Modified couple stress theory applied to dynamic analysis of composite laminated beams by considering different beam theories

Mohammadabadi, Mostafa; Daneshmehr, Alireza

doi:10.1016/j.ijengsci.2014.11.003

Cited by 65 publications

(15 citation statements)

References 37 publications

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“…In addition, λ and μ denote the two Lame constants, ℓ is the material length scale parameter, and δij is the Kronecker delta. Moreover, components of the displacement and rotation vectors are defined by u and θ, respectively, where the rotation vector is related to the displacement vector as 31,32 …”

Section: Preliminariesmentioning

confidence: 99%

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

Mohandes

Ghasemi

2016

Proceedings of the Institution of Mechanical Engineers, Part C:

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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 L ¼ 10h. 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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Section: Preliminariesmentioning

confidence: 99%

“…Substituting equation (32) into equations (27) and (28) and using the dimensionless parameters, the dimensionless form of the equation of motion and boundary conditions based on the finite strain are obtained as follows…”

Section: Static Bendingmentioning

confidence: 99%

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

Mohandes

Ghasemi

2016

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…The boundary value problem of simply supported beam and cantilever beam were solved, and size effect on natural frequencies of beams was studied. Mohammad-Abadi et al [25] analyzed free vibration of composite laminated beams using the modified couple stress theory. The governing equation and boundary condition were obtained by applying Hamilton's principle.…”

Section: Introductionmentioning

confidence: 99%

Analytic solution for size-dependent behaviors of micro-beam under forced vibration

Wang¹,

Wang²,

Wang³

et al. 2020

Mech. Eng. Sci.

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This paper focuses on the size-dependently mechanical behaviors of a micro-beam under forced vibration. Governing equations of a micro-beam under forced vibration are established by using the modified couple stress theory, Bernoulli-Euler beam theory and D’Alembert’s principle together. A simply supported micro-beam under forced vibration is solved according to the established governing equations and the method of separation of variables. The dimensionless deflection, amplitude mode and period mode are defined to investigate the size-dependently mechanical behaviors of a micro-beam under forced vibration. Results show that the performance of a micro-beams under forced vibration is distinctly size-dependent when the ratio of micro-beam height to material length-scale parameter is small enough. Both frequency ratio and loading location are the important factors that determine the size-dependent performance of a micro-beams under forced vibration.

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“…Currently, the generalized beam theory is considered as one of the most complete theories, which has been developed to account for both warping and distortion with shear deformation [9] and transverse extension included, being also applied to multi-cell closed crosssections [10] and composite materials [11]. A comparable theory is the method of Generalized Eigenvectors [12], whose modes are obtained through a cross-section discretization using two-dimensional elements.…”

Section: Introductionmentioning

confidence: 99%

A new approach to the identification of distortion modes of thin-walled structures based on plate/shell theory

Zhang

Zhu

et al. 2019

MATEC Web Conf.

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In this paper, a new approach to identify cross-section deformation modes is presented and utilized in the establishment of a high-order beam model for dynamic analyses of thin-walled structures. Towards this end, a systematic procedure to extract cross-section in-plane vibration shapes for a thin-walled cross-section is developed based on elastic plate/shell theory. Then the distortion shapes are separated from vibration shapes by removing the components of classic modes involved with the minimum value problem of 2-norm. Sequentially, curve fitting method is utilized to approximate the distortion shape functions along the cross-section midline. It should be noticed that these distortion modes are arranged in hierarchy consistent with the order that they are identified and the number of distortions to be identified depends on the required model precision. Based on this, Hamilton's principle is applied to formulate the dynamic governing equations of the beam by constructing its displacement field with the linear superposition of the cross-section mode shapes including distortions. Numerical examples are also presented to validate the new approach and to demonstrate its efficiency in the reproduction of three-dimensional behaviours of thin-walled structures in dynamic analyses.

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Modified couple stress theory applied to dynamic analysis of composite laminated beams by considering different beam theories

Cited by 65 publications

References 37 publications

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

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

Analytic solution for size-dependent behaviors of micro-beam under forced vibration

A new approach to the identification of distortion modes of thin-walled structures based on plate/shell theory

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