A Lumped Parameter Approach to Vibration and Stress Analysis of Elastic Linkages

1973 ◽  
Vol 95 (2) ◽  
pp. 549-557 ◽  
Author(s):  
J. P. Sadler ◽  
G. N. Sandor
Keyword(s):  
Stress Reduction ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Optimization Procedure ◽  
Elastic Vibration ◽  
Finite Difference Approximations ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Uniform Cross Section ◽  
Uniform Case

A method of kineto-elastodynamic analysis is developed employing lumped parameter models for simulating moving mechanism components considered as simply-supported beams subject to in-plane bending. Application of finite difference approximations to Euler’s beam theory leads to a system of nonlinear, ordinary differential equations of motion, and numerical solution of these equations is illustrated for specific examples. Variable as well as uniform cross-section members are analyzed for elastic vibration and stresses. By means of a general optimization procedure presented, nonuniform beam contours are obtained which provide a substantial stress reduction relative to the uniform case, without a corresponding increase in total mass.

Nonlinear Vibration Analysis of Elastic Four-Bar Linkages

1974 ◽  
Vol 96 (2) ◽  
pp. 411-419 ◽  
Author(s):  
J. P. Sadler ◽  
G. N. Sandor
Keyword(s):  
Equations Of Motion ◽  
Beam Theory ◽  
Bernoulli Beam ◽  
Bending Vibrations ◽  
Elastic Bending ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Nonlinear Equations Of Motion ◽  
Four Bar Linkage ◽  
Euler Bernoulli Beam

A method of kineto-elastodynamic analysis is developed employing lumped parameter models for simulating moving mechanism components subject to elastic bending vibrations. The mechanism analyzed is the general planar four-bar linkage and the analytical model includes the response coupling associated with both the transmission of forces at the pin joints and the dependence of the undeformed motion of a link on the elastic motion of other links. Nonlinear equations of motion are derived by way of Euler-Bernoulli beam theory, and numerical solution of these equations is illustrated for specific examples. The model is suitable for the analysis of mechanisms with non-periodic motion and with nonuniform cross-section members.

Dynamic Behavior of Vehicles Travelling on Bridges

1993 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Mehrdaad Ghorashi
Keyword(s):  
Boundary Conditions ◽  
Dynamic Behavior ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Parameter System ◽  
Moving Vehicle ◽  
Lumped Parameter ◽  
Euler Bernoulli Beam ◽  
Two Degree Of Freedom

Abstract An investigation into the dynamic behavior of a bridge with simply supported boundary conditions, carrying a moving vehicle, is performed. The vehicle has been modelled as a two degree of freedom lumped-parameter system travelling at a uniform speed. Furthermore, the bridge is assumed to obey the Euler-Bernoulli beam theory of vibration. This analysis may well be applied to a beam with different boundary conditions, but the computer simulation results given in this paper are set for only the case of freely hinged ends. Numerical solutions for the derived differential equations of motion are obtained and their close agreement, in some extreme cases, with those reported earlier by the authors are observed. Finally, the effect of speed on the maximum dynamic deflection of bridge is shown to be of much importance and hence an estimation for the critical speed of the vehicle is presented.

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.

scholarly journals Enhancing finite difference approximations for double barrier options: mesh optimization and repeated Richardson extrapolation

2021 ◽  
Author(s):  
Luca Vincenzo Ballestra
Keyword(s):  
Finite Difference ◽  
Optimization Procedure ◽  
Richardson Extrapolation ◽  
Mesh Optimization ◽  
Option Prices ◽  
Barrier Option ◽  
Double Barrier ◽  
Finite Difference Approximations ◽  
Barrier Option Pricing ◽  
Richardson Extrapolation Technique

AbstractWe show that the performances of the finite difference method for double barrier option pricing can be strongly enhanced by applying both a repeated Richardson extrapolation technique and a mesh optimization procedure. In particular, first we construct a space mesh that is uniform and aligned with the discontinuity points of the solution being sought. This is accomplished by means of a suitable transformation of coordinates, which involves some parameters that are implicitly defined and whose existence and uniqueness is theoretically established. Then, a finite difference scheme employing repeated Richardson extrapolation in both space and time is developed. The overall approach exhibits high efficacy: barrier option prices can be computed with accuracy close to the machine precision in less than one second. The numerical simulations also reveal that the improvement over existing methods is due to the combination of the mesh optimization and the repeated Richardson extrapolation.

Disk Position Nonlinearity Effects on the Chaotic Behavior of Rotating Flexible Shaft-Disk Systems

2012 ◽  
Vol 28 (3) ◽  
pp. 513-522 ◽  
Author(s):  
H. M. Khanlo ◽  
M. Ghayour ◽  
S. Ziaei-Rad
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Dynamic Behavior ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Disk System ◽  
Partial Differential ◽  
Rayleigh Beam ◽  
Flexible Shaft

AbstractThis study investigates the effects of disk position nonlinearities on the nonlinear dynamic behavior of a rotating flexible shaft-disk system. Displacement of the disk on the shaft causes certain nonlinear terms which appears in the equations of motion, which can in turn affect the dynamic behavior of the system. The system is modeled as a continuous shaft with a rigid disk in different locations. Also, the disk gyroscopic moment is considered. The partial differential equations of motion are extracted under the Rayleigh beam theory. The assumed modes method is used to discretize partial differential equations and the resulting equations are solved via numerical methods. The analytical methods used in this work are inclusive of time series, phase plane portrait, power spectrum, Poincaré map, bifurcation diagrams, and Lyapunov exponents. The effect of disk nonlinearities is studied for some disk positions. The results confirm that when the disk is located at mid-span of the shaft, only the regular motion (period one) is observed. However, periodic, sub-harmonic, quasi-periodic, and chaotic states can be observed for situations in which the disk is located at places other than the middle of the shaft. The results show nonlinear effects are negligible in some cases.

Lumped parameter models for two-ventricle and healthy and failing extracardiac Fontan circulations

2021 ◽  
Author(s):  
Matthew G Doyle ◽  
Marina Chugunova ◽  
S Lucy Roche ◽  
James P Keener
Keyword(s):  
Single Ventricle ◽  
Left Ventricular ◽  
Sensitivity Analyses ◽  
Surgical Strategies ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Fontan Failure ◽  
Existence Of Periodic Solutions ◽  
Mathematical Definitions ◽  
Extracardiac Fontan

Abstract Fontan circulations are surgical strategies to treat infants born with single ventricle physiology. Clinical and mathematical definitions of Fontan failure are lacking, and understanding is needed of parameters indicative of declining physiologies. Our objective is to develop lumped parameter models of two-ventricle and single-ventricle circulations. These models, their mathematical formulations and a proof of existence of periodic solutions are presented. Sensitivity analyses are performed to identify key parameters. Systemic venous and systolic left ventricular compliances and systemic capillary and pulmonary venous resistances are identified as key parameters. Our models serve as a framework to study the differences between two-ventricle and single-ventricle physiologies and healthy and failing Fontan circulations.

Free vibration analysis and post-critical free vibrations of nanocomposite rotating beams reinforced with graphene platelet

2021 ◽  
pp. 107754632110511
Author(s):  
Arameh Eyvazian ◽  
Chunwei Zhang ◽  
Farayi Musharavati ◽  
Afrasyab Khan ◽  
Mohammad Alkhedher
Keyword(s):  
Natural Frequency ◽  
Thermal Environment ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Weight Fraction ◽  
Free Vibrations ◽  
Graphene Platelet ◽  
The Impact

Treatment of the first natural frequency of a rotating nanocomposite beam reinforced with graphene platelet is discussed here. In regard of the Timoshenko beam theory hypothesis, the motion equations are acquired. The effective elasticity modulus of the rotating nanocomposite beam is specified resorting to the Halpin–Tsai micro mechanical model. The Ritz technique is utilized for the sake of discretization of the nonlinear equations of motion. The first natural frequency of the rotating nanocomposite beam prior to the buckling instability and the associated post-critical natural frequency is computed by means of a powerful iteration scheme in reliance on the Newton–Raphson method alongside the iteration strategy. The impact of adding the graphene platelet to a rotating isotropic beam in thermal ambient is discussed in detail. The impression of support conditions, and the weight fraction and the dispersion type of the graphene platelet on the acquired outcomes are studied. It is elucidated that when a beam has not undergone a temperature increment, by reinforcing the beam with graphene platelet, the natural frequency is enhanced. However, when the beam is in a thermal environment, at low-to-medium range of rotational velocity, adding the graphene platelet diminishes the first natural frequency of a rotating O-GPL nanocomposite beam. Depending on the temperature, the post-critical natural frequency of a rotating X-GPL nanocomposite beam may be enhanced or reduced by the growth of the graphene platelet weight fraction.

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