The second strain gradient theory-based Timoshenko beam model

2015 ◽  
Vol 23 (13) ◽  
pp. 2155-2166 ◽  
Author(s):  
M Asghari ◽  
SA Momeni ◽  
R Vatankhah
Keyword(s):  
Timoshenko Beam ◽  
Strain Gradient ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Beam Model ◽  
Timoshenko Beam Model

Size-dependent dynamic modeling of inhomogeneous curved nanobeams embedded in elastic medium based on nonlocal strain gradient theory

2016 ◽  
Vol 231 (23) ◽  
pp. 4457-4469 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad R Barati
Keyword(s):  
Stress Field ◽  
Elastic Medium ◽  
Strain Gradient ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Beam Model ◽  
Simply Supported ◽  
Size Dependent ◽  
Nonlocal Strain Gradient

In this paper, size-dependent free vibration analysis of curved functionally graded nanobeams embedded in Winkler–Pasternak elastic medium is carried out via an analytical solution method. Three kinds of boundary condition namely, simply supported-simply supported, simply supported-clamped and clamped-clamped are investigated. Material properties of curved functionally graded beam change in thickness direction according to the Mori–Tanaka model. Nonlocal strain gradient elasticity theory is adopted to capture the size effects in which the stress is considered for not only the nonlocal stress field but also the strain gradients stress field. Nonlocal governing equations of curved functionally graded nanobeam are obtained from Hamilton’s principle based on Euler–Bernoulli beam model. Finally, the influences of length scale parameter, nonlocal parameter, opening angle, elastic medium, material composition, slenderness ratio and boundary conditions on the vibrational characteristics of nanosize curved functionally graded beams are explored.

scholarly journals Free Vibration Analysis of Triclinic Nanobeams Based on the Differential Quadrature Method

2019 ◽  
Vol 9 (17) ◽  
pp. 3517 ◽  
Author(s):  
Behrouz Karami ◽  
Maziar Janghorban ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Strain Gradient ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Differential Quadrature ◽  
Vibration Response ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Beam Model

In this work, the nonlocal strain gradient theory is applied to study the free vibration response of a Timoshenko beam made of triclinic material. The governing equations of the problem and the associated boundary conditions are obtained by means of the Hamiltonian principle, whereby the generalized differential quadrature (GDQ) method is implemented as numerical tool to solve the eigenvalue problem in a discrete form. Different combinations of boundary conditions are also considered, which include simply-supports, clamped supports and free edges. Starting with some pioneering works from the literature about isotropic nanobeams, a convergence analysis is first performed, and the accuracy of the proposed size-dependent anisotropic beam model is checked. A large parametric investigation studies the effect of the nonlocal, geometry, and strain gradient parameters, together with the boundary conditions, on the vibration response of the anisotropic nanobeams, as useful for practical engineering applications.

scholarly journals Stability analysis of nanobeams in hygrothermal environment based on a nonlocal strain gradient Timoshenko beam model under nonlinear thermal field

2020 ◽  
Vol 7 (6) ◽  
pp. 685-699 ◽  
Author(s):  
Subrat Kumar Jena ◽  
S Chakraverty ◽  
Mohammad Malikan
Keyword(s):  
Stress Field ◽  
Elasticity Theory ◽  
Timoshenko Beam ◽  
Strain Gradient ◽  
Scale Parameter ◽  
Thermal Environment ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Buckling Loads ◽  
Nonlocal Strain Gradient

Abstract This article is dedicated to analyzing the buckling behavior of nanobeam subjected to hygrothermal environments based on the principle of the Timoshenko beam theory. The hygroscopic environment has been considered as a linear stress field model, while the thermal environment is assumed to be a nonlinear stress field based on the Murnaghan model. The size-dependent effect of the nanobeam is captured by the nonlocal strain gradient theory (NSGT), and the governing equations of the proposed model have been derived by implementing a variational principle. The critical buckling loads have been calculated for the hinged–hinged boundary condition by incorporating the Navier approach and considering other elasticity theories such as classical elasticity theory, Eringen nonlocal elasticity theory, and strain gradient theory along with the NSGT. The present model is also validated with the pre-existing model in exceptional cases. Further, a parametric investigation has been performed to report the influence of various scaling parameters like hygroscopic environment, thermal environment, length-to-diameter ratio, small scale parameter, and length scale parameter on critical buckling loads by considering both the linear and nonlinear temperature distributions.

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