scholarly journals Corrigendum to: Nonlinear free vibration of size-dependent microbeams with nonlinear elasticity under various boundary conditions

2021 ◽  
Vol 37 ◽  
pp. 466-466
Author(s):  
F Lin ◽  
J S Peng ◽  
S F Xue ◽  
L Yang ◽  
J Yang
2021 ◽  
Vol 37 ◽  
pp. 380-403
Author(s):  
F Lin ◽  
J S Peng ◽  
S F Xue ◽  
L Yang ◽  
J Yang

Abstract In this study, nonlinear couple stress–strain constitutive relationships in the modified couple stress theory (MCST) are derived on the basis of previous classical stress–strain constitutive relationships of nonlinear elasticity materials. Hamilton's principle is employed to obtain higher-order nonlinear governing equations within the framework of the updated MCST, von Kármán geometric nonlinearity and Bernoulli–Euler beam theory. These mathematical formulations are solved numerically by the differential quadrature method together with an iterative algorithm to determine the nonlinear dynamic features of microbeams with four groups of boundary conditions. A detailed parametric study is conducted to analyze the influences of nonlinear elasticity properties on the nonlinear free vibration characteristics of the microbeams. Results show that these microbeams exhibiting nonlinear couple constitutive relationships have lower frequencies than their approximately simplified linear couple constitutive relationships. In addition, the frequencies of microbeams with nonlinear elasticity properties decrease as the vibration amplitude increases.


2014 ◽  
Vol 84 (12) ◽  
pp. 1691-1700 ◽  
Author(s):  
Benyamin Gholami Bazehhour ◽  
Seyed Mahmoud Mousavi ◽  
Anoushiravan Farshidianfar

2001 ◽  
Vol 01 (01) ◽  
pp. 125-144 ◽  
Author(s):  
HUAN ZENG ◽  
CHARLES W. BERT

Stiffened skew plates find application in various engineering fields. The free vibration characteristics of such plates have been studied by various methods. An orthogonally stiffened skew plate is a skew plate with stiffeners running orthogonal to two opposite edges. To the best knowledge of the present investigators, no previous work has been done for free vibration characteristics of skew plates of such stiffening geometry. The present work studies the free vibration of such plates. The pb-2 Rayleigh–Ritz method was employed due to its accuracy and computational efficiency. The conventional finite element method was also used as a comparative check. A convergence study was first performed for various boundary conditions. Then the vibration of orthogonally stiffened skew plates with different boundary conditions was studied. Close agreement was found between these two methods. The variations of natural frequencies with different parameters, including skew angle ϕ, edge ratio b/a, and height-thickness ratio f/h, were investigated for three types of boundary conditions.


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