Mathematical analysis and numerical study to free vibrations of annular plates using BIEM and BEM

2005 ◽  
Vol 65 (2) ◽  
pp. 236-263 ◽  
Author(s):  
J. T. Chen ◽  
S. Y. Lin ◽  
I. L. Chen ◽  
Y. T. Lee
Keyword(s):  
Mathematical Analysis ◽  
Numerical Study ◽  
Free Vibrations ◽  
Annular Plates

A GENERAL APPROXIMATE SOLUTION OF THE PROBLEM OF FREE VIBRATIONS OF ANNULAR PLATES OF STEPPED THICKNESS

1996 ◽  
Vol 196 (3) ◽  
pp. 275-283 ◽  
Author(s):  
D.R. Avalos ◽  
H.A. Larrondo ◽  
V. Sonzogni ◽  
P.A.A. Laura
Keyword(s):  
Approximate Solution ◽  
Free Vibrations ◽  
Annular Plates

FREE VIBRATIONS OF ANNULAR PLATES COUPLED WITH FLUIDS

1996 ◽  
Vol 191 (5) ◽  
pp. 825-846 ◽  
Author(s):  
M. Amabili ◽  
G. Frosali ◽  
M.K. Kwak
Keyword(s):  
Free Vibrations ◽  
Annular Plates

Free vibrations of annular plates of variable thickness

1980 ◽  
Vol 12 (4) ◽  
pp. 508-512
Author(s):  
A. D. Lizarev ◽  
V. P. Kuz'mentsov
Keyword(s):  
Variable Thickness ◽  
Free Vibrations ◽  
Annular Plates ◽  
Plates Of Variable Thickness

scholarly journals SYNCHRONIZATION OF PENDULUMS (NUMERICAL STUDY)

2021 ◽  
Vol 6 (3) ◽  
pp. 16-25
Author(s):  
Robert A. Sunarchin ◽  
Pavel V. Petrov
Keyword(s):  
Strouhal Number ◽  
High Efficiency ◽  
Numerical Study ◽  
Auxiliary Problem ◽  
Free Vibrations ◽  
Mutual Synchronization ◽  
Wide Range

This paper presents the results of a numerical study of synchronization of pendulums, chronometers, and mechanical clocks suspended from a common movable beam. An auxiliary problem is considered about the oscillations of a pendulum with a swinging weight, then the mutual synchronization of free vibrations of two and four pendulums (and pendulums with the supply of a moment pulse-clock) on a common movable spring-loaded beam. It is shown that in the considered simplest configuration, mutual synchronization (equality of frequencies or oscillation periods) is performed with high efficiency. The frequency of synchronized oscillations of the pendulums is close to the frequency of vibrations of the platform in a wide range of changes in its rigidity. The degree of connectivity of pendulums and synchronization of their oscillations is determined by the Strouhal number. Synchronization of clocks does not guarantee the accuracy of their movement, which is achieved only when the Strouhal number is equal to one.

scholarly journals Diffusion–reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19, mathematical analysis, and numerical study

2020 ◽  
Vol 66 (5) ◽  
pp. 1131-1152 ◽  
Author(s):  
Alex Viguerie ◽  
Alessandro Veneziani ◽  
Guillermo Lorenzo ◽  
Davide Baroli ◽  
Nicole Aretz-Nellesen ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Continuum Mechanics ◽  
Mathematical Analysis ◽  
Numerical Study ◽  
Interdisciplinary Collaboration ◽  
Compartmental Models ◽  
Diffusion Reaction ◽  
Pde Model ◽  
Fundamental Equations ◽  
Detailed Derivation

Abstract The outbreak of COVID-19 in 2020 has led to a surge in interest in the research of the mathematical modeling of epidemics. Many of the introduced models are so-called compartmental models, in which the total quantities characterizing a certain system may be decomposed into two (or more) species that are distributed into two (or more) homogeneous units called compartments. We propose herein a formulation of compartmental models based on partial differential equations (PDEs) based on concepts familiar to continuum mechanics, interpreting such models in terms of fundamental equations of balance and compatibility, joined by a constitutive relation. We believe that such an interpretation may be useful to aid understanding and interdisciplinary collaboration. We then proceed to focus on a compartmental PDE model of COVID-19 within the newly-introduced framework, beginning with a detailed derivation and explanation. We then analyze the model mathematically, presenting several results concerning its stability and sensitivity to different parameters. We conclude with a series of numerical simulations to support our findings.

Numerical Study of Effect of Using Nanofluids Flowing in Simply Supported Pipes on Vibrations Characteristics

2020 ◽  
Vol 38 (1A) ◽  
pp. 43-56
Author(s):  
Kadhum A. Jehhef ◽  
Mohamed A. Siba ◽  
Hayder S. Abdulamir
Keyword(s):  
Natural Frequency ◽  
Volume Fraction ◽  
Numerical Study ◽  
Free Vibrations ◽  
Working Fluid ◽  
Pipeline System ◽  
Pipe Length ◽  
Simply Supported ◽  
General Internal ◽  
Flow Induced Vibrations

In general, internal vibrations within the pipelines caused by fluids being passing through a pipeline system can cause. These pipeline system can damage by the sudden amplified vibrations that weren’t considered at the design of the system, and flow induced vibrations resonate with the pipes natural frequency. Therefore, it is important to predict and identify the pipeline system vibrations during its lifetime. In this study by using MATLAB code as a CFD solver, it studied the forced and free vibrations caused by fluid flows at Reynolds number ranged as 0 < Re < 2500 for laminar flow and ranged as 104 < Re < 105 for turbulent flow. The working fluid has chosen as of (Al2O3, TiO2, SiO2 and water) with different nanoparticle volume fraction of (0 to 2% vol.). These fluids flow in simply supported pipe with different lengths and diameters. The results presented the effect of pipe and fluid parameter upon the fluid critical velocity and fundamental natural frequencies. The results showed that the pipe natural frequency increased with increasing with decreasing the pipe length and diameter. In addition, it showed that the pipe natural frequency decreased when using the different nanoparticle depressed in the water and with increasing the volume fraction.

Integral Equation Method for Free Vibration of Annular Plates with Elastic Supports

2011 ◽  
Vol 52-54 ◽  
pp. 573-577
Author(s):  
Gang Cheng ◽  
Wei Dong Wang ◽  
Quan Cheng
Keyword(s):  
Integral Equation ◽  
Eigenvalue Problem ◽  
Free Vibration ◽  
Infinite Order ◽  
Integral Equation Method ◽  
Free Vibrations ◽  
Equation Method ◽  
Orthogonal Functions ◽  
Elastic Supports ◽  
Annular Plates

Annular plates are commonly found in the fields of engineering. The present study is concerned with the integral equation method for the free vibrations of annular plates with elastic supports. A set of complete systems of orthogonal functions, which is constructed by Bessel functions of the first and the second kind is used to construct the Green's function of annular plates. The eigenvalue problem of free vibration of annular plates with Elastic Supports is transformed into the eigenvalue problem of integral equation. And then, the problem of integral equation is transformed into a standard eigenvalue problem of a matrix with infinite order. Numerical example shows the significant advantages of the present method.

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