Highly Reduced Lumped Parameter Models Representing Impedance Functions at the Interface of One-Dimensional Viscoelastic Continua

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Masato Saitoh
Keyword(s):  
Degrees Of Freedom ◽  
Reaction Force ◽  
Lumped Parameter Model ◽  
Computational Time ◽  
Dynamic Problems ◽  
Modal Expansion ◽  
Mass Element ◽  
Lumped Parameter ◽  
In Series ◽  
Impedance Functions

In recent dynamic problems dealing with high-frequency excitations, such as ultrasonic vibrations, a proper representation of rods transmitting kinetic energy from the interface attached to the vibrating system to the other end is strongly demanded for effectively reducing computational time and domain. A highly reduced lumped parameter model that properly simulates the dynamic characteristics of a uniform, isotropic, homogeneous, and viscoelastic rod subjected to excitations at its end is proposed in this paper. The model consists of springs, dashpots, and so called “gyro-mass elements.” The gyro-mass element generates a reaction force proportional to the relative acceleration of the nodes between which it is placed. This model consists of units arranged in series, each unit consisting of a spring, a dashpot, and a gyro-mass element arranged in parallel. A formula is proposed for determining the properties of the elements in the units based on the modal expansion. The results show that a notable reduction of 90% in the degrees of freedom is accomplished with high accuracy by using the proposed model consisting of a set of units associated with modes in a target frequency region and a supplemental unit associated with residual stiffness, which is advantageous for efficient numerical computations in recent dynamic problems.

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

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.

scholarly journals Lumped Parameter Model and Electromagnetic Performance Analysis of a Single-Sided Variable Flux Permanent Magnet Linear Machine

Energies ◽  
2021 ◽  
Vol 14 (17) ◽  
pp. 5494
Author(s):  
Basharat Ullah ◽  
Faisal Khan ◽  
Muhammad Qasim ◽  
Bakhtiar Khan ◽  
Ahmad H. Milyani ◽  
...  
Keyword(s):  
Permanent Magnet ◽  
Thrust Force ◽  
Lumped Parameter Model ◽  
Computational Time ◽  
Design Parameters ◽  
3D Analysis ◽  
Flux Linkage ◽  
Lumped Parameter ◽  
Variable Flux ◽  
Linear Machine

A new Single-sided Variable Flux Permanent Magnet Linear Machine with flux bridge in mover core is proposed in this paper. The flux bridge prevents the leakage flux from the mover and converts it into flux linkage, which greatly influences the performance of the machine. First, a lumped parameter model is used to find the suitable coil combination and no-load flux linkage of the proposed machine, which greatly reduces the computational time and drive storage. Secondly, the proposed machine replaces the expensive rare earth permanent magnets with ferrite magnets and provides improved flux controlling capability under variable excitation currents. Multivariable geometric optimization is utilized to optimize the leading design parameters like split ratio, stator pole width, width and height of permanent magnet, flux bridge width, the width of mover’s tooth, and stator slot depth at constant electric and magnetic loading. The optimized design increases the flux linkage by 44.11%, average thrust force by 35%, thrust force density by 35.02%, minimizes ripples in thrust force by 23%, and detent force by 87.5%. Furthermore, the results obtained by 2D analysis are verified by 3D analysis. Thermal analysis is done to set the operating limit of the proposed machine.

Parameter Sensitivity Analysis of a Lumped-Parameter Model of Lymphangions in Series

2012 ◽  
Author(s):  
Samira Jamalian ◽  
James E. Moore ◽  
Christopher D. Bertram ◽  
Will Richardson
Keyword(s):  
Sensitivity Analysis ◽  
Interstitial Fluid ◽  
Lymphatic System ◽  
Lumped Parameter Model ◽  
Node Dissection ◽  
Parameter Sensitivity Analysis ◽  
Protein Balance ◽  
Vital Functions ◽  
Lumped Parameter ◽  
In Series

The lymphatic system is responsible for vital functions in the human body. In particular, it plays an important role in the immune system mechanism whereby undesirable elements are destroyed in the lymph nodes. But cancer cells also spread via the lymphatic system. The system maintains fluid and protein balance by gathering approximately 4 L/day of interstitial fluid and returning it to the venous system. Lymphedema, an ailment of the system for which there is no known cure, primarily affects cancer patients who have undergone lymph node dissection [1]. To understand how to treat such pathologies of the lymphatic system, it is first necessary to examine its fluid flow and pumping mechanisms quantitatively.

Analysis and Design of Cam-Driven Mechanisms With Nonlinearities

1973 ◽  
Vol 95 (3) ◽  
pp. 685-694 ◽  
Author(s):  
F. Y. Chen
Keyword(s):  
Computer Aided Design ◽  
Degrees Of Freedom ◽  
Lumped Parameter Model ◽  
Analysis Tool ◽  
Analysis And Design ◽  
Lumped Parameter ◽  
Method Of Solution ◽  
Parametric Studies ◽  
Rational Procedure ◽  
Aided Design

The cam-and-follower mechanism is represented by a lumped parameter model of finite degrees of freedom, in which nonlinear system parameters may be taken into account. An approximate dynamic analysis of the system excited by either functional or numerical form of the base motion of a cam is obtained. The method of solution which uses an interpolating polynomial for approximating the excitation function and mechanical quadrature for evaluating the convolution integral is well suited for computer programming. A digital computer program for analysis based on this scheme is developed. In order to utilize the analysis tool for design purposes, parametric studies are conducted, design stratagems are presented and a rational procedure of closed loop computer-aided design is outlined and discussed.

Vibration Modes of Helical Planetary Gears

2009 ◽  
Author(s):  
Tugan Eritenel ◽  
Robert G. Parker
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Lumped Parameter Model ◽  
Vibration Modes ◽  
Planetary Gears ◽  
Gear Mesh ◽  
Modal Properties ◽  
Lumped Parameter

This paper examines the vibration modes of single stage helical planetary gears in three dimensions with equally spaced planets. A lumped-parameter model is formulated to obtain the equations of motion. The gears and shafts are modeled as rigid bodies with compliant bearings at arbitrary axial locations on the shafts. A translational and a tilting stiffness account for the force and moment transmission at the gear mesh interface. The modal properties generalize those of two-dimensional spur planetary gears; there are twice as many degrees of freedom and natural frequencies due to the added tilting and axial motion. All vibration modes are categorized as planet, rotational-axial, and translational-tilting modes. The modal properties are shown to hold even for configurations that are not symmetric about the gear plane, due to, for example, shaft bearings not being equidistant from the gear plane. Computational modal analysis are performed to numerically verify the findings.

Segmental vibration transmissibility of seated occupant from lumped parameter models

2011 ◽  
Vol 18 (11) ◽  
pp. 1683-1689 ◽  
Author(s):  
Masilamany Santha Alphin ◽  
Krishnaswamy Sankaranarayanasamy ◽  
Suthangathan Paramashivan Sivapirakasam
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Biomechanical Model ◽  
Dynamic Parameter ◽  
Experimental Results ◽  
Lumped Parameter Model ◽  
Whole Body ◽  
Driving Frequency ◽  
Lumped Parameter ◽  
Lumped Parameter Models

One of the important parameters for the comfort of a seated occupant of a vehicle is the dynamic parameter. The effects of vibration depend on biomechanical characteristics, transmissibility (TR) and apparent mass. The range of input vibration at the seat and TR at the driving frequency will decide the magnitude of the displacement at any point of the human occupant. The most preferred form of biomechanical model for unidirectional whole body vibration is the lumped parameter model. Lumped parameter models are formulated by number of masses depending on the number of degrees-of-freedom (d.f.). The objective of this work is to study the vibration TR by developing the equations of motion (EOM) for different d.f. models for the seated occupant. Then the generated equations of motion for lumped parameter models are solved using the frequency domain technique. In this paper two, four, seven and 11 d.f. models are considered. The TR values are determined by solving the derived parameters using the MATLAB program. The maximum seats to head TR in the case of two, four, seven and 11 d.f. are obtained at the frequency of 2 Hz, 2.5 Hz, 3.15 Hz, and 4 Hz respectively. The TR obtained from models is compared with real time experimental results. The comparison shows a better fit for the TR obtained from the four and seven d.f. models. There is a wide deviation from the TR observed with two and 11 degrees of models when compared with experimental results of the past literature.

Effect of Sitting Occupancy on Lateral Dynamics and Trajectory of a Passenger Car

2015 ◽  
Author(s):  
Divyanshu Joshi ◽  
Anindya Deb
Keyword(s):  
Degrees Of Freedom ◽  
Coupled Model ◽  
Nonlinear Behavior ◽  
Lumped Parameter Model ◽  
Vehicle Model ◽  
Passenger Car ◽  
Yaw Rate ◽  
Environment Model ◽  
Lumped Parameter ◽  
Vehicle Trajectory

In the current work, the effects of sitting locations and combinations of occupants on handling performance of a four-wheeled passenger car have been investigated. A new multi-occupant nonlinear lumped parameter model (LPM) is developed by coupling 1-DOF longitudinal vehicle model, 2-DOF lateral vehicle model, 13-DOF nonlinear vehicle ride model including seats, 6-DOF nonlinear human occupant model, and 1-DOF tire model. The combined model with a maximum of 50 degrees-of-freedom (in case of all five seats occupied) is simulated in MATLAB/SIMULINK environment. Model subsystems i.e. occupant and vehicle models including tires are validated independently by comparing biodynamic responses of seated occupants, vehicle vertical response and handling behavior with published results. The coupled model can facilitate the study of vehicle dynamics considering the combined effects of road inputs, vehicle maneuvering and seat occupancy while taking into account the nonlinear behavior of vehicle suspension. Further the yaw rate and vehicle trajectories are compared and studied for various cases of sitting occupancies at a given vehicle velocity with a road input representing harsh and abrupt scenario. The current study shows that appreciable changes in yaw rate and vehicle trajectory can be caused due to varying sitting occupancies and vehicle velocities.

Evaluation of the Human Body Equilibrium in a Vibration Environment

2015 ◽  
Vol 801 ◽  
pp. 295-299
Author(s):  
Daniela Mariana Barbu ◽  
Mihaela Ioana Baritz
Keyword(s):  
Human Body ◽  
Degrees Of Freedom ◽  
Soft Tissues ◽  
Lumped Parameter Model ◽  
Internal Organs ◽  
Vibratory System ◽  
Lumped Parameter ◽  
Body Dynamics ◽  
Human Balance ◽  
External Sources

In the human body, vibrations are generated by internal or external sources. Because of the soft tissues, bones, joints, internal organs and also because of its anatomical particularities components in general, the human body is a complex vibratory system. The vibrations from external sources can be transmitted to the human body when it is positioned in different manners: standing, sitting, recumbent and moving or at work. The effect of vibration on the human body is related to the natural frequency of affected parts in the human body. This paper studies the dynamic characteristics of a human body system in a vibration environment and sets limits to which the balance is affected. The main result is a multi degrees of freedom lumped parameter model. The model provides an analytical tool for human body dynamics research. The relative displacements of human parts are evaluated, which can be a basis for the assessment of vibration risk and setting limits for keeping human balance.

Lumped Parameter Model of Planetary Gear Systems

1978 ◽  
Vol 192 (1) ◽  
pp. 251-258 ◽  
Author(s):  
J. W. Polder
Keyword(s):  
Degrees Of Freedom ◽  
Planetary Gear ◽  
Lumped Parameter Model ◽  
Damping Coefficients ◽  
Planetary Gear Trains ◽  
Lumped Parameter ◽  
Vibration Model ◽  
Close Relationship ◽  
Angular Velocities ◽  
Gear Trains

A model system is described by parameters for shafts, planetary gear trains and nodes. Moments of inertia, spring stiffnesses and damping coefficients are assigned to the shafts; gear ratios and efficiencies are assigned to planetary gear trains. The equivalence of angular velocities and torques is demonstrated for shafts (vibration model), as well as for planetary gear trains and nodes (configuration of the system). This brings about a new view on the concept of degrees of freedom. The close relationship between gear ratios and torque ratios yields identical functions for these ratios when applied to the input and output shafts of a system. The full use of this relationship requires strict conventions of signs and an extension of the interpretation of values. The introduction of a new concept, named responsivity, expresses the relationships between torques and between powers of arbitrary shafts. With suitable equations, it becomes possible to investigate torque and power distributions exhaustively.

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