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Volume 8, Number 4, May 2020

A study that primarily focuses on nonlocal strain gradient plate model for the sole purpose of vibration examination, for graphene sheets under linearly variable in-plane mechanical loads. To study a better or more precise examination on graphene sheets, a new advance model was conducted which carries two scale parameters that happen to be related to the nonlocal as well as the strain gradient influences. Through the usage of two-variable shear deformation plate approach, that does not require the inclusion of shear correction factors, the graphene sheet is designed. Based on Hamilton's principle, fundamental expressions in regard to a nonlocal strain gradient graphene sheet on elastic half-space is originated. A Galerkin's technique is applied to resolve the fundamental expressions for distinct boundary conditions. Influence of distinct factors which can be in-plane loading, length scale parameter, load factor, elastic foundation, boundary conditions, and nonlocal parameter on vibration properties of the graphene sheets then undergo investigation.

Key Words
graphene sheets; free vibration; in-plane bending; nonlocal strain gradient; refined plate theory

(1) Ali Shariati:
Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, 758307, Vietnam;
(2) Ali Shariati:
Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, 758307, Vietnam;
(3) Mohammad Reza Barati, Farzad Ebrahimi:
Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran;
(4) Abhinav Singhal:
Department of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle, Andhra Pradesh, 517325, India;
(5) Ali Toghroli:
Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam.

Axially damped forced vibration responses of viscoelastic nanorods are investigated within the frame of the modal analysis. The nonlocal elasticity theory is used in the constitutive relation of the nanorod with the Kelvin-Voigt viscoelastic model. In the forced vibration problem, a cantilever nanorod subjected to a harmonic load at the free end of the nanorod is considered in the numerical examples. By using the modal technique, the modal expressions of the viscoelastic nanorods are presented and solved exactly in the nonlocal elasticity theory. In the numerical results, the effects of the nonlocal parameter, damping coefficient, geometry and dynamic load parameters on the dynamic responses of the viscoelastic nanobem are presented and discussed. In addition, the difference between the nonlocal theory and classical theory is investigated for the damped forced vibration problem.

Key Words
nanorods; nonlocal elasticity theory; damped forced vibration; modal analysis

Department of Civil Engineering, Bursa Technical University, Yıldırım Campus, Yıldırım, Bursa 16330, Turkey.

In the present research, differential quadrature (DQ) method has been utilized for investigating free vibrations of porous functionally graded (FG) micro/nano beams in thermal environments. The exact location of neutral axis in FG material has been assumed where the material properties are described via porosity-dependent power-law functions. A scale factor related to couple stresses has been employed for describing size effect. The formulation of scale-dependent beam has been presented based upon a refined beam theory needless of shear correction factors. The governing equations and the associated boundary conditions have been established via Hamilton's rule and then they are solved implementing DQ method. Several graphs are provided which emphasis on the role of porosity dispersion type, porosity volume, temperature variation, scale factor and FG material index on free vibrational behavior of small scale beams.

Key Words
free vibrations; thermal effects; porosity; FG beam; modified couple stress theory

Al-Mustansiriah University, Engineering Collage P.O. Box 46049, Bab-Muadum, Baghdad 10001, Iraq.

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.

Key Words
FG nano-beam; vibrational behavior; Integral Timoshenko beam theory; hygro-thermal effect

(1) Hakima Matouk, Abdelmoumen Anis Bousahla, Houari Heireche, Abdelouahed Tounsi, S.R. Mahmoud, Abdeldjebbar Tounsi:
Laboratoire de Modélisation et Simulation Multi-échelle, Départment de Physique, Faculté des Sciences Exactes, Université de Sidi Bel Abbés, Algeria;
(2) Abdelmoumen Anis Bousahla:
Centre Universitaire de Relizane, Algérie;
(3) Abdelmoumen Anis Bousahla, E.A. Adda Bedia, Abdelouahed Tounsi:
Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia;
(4) Fouad Bourada, Abdelouahed Tounsi, K.H. Benrahou:
Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria;
(5) Fouad Bourada:
Département des Sciences et de la Technologie, centre universitaire de Tissemsilt, BP 38004 Ben Hamouda, Algeria;
(6) S.R. Mahmoud:
GRC Department, Jeddah Community College, King Abdulaziz University, Jeddah, Saudi Arabia.

In this article, free vibration of double-walled carbon nanotubes (DWNT) based on nonlocal Kelvin\'s model have been investigated. For this purpose, a nonlocal Kelvin\'s model is established to observe the small scale effect. The wave propagation is employed to frame the governing equations as eigenvalue system. The influence of nonlocal parameter subjected to different end supports has been overtly examined. The new set of inner and outer tubes radii investigated in detail against aspect ratio. The influence of boundary conditions via nonlocal parameter is shown graphically. Due to small scale effect fundamental frequency ratio decreases as length to diameter ratio increases. Small scale effect becomes negligible on all end supports for the higher values of aspect ratio. With the smaller inner tube radius double-walled CNT behaves more sensitive towards nonlocal parameter. The results generated furnish the evidence regarding applicability of nonlocal model and also verified by earlier published literature.

Key Words
free vibration; nonlocal material; double-walled CNTs; Kelvin\'s model; WPA

(1) Muzamal Hussain, Muhammad N. Naeem, Sehar Asghar:
Department of Mathematics, Government College University Faisalabad, 38000, Faisalabad, Pakistan;
(2) Abdelouahed Tounsi:
Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Algeria Faculty of Technology Civil Engineering Department, Algeria;
(3) Abdelouahed Tounsi:
Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia.

In recent years, there has been an upsurge for the usage of buckling restrained braces (BRB) rather than ordinary braces, as they have evidently performed better. If the overall brace buckling is ignored, BRBs are proven to have higher energy absorption capacity and flexibility. This article aims to deliberate an economically efficient yet adequate type of all-steel BRB, comprised of the main components as in traditional ones, such as : (1) a steel core that holds all axial forces and (2) a steel restrainer tube that hinders buckling to occurr in the core; there is a more practical detailing in the BRB system due to the elimination of a filling mortar. An investigation has been conducted for the proposed rectangular-tube core BRB and it is hysteric behavioral results have been compared to previous researches conducted on a structure containing a similar plate core profile that has the same cross-sectional area in its core. A loss of strength is known to occur in the BRB when the limiting condition of local buckling is not satisfied, thus causing instability. This typically occurs when the thickness of the restrainer tube

Key Words
buckling restrained braces; hysteretic response; tubular profile; seismic performance

(1) Yan Cao:
School of Mechatronic Engineering, Xi\'an Technological University, Xi\'an, 710021, China;
(2) Sadaf Mahmoudi Azar:
Department of Civil Engineering, Faculty of Engineering, University of Malaya, Malaysia;
(3) S.N.R. Shah:
Department of Civil Engineering, Mehran University of Engineering and Technology, SZAB Campus, Pakistan;
(4) Ahmed Fathi Mohamed Salih:
Civil Engineering Department, College of Engineering, University of Bisha, Bisha 67714, Saudi Arabia;
(5) Ahmed Fathi Mohamed Salih:
Civil Engineering Department, College of Engineering, University of Bahri, Khartoum, Sudan;
(6) Tiana Thiagi:
Sunway Group Education Malaysia, Malaysia;
(7) Kittisak Jermsittiparsert:
Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam;
(8) Kittisak Jermsittiparsert:
Faculty of Social Sciences and Humanities, Ton Duc Thang University, Ho Chi Minh City, Vietnam;
(9) Lanh Si Ho:
Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam.

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