The thermal effect on nonlinear oscillations of carbon nanotubes with arbitrary boundary conditions

2011 ◽  
Vol 11 (3) ◽  
pp. 692-697 ◽  
Author(s):  
R. Ansari ◽  
M. Hemmatnezhad ◽  
J. Rezapour
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Thermal Effect ◽  
Nonlinear Oscillations ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions

An efficient solution method for the longitudinal vibration of nanorods with arbitrary boundary conditions via a hardening nonlocal approach

2016 ◽  
Vol 24 (11) ◽  
pp. 2230-2246 ◽  
Author(s):  
Mustafa Özgür Yayli
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Longitudinal Vibration ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Dynamical Analysis ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Fourier Sine Series ◽  
Nonlocal Approach

The free longitudinal vibration analysis of nanorods (carbon nanotubes) with arbitrary boundaries is presented via a hardening nonlocal approach. Stokes’ transformation incorporated with Fourier sine series is employed for the simulation of nanorod deformation. The Fourier coefficients for nanorods having ends with axial restraints are obtained by the substitution of a deformation function and its derivatives into the governing equation. The explicit expressions are derived for the angular frequencies by using nonlocal boundary conditions in terms of nondimensional parameters. A detailed parametric investigation has been carried out to study the effects of the nonlocal and spring parameters on the size-dependent vibration characteristics of the nanorods. The main objective of this study is to present a general analytical approach for the dynamical analysis of nanorods (carbon nanotubes) with arbitrary boundary conditions (restrained or rigid).

scholarly journals A Unified Spectro-Geometric-Ritz Method for Vibration Analysis of Open and Closed Shells with Arbitrary Boundary Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-30 ◽  
Author(s):  
Dongyan Shi ◽  
Yunke Zhao ◽  
Qingshan Wang ◽  
Xiaoyan Teng ◽  
Fuzhen Pang
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Analysis Model ◽  
Arbitrary Boundary ◽  
Fourier Cosine ◽  
Auxiliary Functions ◽  
Arbitrary Boundary Conditions ◽  
Closed Shells

This paper presents free vibration analysis of open and closed shells with arbitrary boundary conditions using a spectro-geometric-Ritz method. In this method, regardless of the boundary conditions, each of the displacement components of open and closed shells is represented simultaneously as a standard Fourier cosine series and several auxiliary functions. The auxiliary functions are introduced to accelerate the convergence of the series expansion and eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries. The boundary conditions are modeled using the spring stiffness technique. All the expansion coefficients are treated equally and independently as the generalized coordinates and determined using Rayleigh-Ritz method. By using this method, a unified vibration analysis model for the open and closed shells with arbitrary boundary conditions can be established without the need of changing either the equations of motion or the expression of the displacement components. The reliability and accuracy of the proposed method are validated with the FEM results and those from the literature.

Free vibration analysis of three-layer thin cylindrical shell with variable thickness two-dimensional FGM middle layer under arbitrary boundary conditions

2021 ◽  
pp. 109963622110204
Author(s):  
Xue-Yang Miao ◽  
Chao-Feng Li ◽  
Yu-Lin Jiang ◽  
Zi-Xuan Zhang
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Volume Fraction ◽  
Ritz Method ◽  
Admissible Function ◽  
Free Vibration Analysis ◽  
Middle Layer ◽  
Two Dimensional ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions

In this paper, a unified method is developed to analyze free vibrations of the three-layer functionally graded cylindrical shell with non-uniform thickness. The middle layer is composed of two-dimensional functionally gradient materials (2D-FGMs), whose thickness is set as a function of smooth continuity. Four sets of artificial springs are assigned at the ends of the shells to satisfy the arbitrary boundary conditions. The Sanders’ shell theory is used to obtain the strain and curvature-displacement relations. Furthermore, the Chebyshev polynomials are selected as the admissible function to improve computational efficiency, and the equation of motion is derived by the Rayleigh–Ritz method. The effects of spring stiffness, volume fraction indexes, configuration on of shell, and the change in thickness of the middle layer on the modal characteristics of the new structural shell are also analyzed.

scholarly journals Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Huimin Liu ◽  
Fanming Liu ◽  
Xin Jing ◽  
Zhenpeng Wang ◽  
Linlin Xia
Keyword(s):  
Boundary Conditions ◽  
Admissible Function ◽  
Three Dimensional ◽  
Future Research ◽  
Pasternak Foundation ◽  
Arbitrary Boundary ◽  
Thick Plates ◽  
Arbitrary Boundary Conditions ◽  
Ritz Procedure ◽  
Three Dimensional Elasticity

This paper presents the first known vibration characteristic of rectangular thick plates on Pasternak foundation with arbitrary boundary conditions on the basis of the three-dimensional elasticity theory. The arbitrary boundary conditions are obtained by laying out three types of linear springs on all edges. The modified Fourier series are chosen as the basis functions of the admissible function of the thick plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges. The exact solution is obtained based on the Rayleigh–Ritz procedure by the energy functions of the thick plate. The excellent accuracy and reliability of current solutions are demonstrated by numerical examples and comparisons with the results available in the literature. In addition, the influence of the foundation coefficients as well as the boundary restraint parameters is also analyzed, which can serve as the benchmark data for the future research technique.

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