Novel differential quadrature element method for vibration analysis of hybrid nonlocal Euler-Bernoulli beams

被引：37

作者：

Wang, Xinwei ^{[1
]}

机构：

[1] Nanjing Univ Aeronaut & Astronaut, State Key Lab Mech & Control Mech Struct, Nanjing 210016, Jiangsu, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2018年 / 77卷

关键词：

Differential quadrature element method; Multiple boundary conditions; Hybrid nonlocal Euler-Bernoulli beam; Free vibration; ELASTIC MATRIX;

D O I：

10.1016/j.aml.2017.10.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A novel differential quadrature element method is presented for free vibration analysis of hybrid nonlocal Euler-Bernoulli beams with any combination of boundary conditions. Explicit formulas of computing the weighting coefficients of various derivatives are derived. Sixth-order differential equations are successfully solved by using the proposed method. Accurate frequencies are obtained and presented. The proposed method can be also used for accurate solutions of various sixth-order differential equations and beam structures with minimum computational effort. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：94 / 100

页数：7

共 14 条

[1] Recent Researches on Nonlocal Elasticity Theory in the Vibration of Carbon Nanotubes Using Beam Models: A Review [J].

Behera, L. ;

Chakraverty, S. .

ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING, 2017, 24 (03) :481-494

[2] A numerical comparison of seven grids for polynomial interpolation on the interval [J].

Boyd, JP .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1999, 38 (3-4) :35-50

[3] On the DQ analysis of geometrically non-linear vibration of immovably simply-supported beams [J].

Chen, W ;

Zhong, TX ;

Liang, SP .

JOURNAL OF SOUND AND VIBRATION, 1997, 206 (05) :745-748

[4] A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method [J].

Civalek, Omer ;

Demir, Cigdem .

APPLIED MATHEMATICS AND COMPUTATION, 2016, 289 :335-352

[5] A new nonlocal FEM via Hermitian cubic shape functions for thermal vibration of nano beams surrounded by an elastic matrix [J].

Demir, Cigdem ;

Civalek, Omer .

COMPOSITE STRUCTURES, 2017, 168 :872-884

[6] FREE VIBRATION ANALYSIS OF CARBON NANOTUBES BASED ON SHEAR DEFORMABLE BEAM THEORY BY DISCRETE SINGULAR CONVOLUTION TECHNIQUE [J].

Demir, Cigdem ;

Civalek, Omer ;

Akgoz, Bekir .

MATHEMATICAL & COMPUTATIONAL APPLICATIONS, 2010, 15 (01) :57-65

[7] Novel weak form quadrature element method with expanded Chebyshev nodes [J].

Jin, Chunhua ;

Wang, Xinwei ;

Ge, Luyao .

APPLIED MATHEMATICS LETTERS, 2014, 34 :51-59

[8] A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation [J].

Lim, C. W. ;

Zhang, G. ;

Reddy, J. N. .

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 2015, 78 :298-313

[9] Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey [J].

Tornabene, Francesco ;

Fantuzzi, Nicholas ;

Ubertini, Francesco ;

Viola, Erasmo .

APPLIED MECHANICS REVIEWS, 2015, 67 (02)

[10]

Wang X., 2015, Differential Quadrature and Differential Quadrature Based Element Meth- ods: Theory and Applications

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