Elastic vibration of rotationally ring-shaped periodic structure subjected to three-axis angular velocity components

2021 ◽  
pp. 095440622198937
Author(s):  
Jinlong Liu ◽  
Shiyu Wang ◽  
Dongsheng Zhang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Angular Velocity ◽  
Analytical Model ◽  
Periodic Structure ◽  
Elastic Vibration ◽  
Superposition Method ◽  
Revolution Speed ◽  
Support Count ◽  
Angular Velocities

The elastic vibration of rotationally ring-shaped periodic structure (RRPS) subjected to angular velocities applied about three orthogonal directions are examined. An analytical model having in-plane radial and tangential displacements is developed by using Hamilton's principle. The modeling leads to a partial differential equation with revolution effect, based on which the eigenvalue splitting, mode contamination and vibration instability are examined by focusing on their evolutions with the support count, support strength and revolution speed. The eigensolutions are formulated by perturbation-superposition method. The results imply that the splitting, contamination and instability follow similar rules with those of stationary RRPS, which are heavily affected by the revolution speed. The dependence of parameters on eigensolutions and especially the relationships between eigenvalue splitting and principal instability, and those between mode contamination and combination instability are demonstrated based on a sample RRPS. The principal instability can occur at splitting eigenvalues, and the combination instability can arise in the presence of mode contamination. Main results are compared with the existing ones in the open literature.

The Analysis of Proprioception Alteration during First Five Months after Anterior Cruciate Ligament Reconstruction

2018 ◽  
Vol 1 (84) ◽  
Author(s):  
Vilma Jurevičienė ◽  
Albertas Skurvydas ◽  
Juozas Belickas ◽  
Giedra Bušmanienė ◽  
Dovilė Kielė ◽  
...  
Keyword(s):  
Anterior Cruciate Ligament ◽  
Angular Velocity ◽  
Knee Joint ◽  
Cruciate Ligament ◽  
Position Sense ◽  
Joint Position Sense ◽  
Joint Position ◽  
Starting Position ◽  
Angular Velocities ◽  
Anterior Cruciate

Research  background  and  hypothesis.  Proprioception  is  important  in  the  prevention  of  injuries  as  reduced proprioception  is  one  of  the  factors  contributing  to  injury  in  the  knee  joint,  particularly  the  ACL.  Therefore, proprioception appears not only important for the prevention of ACL injuries, but also for regaining full function after ACL reconstruction.Research aim. The aim of this study was to understand how proprioception is recovered four and five months after anterior cruciate ligament (ACL) reconstruction.Research methods. The study included 15 male subjects (age – 33.7 ± 2.49 years) who had undergone unilateral ACL reconstruction with a semitendinosus/gracilis (STG) graft in Kaunas Clinical Hospital. For proprioceptive assessment, joint position sense (JPS) was measured on both legs using an isokinetic dynamometer (Biodex), at knee flexion of 60° and 70°, and at different knee angular velocities of 2°/s and 10°/s. The patients were assessed preoperatively and after 4 and 5 months, postoperatively.Research results. Our study has shown that the JPS’s (joint position sense) error scores  to a controlled active movement is significantly higher in injured ACL-deficient knee than in the contralateral knee (normal knee) before surgery and after four and five months of rehabilitation.  After 4 and 5 months of rehabilitation we found significantly lower values in injured knees compared to the preoperative data. Our study has shown that in injured knee active angle reproduction errors after 4 and 5 months of rehabilitation were higher compared with the ones of the uninjured knee. Proprioceptive ability on the both legs was  independent of all differences angles for target and starting position for movement. The knee joint position sense on both legs depends upon the rate of two different angular velocities and the mean active angle reproduction errors at the test of angular velocity slow speed was the highest compared with the fast angular velocity. Discussion and conclusions. In conclusion, our study shows that there was improvement in mean JPS 4 and 5 months after ACL reconstruction, but it did not return to normal indices.Keywords: knee joint, joint position sense, angular velocity, starting position for movement.

Finite difference code for velocity and surface traction of a Fluid between Two Eccentric Spheres

2015 ◽  
Vol 11 (1) ◽  
pp. 2960-2971
Author(s):  
M.Abdel Wahab
Keyword(s):  
Velocity Field ◽  
Angular Velocity ◽  
Finite Difference ◽  
Numerical Study ◽  
Outer Sphere ◽  
Equation Of Motion ◽  
Annular Region ◽  
Surface Traction ◽  
Angular Velocities ◽  
Axis Passing

The Numerical study of the flow of a fluid in the annular region between two eccentric sphere susing PHP Code isinvestigated. This flow is created by considering the inner sphere to rotate with angular velocity 1  and the outer sphererotate with angular velocity 2  about the axis passing through their centers, the z-axis, using the three dimensionalBispherical coordinates (, ,) .The velocity field of fluid is determined by solving equation of motion using PHP Codeat different cases of angular velocities of inner and outer sphere. Also Finite difference code is used to calculate surfacetractions at outer sphere.

Qxygen transfer in gravity flow sewers

2000 ◽  
Vol 42 (3-4) ◽  
pp. 417-422 ◽  
Author(s):  
T.Y. Pai ◽  
C.F. Ouyang ◽  
Y.C. Liao ◽  
H.G. Leu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dissolved Oxygen ◽  
Flow Velocity ◽  
Molecular Diffusion ◽  
Eddy Diffusion ◽  
Partial Differential ◽  
Diffusion Term ◽  
Sewer Pipes ◽  
Gravity Sewer

Oxygen diffused to water in gravity sewer pipes was studied in a 21 m long, 0.15 m diameter model sewer. At first, the sodium sulfide was added into the clean water to deoxygenate, then the pump was started to recirculate the water and the deoxygenated water was reaerated. The dissolved oxygen microelectrode was installed to measure the dissolved oxygen concentrations varied with flow velocity, time and depth. The dissolved oxygen concentration profiles were constructed and observed. The partial differential equation diffusion model that considered Fick's law including the molecular diffusion term and eddy diffusion term were derived. The analytic solution of the partial differential equation was used to determine the diffusivities by the method of nonlinear regression. The diffusivity values for the oxygen transfer was found to be a function of molecular diffusion, eddy diffusion and flow velocity.

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