scholarly journals Investigation of dynamics of elastic element of vibration device

Author(s):  
П.А. Вельмисов ◽  
А.В. Анкилов ◽  
Г.А. Анкилов

ва подхода к решению аэрогидродинамической части задачи, основанные на методах теории функций комплексного переменного и методе Фурье. В результате применения каждого подхода решение исходной задачи сведено к исследованию дифференциального уравнения с частными производными для деформации элемента, позволяющего изучать его динамику. На основе метода Галеркина произведены численные эксперименты для конкретных примеров механической системы, подтверждающие идентичность решений, найденных для каждого дифференциального уравнения с частными производными. The dynamics of an elastic element of a vibration device, simulated by a channel, inside which a stream of a liquid flows, is investigated. Two approaches to solving the aerohydrodynamic part of the problem, based on the methods of the theory of functions of a complex variable and the Fourier method, are given. As a result of applying each approach, the solution to the original problem is reduced to the study of a partial differential equation for the deformation of an element, which makes it possible to study its dynamics. Based on the Galerkin method, the numerical experiments were carried out for specific examples of mechanical system, confirming the identity of the solutions found for each partial differential equation.

2019 ◽  
pp. 175-184
Author(s):  
Petr A. Velmisov ◽  
Andrey V. Ankilov

The dynamics and stability of the elastic elements of vibration devices, modeled by a channel containing elastic elements, are investigated. Inside the channel flows a stream of stirred liquid. The model of the device with two elastic elements is considered. The solution of the aerohydrodynamic part of the problem, based on the methods of the theory of functions of a complex variable, is given. The solution of the original problem is reduced to the study of a coupled system of partial differential equations for the deformations of elements, which makes it possible to study their dynamics. On the basis of the constructed functional for this system, the sufficient conditions of stability are obtained. The conditions impose restrictions on the parameters of the mechanical system. Based on the Galerkin method, the numerical experiments for specific examples of mechanical systems were carried out, confirming the reliability of the investigations. A special case of the model of device with one elastic element is considered. Based on this case, a comparison with the model of the vibration device considered earlier is made.


2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Guanglu Zhou ◽  
Boying Wu ◽  
Wen Ji ◽  
Seungmin Rho

This study presents numerical schemes for solving a parabolic partial differential equation with a time- or space-dependent coefficient subject to an extra measurement. Through the extra measurement, the inverse problem is transformed into an equivalent nonlinear equation which is much simpler to handle. By the variational iteration method, we obtain the exact solution and the unknown coefficients. The results of numerical experiments and stable experiments imply that the variational iteration method is very suitable to solve these inverse problems.


Author(s):  
N. G. Barton ◽  
C.-H. Li ◽  
S. J. Spencer

AbstractThis paper examines the control of an interface between a suspension of sedimenting particles in liquid and a bed of dense-packed particles at the bottom of the suspension. The problem arises in the operation of continuous thickeners (e.g. in mineral processing) and is here mathematically described by a first order inhomogeneous partial differential equation for the concentration C(x, t) of particles. The controlled variable is the height H* of the bed, and the control variables are the volume fluxes injected at the feed level and removed at the bed. A strategy to control the interface is devised, and control is confirmed and demonstrated by a series of numerical experiments.


2021 ◽  
Vol 64 (1) ◽  
pp. 103-111
Author(s):  
Li Li ◽  
◽  
Raquel Martínez ◽  

In order to overcome the problems of long analysis time, low accuracy and high energy consumption in traditional lateral vibration analysis methods of high-rise buildings, a new method of lateral vibration analysis of high-rise buildings based on partial differential equation is proposed. Based on Hamilton's principle, the partial differential equation of lateral vibration of high-rise buildings is established, and the Galerkin method is used to solve the partial differential equation until the discrete solution is obtained, and then the displacement response of high-rise buildings under different excitation frequencies is obtained. The experimental results show that compared with the traditional method, the proposed method has the advantages of short calculation time, high accuracy and low energy consumption.


2013 ◽  
Vol 210 ◽  
pp. 265-270 ◽  
Author(s):  
Anna Obrączka ◽  
Wojciech Mitkowski

In this paper the parameter identification methods for nonlinear models were compared for fractional, partial differential equation. The compared three methods are: the Levenberg-Marquardt algorithm, the Gauss-Newton algorithm and Nelder-Mead Simplex method. The series of numerical experiments were performed to test their robustness and calculation speed. The result of this tests were presented and described.


2016 ◽  
Vol 30 (28n29) ◽  
pp. 1640020 ◽  
Author(s):  
Mogtaba Mohammed ◽  
Mamadou Sango

This paper deals with the homogenization of a linear hyperbolic stochastic partial differential equation (SPDE) with highly oscillating periodic coefficients. We use Tartar’s method of oscillating test functions and deep probabilistic compactness results due to Prokhorov and Skorokhod. We show that the sequence of solutions of the original problem converges in suitable topologies to the solution of a homogenized linear hyperbolic SPDE with constant coefficients. We also prove the convergence of the associated energies.


2018 ◽  
Vol 24 (1) ◽  
pp. 55-70 ◽  
Author(s):  
Anthony Le Cavil ◽  
Nadia Oudjane ◽  
Francesco Russo

Abstract The paper is devoted to the construction of a probabilistic particle algorithm. This is related to a nonlinear forward Feynman–Kac-type equation, which represents the solution of a nonconservative semilinear parabolic partial differential equation (PDE). Illustrations of the efficiency of the algorithm are provided by numerical experiments.


1994 ◽  
Vol 50 (3) ◽  
pp. 425-433 ◽  
Author(s):  
T.R. Cranny

This article is a sequel to a paper in which a quasilinear partial differential equation with nonlinear boundary condition was approximated using mollifiers, and the existence of solutions to the approximating problem shown under quite general conditions. In this paper we show that standard a priori Hölder estimates ensure the convergence of these solutions to a classical solution of the original problem. Some partial results giving such estimates for special cases are described.


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