Formulae for errors for initial displacement and velocity problems using the Newmark method

1989 ◽  
Vol 18 (4) ◽  
pp. 565-573 ◽  
Author(s):  
G. B. Warburton
Keyword(s):  
Newmark Method ◽  
Initial Displacement

scholarly journals Comparison of Common Methods in Dynamic Response Predictions of Rotor Systems with Malfunctions

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hongliang Yao ◽  
Qian Zhao ◽  
Qi Xu ◽  
Bangchun Wen
Keyword(s):  
Frequency Domain ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Newmark Method ◽  
Incremental Harmonic Balance Method ◽  
Rotor Systems ◽  
Double Frequency ◽  
Frequency Domain Methods ◽  
Incremental Harmonic Balance

The efficiency and accuracy of common time and frequency domain methods that are used to simulate the response of a rotor system with malfunctions are compared and analyzed. The Newmark method and the incremental harmonic balance method are selected as typical representatives of time and frequency domain methods, respectively. To improve the simulation efficiency, the fixed interface component mode synthesis approach is combined with the Newmark method and the receptance approach is combined with the incremental harmonic balance method. Numerical simulations are performed for rotor systems with single and double frequency excitations. The inherent characteristic that determines the efficiency of the two methods is analyzed. The results of the analysis indicated that frequency domain methods are suitable single and double frequency excitation rotor systems, whereas time domain methods are more suitable for multifrequency excitation rotor systems.

scholarly journals Reliability Analysis of a Filtering Reducer under the Discrete Space Environmental Shocks

2014 ◽  
Vol 6 ◽  
pp. 921720 ◽  
Author(s):  
Jing Lu ◽  
Zhonglai Wang ◽  
Wei Chen ◽  
Xuefei Zhang ◽  
Hao Liu
Keyword(s):  
Differential Equations ◽  
Dynamic System ◽  
Mechanism Design ◽  
Reliability Analysis ◽  
Dynamic Model ◽  
Space Environment ◽  
Newmark Method ◽  
Lumped Mass ◽  
Dynamic Reliability ◽  
Environmental Shocks

Dynamic reliability analysis of a filtering reducer is performed by accounting for discrete shocks from the space environment. Gears are considered as the lumped mass and meanwhile the meshing between different gears is equivalent to a dynamic system consisting of springs and dampers during construction of the dynamic model. The Newmark method is employed to resolve differential equations, and then the additional acceleration could be obtained, caused by shocks to the filtering reducer. Dynamic reliability analysis is conducted with the help of the Simulink tool for the outputs. The results are hopefully useful for spacecraft mechanism design.

Comparison of distal radius fracture intra-articular step reduction with volar locking plates and K wires: a retrospective review of quality and maintenance of fracture reduction

2016 ◽  
Vol 42 (2) ◽  
pp. 144-150 ◽  
Author(s):  
N. A. Johnson ◽  
J. J. Dias ◽  
C. J. Wildin ◽  
L. Cutler ◽  
B. Bhowal ◽  
...  
Keyword(s):  
Distal Radius ◽  
Retrospective Review ◽  
Locking Plate ◽  
Treatment Method ◽  
Volar Locking Plate ◽  
Initial Displacement ◽  
Level Of Evidence ◽  
Initial Reduction ◽  
Multiple Variables ◽  
K Wires

This study investigated the accuracy and maintenance of reduction of intra-articular steps achieved with closed reduction and percutaneous K wires and open reduction and a volar locking plate for the treatment of intra-articular distal radius fractures. We performed a retrospective review of 359 patients with an intra-articular fracture of their distal radius. Multivariate linear regression was undertaken to investigate the influence of multiple variables such as age, gender, initial displacement and treatment method on reduction despite differences between groups. A total of 36% of patients treated with K wires and 29% with volar locking plate had a step greater than or equal to 1 mm present on the first post-operative radiograph. A total of 23% treated with K wires and 28% with volar locking plate had a residual step of 1 mm or more on the last available radiograph. There was no difference identified between the two techniques for quality of initial reduction or persisting step on the last available radiographs. Step behaviour and further reduction of step post-operatively was similar for both treatment methods. Initial displacement and increased age influenced initial reduction. Initial fracture displacement shown radiologically was the only variable identified that influenced the persistence of a step on post-operative radiographs. Level of evidence: IV

scholarly journals May 24, 1968 at Inangahua Junction

1969 ◽  
Vol 2 (1) ◽  
pp. 37-38
Author(s):  
T. Hogue
Keyword(s):  
Shock Waves ◽  
High Frequency ◽  
Initial Displacement ◽  
North East ◽  
The North ◽  
Upward Displacement ◽  
The Town

The twin communities of Inangahua Camp and Inangahua Junction were rudely awakened at approximately 5.25 a.m.by a severe earthquake. About a minute before the quake all the birdlife suddenly stopped their noisy callingand an uncanny stillness settled over the area. The first movement of the earthquake was an upward displacement although a few argue that the initial displacement was to the north east. No longer than two seconds later the high frequency vibrating and confusion of noise enveloped the town, then came the jolting of no discriminate pattern as shock-waves started to rebound through the region. During the peak of the earthquake most people who. were by now fully awakened thought that "this was the end", any dissenters from this view acknowledged that it was "at least a beaut”.

A mathematical analysis of tsunami generation in shallow water due to seabed deformation

2011 ◽  
Vol 141 (3) ◽  
pp. 551-608 ◽  
Author(s):  
Tatsuo Iguchi
Keyword(s):  
Velocity Field ◽  
Shallow Water ◽  
Water Wave ◽  
Initial Velocity ◽  
Tsunami Generation ◽  
Wave Problem ◽  
Initial Displacement ◽  
Water Wave Problem ◽  
Submarine Earthquakes ◽  
Tsunami Model

In numerical computations of tsunamis due to submarine earthquakes, it is frequently assumed that the initial displacement of the water surface is equal to the permanent shift of the seabed and that the initial velocity field is equal to zero and the shallow-water equations are often used to simulate the propagation of tsunamis. We give a mathematically rigorous justification of this tsunami model starting from the full water-wave problem by comparing the solution of the full problem with that of the tsunami model. We also show that, in some cases, we have to impose a non-zero initial velocity field, which arises as a nonlinear effect.

APPLICATION OF THE FINITE STRIP METHOD TO MODELING OF VIBRATIONS OF COLLECTING ELECTRODES

2013 ◽  
Vol 13 (07) ◽  
pp. 1340001 ◽  
Author(s):  
IWONA ADAMIEC-WÓJCIK ◽  
ANDRZEJ NOWAK ◽  
STANISŁAW WOJCIECH
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Geometrical Parameters ◽  
Experimental Measurements ◽  
Newmark Method ◽  
Algebraic Equations ◽  
Finite Strip ◽  
Strip Method ◽  
Finite Strip Method ◽  
Large Length

The paper presents an application of the finite strip method to modeling of vibrations of the collecting electrodes, which are shells with large length (up to 16 m), width of 0.5 m and thickness of 0.002 m. The models and computer programs have been worked out and validated. Comparison of results obtained from numerical simulations and experimental measurements are presented and discussed. The equations of motion have been solved using methods for solution of sparse algebraic equations and Newmark method. The strip method has proved to be numerically effective. The programs enable us to carry out calculations for a system with several hundred thousands of degrees of freedom with time of analysis requiring thousand integration steps during less than 90 min on a PC computer. High numerical efficiency enables the geometrical parameters of the collecting electrodes to be selected in order to ensure large accelerations caused by a beater to be spread evenly over the surface of the electrodes. Conclusions concerning the influence of length of the collecting electrodes on the normal and tangentz accelerations are formulated.

Lipschitz stability for a semi-linear inverse stochastic transport problem

2020 ◽  
Vol 28 (2) ◽  
pp. 185-193
Author(s):  
Zhongqi Yin
Keyword(s):  
Inverse Problem ◽  
Main Tool ◽  
Terminal State ◽  
Lipschitz Stability ◽  
Unknown Parameters ◽  
Initial Displacement ◽  
Stochastic Transport ◽  
Random Term ◽  
Global Carleman Estimate ◽  
Stochastic Transport Equation

AbstractThis paper is addressed to a semi-linear stochastic transport equation with three unknown parameters. It is proved that the initial displacement, the terminal state and the random term in diffusion are uniquely determined by the state on partial boundary and a Lipschitz stability of the inverse problem is established. The main tool we employ is a global Carleman estimate for stochastic transport equations.

scholarly journals Effects of Attachment of Plastic Aligner in Closing of Diastema of Maxillary Dentition by Finite Element Method

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Yukiko Yokoi ◽  
Atsushi Arai ◽  
Jun Kawamura ◽  
Tomoko Uozumi ◽  
Yohei Usui ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Periodontal Ligament ◽  
Tooth Movement ◽  
Initial Displacement ◽  
Bodily Movement ◽  
Long Time ◽  
Maxillary Dentition ◽  
Element Method

The aim of this study was to clarify the effect of attachment on tooth movement produced by a plastic aligner. Closing of a diastema, in which the maxillary right and left central incisors moved bodily, was simulated using a finite element method. Long-term orthodontic movements of the maxillary dentition were simulated by accumulating the initial displacement of teeth produced by elastic deformation of the periodontal ligament. The incisor tipped and rotated just after placement of the aligner irrespective of the attachment. After a sufficiently long time, the incisor was upright and moved bodily in the aligner with attachment, but the incisor remained tipped in the aligner without attachment. It was demonstrated that the attachment was effective for achieving bodily movement.

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