On the computer simulation of the forced vibration characteristics of the microtubes using a couple of von-Kármán and modified couple stress theories

2021 ◽  
pp. 1-22
Author(s):  
Jingchao Liu ◽  
Lin Xu ◽  
Li Bai ◽  
Na Yang
Keyword(s):  
Computer Simulation ◽  
Forced Vibration ◽  
Couple Stress ◽  
Vibration Characteristics ◽  
Von Karman ◽  
Modified Couple Stress ◽  
Von Kármán

A Variant of the Classical Von Kármán Flow for a Couple Stress Fluid

2012 ◽  
Vol 29 (8) ◽  
pp. 084704 ◽  
Author(s):  
A. A. Farooq ◽  
A. M. Siddiqui ◽  
M. A. Rana ◽  
T. Haroon
Keyword(s):  
Couple Stress ◽  
Couple Stress Fluid ◽  
Von Karman ◽  
Von Kármán

scholarly journals Nonlinear Vibration Analysis of Axially Functionally Graded Microbeams Based on Nonlinear Elastic Foundation Using Modified Couple Stress Theory

2020 ◽  
Vol 64 (2) ◽  
pp. 97-108
Author(s):  
Mehdi Alimoradzadeh ◽  
Mehdi Salehi ◽  
Sattar Mohammadi Esfarjani
Keyword(s):  
Differential Equation ◽  
Forced Vibration ◽  
Couple Stress ◽  
Scale Parameter ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Length Scale ◽  
Stress Theory ◽  
Modified Couple Stress

In this study, a non-classical approach was developed to analyze nonlinear free and forced vibration of an Axially Functionally Graded (AFG) microbeam by means of modified couple stress theory. The beam is considered as Euler-Bernoulli type supported on a three-layered elastic foundation with Von-Karman geometric nonlinearity. Small size effects included in the analysis by considering the length scale parameter. It is assumed that the mass density and elasticity modulus varies continuously in the axial direction according to the power law form. Hamilton's principle was implemented to derive the nonlinear governing partial differential equation concerning associated boundary conditions. The nonlinear partial differential equation was reduced to some nonlinear ordinary differential equations via Galerkin's discretization technique. He's Variational iteration methods were implemented to obtain approximate analytical expressions for the frequency response as well as the forced vibration response of the microbeam with doubly-clamped end conditions. In this study, some factors influencing the forced vibration response were investigated. Specifically, the influence of the length scale parameter, the length of the microbeam, the power index, the Winkler parameter, the Pasternak parameter, and the nonlinear parameter on the nonlinear natural frequency as well as the amplitude of forced response have been investigated.

Modified couple stress theory and finite strain assumption for nonlinear free vibration and bending of micro/nanolaminated composite Euler–Bernoulli beam under thermal loading

2016 ◽  
Vol 231 (21) ◽  
pp. 4044-4056 ◽  
Author(s):  
Masood Mohandes ◽  
Ahmad Reza Ghasemi
Keyword(s):  
Free Vibration ◽  
Thermal Loading ◽  
Finite Strain ◽  
Natural Frequencies ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Von Karman ◽  
Modified Couple Stress ◽  
Von Kármán

In this paper, the effect of finite strain on the nonlinear free vibration and bending of the symmetrically micro/nanolaminated composite beam under thermal environment within the framework of the Euler–Bernoulli and modified couple stress theory is studied. The governing equation of motion and boundary conditions are obtained using Hamilton’s principle, and then they are solved by generalized differential quadrature method. The bending and free vibration of the beam are investigated for both carbon/epoxy and glass/epoxy materials based on the finite strain and von Karman assumptions subjected to different boundary conditions. Also, two different fiber orientations including unidirectional and cross-ply are considered in this research. Comparison of the bending results show that there is a significant difference between the finite strain and von Karman particularly for [Formula: see text]. Furthermore, it is found that the natural frequencies predicted by the finite strain are more than the von Karman. Also, when the microbeam is inserted under thermal loading, the natural frequencies increase.

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