Nonlinear vibrations of buckled plates by an asymptotic numerical method

被引：7

作者：

Benchouaf, Lahcen ^{[1
]}

Boutyour, El Hassan ^{[1
]}

机构：

[1] Hassan 1st Univ, Fac Sci & Technol, Dept Appl Phys, POB 577, Settat, Morocco

来源：

COMPTES RENDUS MECANIQUE | 2016年 / 344卷 / 03期

关键词：

Nonlinear vibrations; Buckling; Von Karman plate; Asymptotic numerical method; Harmonic balance method; Finite-element method; THERMAL ENVIRONMENT; PADE APPROXIMANTS; BEAMS;

D O I：

10.1016/j.crme.2016.01.002

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

This work deals with nonlinear vibrations of a buckled von Karman plate by an asymptotic numerical method and harmonic balance approach. The coupled nonlinear static and dynamic problems are transformed into a sequence of linear ones solved by a finite element method. The static behavior of the plate is first computed. The fundamental frequency of nonlinear vibrations of the plate, about any equilibrium state, is obtained. To improve the validity range of the power series, Pade approximants are incorporated. A continuation technique is used to get the whole solution. To show the effectiveness of the proposed methodology, numerical tests are presented. (C) 2016 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

引用

页码：151 / 166

页数：16

共 26 条

[1] An exact solution for vibrations of postbuckled microscale beams based on the modified couple stress theory [J].

Ansari, R. ;

Ashrafi, M. A. ;

Arjangpay, A. .

APPLIED MATHEMATICAL MODELLING, 2015, 39 (10-11) :3050-3062

[2]

Azrar L, 2002, J SOUND VIB, V252, P657, DOI [10.1006/jsvi.2002.4049, 10.1006/jsvi.4049]

[3] An asymptotic-numerical method for large-amplitude free vibrations of thin elastic plates [J].

Azrar, L ;

Benamar, R ;

Potier-Ferry, M .

JOURNAL OF SOUND AND VIBRATION, 1999, 220 (04) :695-727

[4]

Batoz J.-L., 1990, Modelisation des structures par elements finis: Solides elastiques

[5]

Boutyour E.H., 1994, THESIS U METZ FRANCE

[6] Vibration of buckled elastic structures with large rotations by an asymptotic numerical method [J].

Boutyour, EH ;

Azrar, L ;

Potier-Ferry, M .

COMPUTERS & STRUCTURES, 2006, 84 (3-4) :93-101

[7] Bifurcation points and bifurcated branches by an asymptotic numerical method and Pade approximants [J].

Boutyour, EH ;

Zahrouni, H ;

Potier-Ferry, M ;

Boudi, M .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2004, 60 (12) :1987-2012

[8] A PATH-FOLLOWING TECHNIQUE VIA AN ASYMPTOTIC-NUMERICAL METHOD [J].

COCHELIN, B .

COMPUTERS & STRUCTURES, 1994, 53 (05) :1181-1192

[9] Power series analysis as a major breakthrough to improve the efficiency of Asymptotic Numerical Method in the vicinity of bifurcations [J].

Cochelin, Bruno ;

Medale, Marc .

JOURNAL OF COMPUTATIONAL PHYSICS, 2013, 236 :594-607

[10] A numerical continuation method based on Pade approximants [J].

Elhage-Hussein, A ;

Potier-Ferry, M ;

Damil, N .

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2000, 37 (46-47) :6981-7001

← 1 2 3 →