

Matthew Hall

Keyword(s):

Failure Modes ◽

Body Representation ◽

Degree Of Freedom ◽

Lumped Parameter Model ◽

Mooring Line ◽

Mooring System ◽

Mooring Lines ◽

Lumped Parameter ◽

Mooring Dynamics ◽

Six Degree Of Freedom

Abstract MoorDyn, an open-source mooring dynamics model, is being expanded with capabilities for additional mooring system features and load cases. As floating wind turbine technology matures, mooring systems are becoming more sophisticated and more complex scenarios need to be considered in the design process. Mooring systems may have synthetic line materials, ballast/buoyancy bodies along the lines, or interconnections between platforms. Failure modes may involve multiple cascading line failures that depend on mooring system dynamics. Features recently added to MoorDyn aim to address these emerging needs. MoorDyn’s linear elasticity model has been supplemented to support user-defined stress-strain curves, which can be adjusted to represent synthetic mooring materials. Rigid six-degree-of-freedom bodies in the mooring system can now be modeled using two new model objects. “Rod” objects provide an option for rigid cylindrical bodies. They use the existing Morison equation-based hydrodynamics model and can be connected to mooring lines at either end. “Body” objects provide a generic six-degree-of-freedom rigid-body representation based on a lumped-parameter model of translational and rotational properties. Rod objects can be added to Body objects and mooring lines can be attached at any location, allowing a wide variety of submerged structures to be integrated into the mooring system. Lastly, a means of dynamically simulating mooring line failures has been implemented. These new features, currently in the C++ version of MoorDyn, are described and then demonstrated on a two-turbine shared-mooring array. A qualitative view of the results suggests the new features are functioning as expected.

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