• Advances in nano research
• /
• v.16 no.2
• /
• pp.141-154
• /
• 2024

This study aims to develop explicit models to investigate thermo-mechanical interactions in moving nanobeams. These models aim to capture the small-scale effects that arise in continuous mechanical systems. Assumptions are made based on the Euler-Bernoulli beam concept and the fractional Zener beam-matter model. The viscoelastic material law can be formulated using the fractional Caputo derivative. The non-local Eringen model and the two-phase delayed heat transfer theory are also taken into account. By comparing the numerical results to those obtained using conventional heat transfer models, it becomes evident that non-localization, fractional derivatives and dual-phase delays influence the magnitude of thermally induced physical fields. The results validate the significant role of the damping coefficient in the system's stability, which is further dependent on the values of relaxation stiffness and fractional order.

• Coupled systems mechanics
• /
• v.4 no.4
• /
• pp.337-364
• /
• 2015

In this paper we present methodology for parameters identification of constitutive model which is able to present behavior of a connection between two members in a structure. Such a constitutive model for frame connections can be cast in the most general form of the Timoshenko beam, which can present three failure modes. The first failure mode pertains to the bending in connection, which is defined as coupled plasticity-damage model with nonlinear softening. The second failure mode is seeking to capture the shearing of connection, which is defined as plasticity with linear hardening and nonlinear softening. The third failure mode pertains to the diffuse failure in the members; excluding it leads to linear elastic constitutive law. Theoretical formulation of this Timoshenko beam model and its finite element implementation are presented in the second section. The parameter identification procedure that will allow us to define eighteen unknown parameters is given in Section 3. The proposed methodology splits identification in three phases, with all details presented in Section 4 through three different examples. We also present the real experimental results. The conclusions are stated in the last section of the paper.

• Structural Engineering and Mechanics
• /
• v.54 no.4
• /
• pp.693-710
• /
• 2015

This paper presents a nonlocal shear deformation beam theory for bending, buckling, and vibration of functionally graded (FG) nanobeams using the nonlocal differential constitutive relations of Eringen. The developed theory account for higher-order variation of transverse shear strain through the depth of the nanobeam, and satisfy the stress-free boundary conditions on the top and bottom surfaces of the nanobeam. A shear correction factor, therefore, is not required. In addition, this nonlocal nanobeam model incorporates the length scale parameter which can capture the small scale effect and it has strong similarities with Euler-Bernoulli beam model in some aspects such as equations of motion, boundary conditions, and stress resultant expressions. The material properties of the FG nanobeam are assumed to vary in the thickness direction. The equations of motion are derived from Hamilton's principle. Analytical solutions are presented for a simply supported FG nanobeam, and the obtained results compare well with those predicted by the nonlocal Timoshenko beam theory.

• Advances in nano research
• /
• v.4 no.1
• /
• pp.31-44
• /
• 2016

This article is concerned with the free vibration problem for chiral double-walled carbon nanotube (DWCNTs) modelled using the non-local elasticity theory and Euler Bernoulli beam model. According to the governing equations of non-local Euler Bernoulli beam theory and the boundary conditions, the analytical solution is derived and two branches of transverse wave propagating are obtained. The numerical results obtained provide better representations of the vibration behaviour of double-walled carbon nanotube, where the aspect ratio of the (DWCNTs), the vibrational mode number, the small-scale coefficient and chirality of double-walled carbon nanotube on the frequency ratio (${\chi}^N$) of the (DWCNTs) are significant. In this work, the numerical results obtained can be used to predict and prevent the phenomenon of resonance for the forced vibration analyses of double -walled carbon nanotubes.

• Steel and Composite Structures
• /
• v.36 no.3
• /
• pp.293-305
• /
• 2020

This article presented a nanoscale modified continuum model to investigate the free vibration of functionally graded (FG) porous nanobeam by using finite element method. The main novelty of this manuscript is presenting effects of four different porosity models on vibration behaviors of nonlocal nanobeam structure including size effect, that not be discussed before The proposed porosity models are, uniform porosity distribution, symmetric with mid-plane, bottom surface distribution and top surface distribution. The nano-scale effect is included in modified model by using the differential nonlocal continuum theory of Eringen that adding the length scale into the constitutive equations as a material parameter constant. The graded material is distributed through the beam thickness by a generalized power law function. The beam is simply supported, and it is assumed to be thin. Therefore, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Results demonstrate effects of porosity type, material gradation, and nanoscale parameters on the free vibration of nanobeam. The proposed model is effective in vibration analysis of NEMS structure manufactured by porous functionally graded materials.

• Smart Structures and Systems
• /
• v.16 no.6
• /
• pp.1107-1132
• /
• 2015

A damage detection algorithm based on neuro fuzzy hybrid system is presented in this study for location and severity predictions of cracks in beam-like structures. A combination of eigenfrequencies and rotation deviation curves are utilized as input to the soft computing technique. Both single and multiple damage cases are considered. Theoretical expressions leading to modal properties of damaged beam elements are provided. The beam formulation is based on Euler-Bernoulli theory. The cracked section of beam is simulated employing discrete spring model whose compliance is computed from stress intensity factors of fracture mechanics. A hybrid neuro fuzzy technique is utilized to solve the inverse problem of crack identification. Two different neuro fuzzy systems including grid partitioning (GP) and subtractive clustering (SC) are investigated for the highlighted problem. Several error metrics are utilized for evaluating the accuracy of the hybrid algorithms. The study is the first in terms of 1) using the two models of neuro fuzzy systems in crack detection and 2) considering multiple damages in beam elements employing the fused neuro fuzzy procedures. At the end of the study, the developed hybrid models are tested by utilizing the noise-contaminated data. Considering the robustness of the models, they can be employed as damage identification algorithms in health monitoring of beam-like structures.

• International Journal of Precision Engineering and Manufacturing
• /
• v.5 no.4
• /
• pp.50-60
• /
• 2004

A very flexible beam can be used to model various types of continuous mechanical parts such as cables and wires. In this paper, the dynamic properties of a very flexible beam, included in a multibody system, are analyzed using absolute nodal coordinates formulation, which is based on finite element procedures, and the general continuum mechanics theory to represent the elastic forces. In order to consider the dynamic interaction between a continuous large deformable beam and a rigid multibody system, a combined system equations of motion is derived by adopting absolute nodal coordinates and rigid body coordinates. Using the derived system equation, a computation method for the dynamic stress during flexible multibody simulation is presented based on Euler-Bernoulli beam theory, and its reliability is verified by a commercial program NASTRAN. This method is significant in that the structural and multibody dynamics models can be unified into one numerical system. In addition, to analyze a multibody system including a very flexible beam, formulations for the sliding joint between a very deformable beam and a rigid body are derived using a non-generalized coordinate, which has no inertia or forces associated with it. In particular, a very flexible catenary cable on which a multibody system moves along its length is presented as a numerical example.

• Advances in nano research
• /
• v.10 no.1
• /
• pp.15-24
• /
• 2021

Microtubules (MTs) are the main part of the cytoskeleton in living eukaryotic cells. In this article, a mechanical model of MT buckling, considering the modified strain gradient theory, is analytically examined. The MT is assumed as a cylindrical beam and a new single variable trigonometric beam theory is developed in conjunction with a modified strain gradient model. The main benefit of the present formulation is shown in its new kinematic where we found only one unknown as the Euler-Bernoulli beam model, which is even less than the Timoshenko beam model. The governing equations are deduced by considering virtual work principle. The effectiveness of the present method is checked by comparing the obtained results with those reported by other higher shear deformation beam theory involving a higher number of unknowns. It is shown that microstructure-dependent response is more important when material length scale parameters are closer to the outer diameter of MTs. Also, it can be confirmed that influences of shear deformation become more considerable for smaller shear modulus and aspect ratios.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2011.04a
• /
• pp.631-634
• /
• 2011

본 연구에서는 규칙 파랑 중에 있는 부유식 구조물의 유탄성 거동을 해석 하고, 수치모델의 수렴성을 살펴본다. 부유식 구조물은 보로 모델링 하며, 유체는 이상유체로 가정하여 문제를 해결한다. 보 모델의 경우 Euler-Bernoulli 보 모델과 Timoshenko 보 모델로 나누어 그 특성을 비교 해 본다. 문제의 해석법에 있어서 부유식 구조물의 경우는 유한요소법을, 유체의 경우는 경계요소법을 이용하여, 상호 연성된 방정식을 이끌어 낸다. 상호 연성된 방정식을 토대로 Euler-Bernoulli 보 모델과 Timoshenko 보 모델의 거동 특성을 살펴보고 제시된 수치 모델을 기준으로 수렴성을 분석해 본다.

• Structural Engineering and Mechanics
• /
• v.46 no.3
• /
• pp.417-431
• /
• 2013

This paper presents responses of the free end of a cantilever micro beam under the effect of an impact force based on the modified couple stress theory. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. The Kelvin-Voigt model for the material of the beam is used. The considered problem is investigated within the Bernoulli-Euler beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange's equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. In the study, the difference of the modified couple stress theory and the classical beam theory is investigated for the wave propagation. A few of the obtained results are compared with the previously published results. The influences of the material length scale parameter on the wave propagation are investigated in detail. It is clearly seen from the results that the classical beam theory based on the modified couple stress theory must be used instead of the classical theory for small values of beam height.