The self-excited vibrations of an axially retracting cantilever beam using the Galerkin method with fitted polynomial basis functions

2018 ◽  
Vol 32 (1) ◽  
pp. 29-36 ◽  
Author(s):  
Hongliang Hua ◽  
Zhenqiang Liao ◽  
Xiangyan Zhang
Keyword(s):  
Galerkin Method ◽  
Cantilever Beam ◽  
Basis Functions ◽  
The Self ◽  
Polynomial Basis ◽  
The Galerkin Method

scholarly journals Convergence of approximate solution of mixed Hammerstein type integral equations

2018 ◽  
Vol 38 (2) ◽  
pp. 61-74
Author(s):  
Monireh Nosrati Sahlan
Keyword(s):  
Galerkin Method ◽  
Integral Equations ◽  
Basis Functions ◽  
Computational Method ◽  
Operational Matrices ◽  
B Spline ◽  
Spline Wavelets ◽  
Type Integral ◽  
The Galerkin Method ◽  
Dual Functions

In the present paper, a computational method for solving nonlinear Volterra-Fredholm Hammerestein integral equations is proposed by using compactly supported semiorthogonal cubic B-spline wavelets as basis functions. Dual functions and Operational matrices of B-spline wavelets via Galerkin method are utilized to reduce the computation of integral equations to some algebraic system, where in the Galerkin method dual of B-spline wavelets are applied as weighting functions. The method is computationally attractive, and applications are demonstrated through illustrative examples.

scholarly journals Fast convergence of the Coiflet-Galerkin method for general elliptic BVPs

2013 ◽  
Vol 23 (1) ◽  
pp. 17-27 ◽  
Author(s):  
Hani Akbari
Keyword(s):  
Galerkin Method ◽  
Basis Functions ◽  
Fast Convergence ◽  
Effective Evaluation ◽  
General Elliptic ◽  
Fast Convergence Rate ◽  
Low Levels ◽  
The Galerkin Method ◽  
Robin Boundary ◽  
Structured Approach

We consider a general elliptic Robin boundary value problem. Using orthogonal Coifman wavelets (Coiflets) as basis functions in the Galerkin method, we prove that the rate of convergence of an approximate solution to the exact one is O(2 −nN ) in the H1 norm, where n is the level of approximation and N is the Coiflet degree. The Galerkin method needs to evaluate a lot of complicated integrals. We present a structured approach for fast and effective evaluation of these integrals via trivariate connection coefficients. Due to the fast convergence rate, very good approximations are found at low levels and with low Coiflet degrees, hence the size of corresponding linear systems is small. Numerical experiments confirm these claims.

scholarly journals Development of a parallel algorithm based on an implicit scheme for the discontinuous Galerkin method for solving diffusion type equations

2020 ◽  
Vol 22 (1) ◽  
pp. 94-106
Author(s):  
Ruslan V. Zhalnin ◽  
Nikita A. Kuzmin ◽  
Victor F. Masyagin
Keyword(s):  
Galerkin Method ◽  
Parallel Algorithm ◽  
Numerical Study ◽  
Sparse Matrices ◽  
Parabolic Type ◽  
Implicit Scheme ◽  
Basis Functions ◽  
Parabolic Problems ◽  
Diffusion Type ◽  
The Galerkin Method

The paper presents a numerical parallel algorithm based on an implicit scheme for the Galerkin method with discontinuous basis functions for solving diffusion-type equations on triangular grids. To apply the Galerkin method with discontinuous basis functions, the initial equation of parabolic type is transformed to a system of partial differential equations of the first order. To do this, auxiliary variables are introduced, which are the components of the gradient of the desired function. To store sparse matrices and vectors, the CSR format is used in this study. The resulting system is solved numerically using a parallel algorithm based on the Nvidia AmgX library. A numerical study is carried out on the example of solving two-dimensional test parabolic initial-boundary value problems. The presented numerical results show the effectiveness of the proposed algorithm for solving parabolic problems.

Dynamics of a Cantilever Beam With Attached Pendulum

2001 ◽  
Author(s):  
Danuta Sado
Keyword(s):  
Differential Equations ◽  
Galerkin Method ◽  
Cantilever Beam ◽  
Weakly Nonlinear ◽  
Second Mode ◽  
Linear Viscoelastic ◽  
Nonlinear Pendulum ◽  
Analysis Of Dynamics ◽  
The Galerkin Method ◽  
Euler Bernoulli Beam

Abstract This work draws attention to the to the analysis of dynamics of a nonlinear coupled cantilever beam-pendulum oscillator. Dynamical systems of this type have important technical applications, because many mechanical components consist of linear or weakly nonlinear continuos substructures such as beam coupled to nonlinear oscillators. The present paper is a continuation of the author’s previous work where in applying the Galerkin method the modal series was truncated at the first mode. In this work it is assumed that the cantilever beam behaves like an Euler-Bernoulli beam and to its end pendulum is attached. The integro-differential equations are transformed into an ordinary differential equations with the use of Galerkin procedure with beam functions. In this study, in applying the Galerkin method the modal series was truncated at the second mode. Next these equations were solved numerically and there was studied the effect of the internal friction on energy transfer in a coupled structure that consist of a linear viscoelastic beam supporting at its tip a nonlinear pendulum.

The Fundamental Flexural Vibration of a Cantilever Beam of Rectangular Cross Section with Uniform Taper

1965 ◽  
Vol 16 (2) ◽  
pp. 139-144 ◽  
Author(s):  
J. S. Rao
Keyword(s):  
Galerkin Method ◽  
Natural Frequency ◽  
Cantilever Beam ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Flexural Vibration ◽  
The Other ◽  
Correction Factors ◽  
Flexural Mode ◽  
The Galerkin Method

SummaryAn attempt has been made to determine the natural frequency of fundamental flexural mode of a cantilever beam with uniform taper by the Galerkin method. The method suggested considerably reduces the calculations as compared with the other methods available and the results are checked with the correction factors derived by Martin.

Sign in / Sign up

Export Citation Format

Share Document