scispace - formally typeset
Search or ask a question

Showing papers on "Timoshenko beam theory published in 2020"


Journal ArticleDOI
TL;DR: The theory introduces two parameters based on nonlocal elasticity theory and modified couple stress theory to capture the size effects much accurately and involves both stiffness-softening and stiffness-hardening effects on responses of FG nanobeams.
Abstract: This research develops a nonlocal couple stress theory to investigate static stability and free vibration characteristics of functionally graded (FG) nanobeams. The theory introduces two parameters based on nonlocal elasticity theory and modified couple stress theory to capture the size effects much accurately. Therefore, a nonlocal stress field parameter and a material length scale parameter are used to involve both stiffness-softening and stiffness-hardening effects on responses of FG nanobeams. The FG nanobeam is modeled via a higher order refined beam theory in which shear deformation effect is verified needless of shear correction factor. A power-law distribution is used to describe the graded material properties. The governing equations and the related boundary conditions are derived by Hamilton’s principle and they are solved applying Chebyshev–Ritz method which satisfies various boundary conditions. A comparison study is performed to verify the present formulation with the provided data in the literature and a good agreement is observed. The parametric study covered in this paper includes several parameters such as nonlocal and length scale parameters, power-law exponent, slenderness ratio, shear deformation and various boundary conditions on natural frequencies and buckling loads of FG nanobeams in detail.

147 citations


Journal ArticleDOI
TL;DR: In this paper, the dynamic and stability analysis of the simply supported single walled carbon nanotubes (SWCNT) reinforced concrete beam on elastic-foundation using an integral first-order shear deformation beam theory is presented.
Abstract: This paper, presents the dynamic and stability analysis of the simply supported single walled Carbon Nanotubes (SWCNT) reinforced concrete beam on elastic-foundation using an integral first-order shear deformation beam theory The condition of the zero shear-stress on the free surfaces of the beam is ensured by the introduction of the shear correction factors The SWCNT reinforcement is considered to be uniform and variable according to the X, O and V forms through the thickness of the concrete beam The effective properties of the reinforced concrete beam are calculated by employing the rule of mixture The analytical solutions of the buckling and free vibrational behaviors are derived via Hamilton\'s principle and Navier method The analytical results of the critical buckling loads and frequency parameters of the SWCNT-RC beam are presented in the form of explicit tables and graphs Also the diverse parameters influencing the dynamic and stability behaviors of the reinforced concrete beam are discussed in detail

113 citations


DOI
01 May 2020
TL;DR: In this article, the free vibrational behavior of the FG nano-beams integrated in the hygro-thermal environment and reposed on the elastic foundation is investigated using a novel integral Timoshenko beam theory (ITBT).
Abstract: In the current research, the free vibrational behavior of the FG nano-beams integrated in the hygro-thermal environment and reposed on the elastic foundation is investigated using a novel integral Timoshenko beam theory (ITBT). The current model has only three variables unknown and requires the introduction of the shear correction factor because her uniformed variation of the shear stress through the thickness. The effective properties of the nano-beam vary according to power-law and symmetric sigmoid distributions. Three models of the hygro-thermal loading are employed. The effect of the small scale effect is considered by using the nonlocal theory of Eringen. The equations of motion of the present model are determined and resolved via Hamilton principle and Navier method, respectively. Several numerical results are presented thereafter to illustrate the accuracy and efficiency of the actual integral Timoshenko beam theory. The effects of the various parameters influencing the vibrational responses of the P-FG and SS-FG nano-beam are also examined and discussed in detail.

97 citations


Journal ArticleDOI
TL;DR: In this paper, a novel nonlinear vibration isolator in the shape of a circular ring is investigated, which exhibits highly nonlinear geometric stiffness due to the effects of stretching-induced tension coupled with the curvature changes.

94 citations


Journal ArticleDOI
TL;DR: In this paper, the free vibration of non-uniform nano-size beams in thermal environment was studied using nonlocal strain gradient theory within a Timoshenko beam model, and the governing equations as well as boundary conditions were obtained according to a variational approach, which is solved numerically using the generalized differential quadrature method.
Abstract: In this contribution, we study the free vibration of non-uniform nano-size beams in thermal environment. In order to capture the size-dependent effects, we adopt nonlocal strain gradient theory within a Timoshenko beam model. The nanobeam is made of functionally graded materials, which properties are both temperature and porosity dependent and vary continuously along the length and thickness directions. The governing equations as well as boundary conditions are obtained according to a variational approach, which is solved numerically using the generalized differential quadrature method. We compute the natural frequencies and analyze the sensitivity of the vibration response for different non-uniformity, power indices along x and z-directions, porosity coefficients, small-scaling parameters, thermal effect, and geometry conditions. We also study the influence of various boundary conditions including simply-supported, clamped or a combination of them. We find for all boundaries that an increasing nonlocal (strain gradient) parameter leads to decreasing (increasing) natural frequencies.

79 citations


Journal ArticleDOI
TL;DR: In this paper, different homogenization schemes are employed to analyze both size-dependent postbuckling and nonlinear bending behavior of micro/nano-beams, made of a bi-directional functionally graded material (BDFGM), under external axial compression and distributed load.

74 citations


Journal ArticleDOI
TL;DR: In this paper, the flexure performances of pultruded glass FRP (P-GFRP) composite beams were investigated experimentally and theoretically with the help of variational methods.

67 citations


Journal ArticleDOI
TL;DR: In this paper, the nonlinear free vibration of edge-cracked graphene nanoplatelet (GPL)-reinforced composite laminated beams resting on a two-parameter elastic foundation in thermal environments is investigated.

66 citations


Journal ArticleDOI
TL;DR: In this article, the static and free vibration responses of functionally graded (FG) porous plates with graphene platelets (GPLs) reinforcement using an efficient polygonal finite element method (PFEM).
Abstract: In this study, we numerically investigate static and free vibration responses of functionally graded (FG) porous plates with graphene platelets (GPLs) reinforcement using an efficient polygonal finite element method (PFEM). While the bending strain field is approximated through quadratic serendipity shape functions, the shear strain field is calculated by employing Wachspress basis functions. In order to eliminate the shear locking phenomenon, Timoshenko's beam theory is utilized to determine assumed strain fields on each side of polygonal domain. The present formulation possesses various outstanding features: (a) is valid for triangular, quadrilateral and polygonal elements; (b) can conveniently implement various different plate theories via choosing appropriate transverse shear function; (c) eliminates the shear locking phenomenon; (d) does not increase degrees of freedom (DOFs) per polygonal element despite employing the quadratic serendipity shape functions and (e) obtains more accurate and stable results than those of other PFEMs. Various dispersions of internal pores as well as GPLs into metal matrix through the thickness of plate are examined. The effective material properties varying across the plate's thickness can be estimated by Halpin-Tsai model for Young's modulus and the rule of a mixture for Poisson's ratio and mass density. The effect of several important parameters such as porosity coefficient, weight fraction and dimensions of GPLs, distribution of porosity and GPLs into metal matrix are thoroughly investigated via various numerical examples.

63 citations


Journal ArticleDOI
TL;DR: In this article, size-dependent static bending analysis of functionally graded (FG) curved nanobeams based on the Timoshenko beam theory is performed with the application of a stress-driven nonlocal integral model.

62 citations


Journal ArticleDOI
TL;DR: It is proved that, also when shear deformation effects are of relevance, the enriched, yet simple, model and numerical computation scheme herein proposed can be profitably used for efficient structural analyses of non-linear mechanical systems in rather nonstandard situations.
Abstract: Among the most studied models in mathematical physics, Timoshenko beam is outstanding for its importance in technological applications. Therefore it has been extensively studied and many discretizations have been proposed to allow its use in the most disparate contexts. However, it seems to us that available discretization schemes present some drawbacks when considering large deformation regimes. We believe these drawbacks to be mainly related to the fact that they are formulated without keeping in mind the mechanical phenomena for describing which Timoshenko continuum model has been proposed. Therefore, aiming to analyze the deformation of complex plane frames and arches in elastic large displacements and deformation regimes, a novel intrinsically discrete Lagrangian model is here introduced whose phenomenological application range is similar to that for which Timoshenko beam has been conceived. While being largely inspired by the ideas outlined by Hencky in his renowned doctoral dissertation, the presented approach overcomes some specific limitations concerning the stretch and shear deformation effects. The proposed model is applied to get the solutions for some relevant benchmark tests, both in the case of arch and frame structures. It is proved that, also when shear deformation effects are of relevance, the enriched, yet simple, model and numerical computation scheme herein proposed can be profitably used for efficient structural analyses of non-linear mechanical systems in rather nonstandard situations.

Journal ArticleDOI
TL;DR: It is established that the beam theory that incorporates both the rotary inertia and shear deformation as is known presently, with shear correction factor included, should be referred to as the Timoshenko-Ehrenfest beam theory.
Abstract: The use of the Google Scholar produces about 78,000 hits on the term “Timoshenko beam.” The question of priority is of great importance for this celebrated theory. For the first time in the world l...

Journal ArticleDOI
TL;DR: In this paper, the effect of porosity distributions on the mechanics of nanostructures is investigated based on the higher-order nonlocal strain gradient theory, where the displacements gradients are assumed to be small so that the components of the Green-Lagrange strain tensor are linear and infinitesimal.

Journal ArticleDOI
TL;DR: In this paper, a non-local model for free vibration and thermal buckling analysis of rotating temperature-dependent functionally graded (FG) nanobeams in thermal environment is developed by introducing an axial nonlinear second-order coupling deformation based upon the Eringen's nonlocal elasticity theory (ENET) and Euler-Bernoulli beam theory (EBT).

Journal ArticleDOI
TL;DR: In this paper, the nonlinear flexural behavior of auxetic laminated beams with each layer is made of carbon nanotube-reinforced composites (CNTRCs), where the functional grading occurs in the thickness direction of the beam in the piece-wise pattern.

Journal ArticleDOI
TL;DR: In this article, the authors proposed a modal analysis approach to obtain analytical expressions for the edge frequencies of the created bandgaps, where the lattice constant of the resulting metastructure is much smaller than the operating flexural wavelength of the host beam.

Journal ArticleDOI
Ismail Esen1
TL;DR: In this article, the stiffness and mass property matrices of small-scale size-dependant two-node finite element are obtained by using new shape functions derived from the static state of motion equations created using classical Timoshenko beam theory and modified couple stress theory.

Journal ArticleDOI
TL;DR: In this paper, a generalized bond-based micropolar peridynamic model is proposed to simulate the nonlinear deformation and mixed-mode crack propagation of quasi-brittle materials under arbitrary dynamic loads.

Journal ArticleDOI
TL;DR: In this article, a new model was developed for transversely isotropic magneto-electro-elastic Timoshenko beams by using a variational formulation based on Hamilton's principle.

Journal ArticleDOI
TL;DR: In this article, the flutter vibrations of fluid-conveying thin-walled nanotubes subjected to magnetic field are investigated and the size-dependent governing equations and associated boundary conditions are derived based on the extended Hamilton's principle.

Journal ArticleDOI
TL;DR: In this paper, a granular system with a specific grain-pair interaction has been designed and its mechanical behavior under different types of loading has been evaluated via numerical simulations using COMSOL multiphysics.

Journal ArticleDOI
TL;DR: In this article, a beam model consisting of a novel shape function for the distribution of shear stress deformation in the transverse coordinate was proposed, and the beam theory also incorporated the stretching effect to present an indirect effect of thickness variations.

Journal ArticleDOI
TL;DR: In this article, the nonlinear free and forced vibrations of fluid-conveying pipes that are made of porous functionally graded materials and supported on a nonlinear elastic foundation were investigated analytically, by employing the variational iteration method and the direct method of multiple scales.

Journal ArticleDOI
TL;DR: In this paper, a new refined beam theory, namely one variable first-order shear deformation theory, has been employed to study the vibration and buckling characteristics of nonlocal beam.
Abstract: In this article, a new refined beam theory, namely one variable first-order shear deformation theory, has been employed to study the vibration and buckling characteristics of nonlocal beam. The beam is exposed to an axial magnetic field and embedded in Winkler–Pasternak foundation. The von Karman hypothesis along with Hamilton’s principle has been implemented to derive the governing equations for both the vibration and buckling studies, and closed-form solutions are obtained for simply supported beam using the Navier’s approach. Further, a parametric study has been conducted to explore the impacts of small-scale parameter, Winkler modulus, shear modulus and magnetic field intensity on natural frequencies and critical buckling loads.

Journal ArticleDOI
TL;DR: In this paper, the effects of material properties, nonlocal parameter, Lorentz and electric forces on maximum static deflections and natural frequencies of actuated hybrid carbon/boron-nitride nanotubes (CBNNT) subjected to thermal loads are studied for the first time.

Journal ArticleDOI
TL;DR: In this paper, a 3D compression-torsion cubic mechanical metamaterial (CTCMM) with double inclined rods is proposed to convert axial compression into a torsion.

Journal ArticleDOI
TL;DR: In this article, the bending, buckling and free vibration analysis of functionally graded (FG) sandwich microbeams using the third-order beam theory was studied, and the modified strain gradient theory (MSGT) with three material length scale parameters (MLSPs) was used to capture the size effect.

Journal ArticleDOI
TL;DR: Simulation results show that the proposed control method successfully stabilizes the uncertain system in a finite time.
Abstract: This article is concerned with suppression of nonlinear forced vibration of a single-wall carbon nanotube conveying fluid based on the nonlocal elasticity theory and Euler–Bernoulli beam theory. El...

Journal ArticleDOI
TL;DR: In this article, the static bending response of a functionally graded polymer composite (FG-PC) curved beam reinforced with carbon nanotubes (CNTs) subjected to sinusoidal and uniform loads is analyzed.
Abstract: This article deals with the static bending response of a functionally graded polymer composite (FG-PC) curved beam reinforced with carbon nanotubes (CNTs) subjected to sinusoidal and uniform loads. The effective material properties of beam are approximated according to modified rule of mixture. Four types of CNT distribution are also considered. Assuming Timoshenko beam theory and a higher-order strain gradient theory, size-dependent equilibrium equations are extracted. Using Navier solution procedure, nonlocal strain gradient governing equations are solved for simply-supported edges. Ultimately, numerical results are expanded to show the influence of weight fraction and distribution patterns of CNTs, small scale parameters, and opening angle on the static bending response of CNTs reinforced nanocomposite curved beam.

Journal ArticleDOI
TL;DR: In this paper, the size-dependent buckling instability of shear deformable nanobeams rested on a two-parameter elastic foundation is studied through the stress-driven nonlocal theory of elasticity and the kinematic assumptions of the Timoshenko beam theory.