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CONTENTS
Volume 69, Number 2, January10 2019
 

Abstract
The present study investigates the propagation of shear waves in a composite structure comprised of imperfectly bonded piezoelectric layer with a micropolar half space. Piezoelectric layer is considered to be initially stressed. Micropolar theory of elasticity has been employed which is most suitable to explain the size effects on small length scale. The general dispersion equations for the existence of waves in the coupled structure are obtained analytically in the closed form. Some particular cases have been discussed and in one particular case the dispersion relation is in well agreement to the classical-Love wave equation. The effects of various parameters viz. initial stress, interfacial imperfection and micropolarity on the phase velocity are obtained for electrically open and mechanically free system. Numerical computations are carried out and results are depicted graphically to illustrate the utility of the problem. The phase velocity of the shear waves is found to be influenced by initial stress, interface imperfection and the presence of micropolarity in the elastic half space. The theoretical results obtained are useful for the design of high performance surface acoustic devices.

Key Words
shear wave; micropolar; piezoelectric; dispersion; phase velocity

Address
Rajneesh Kumar: Department of Mathematics, Kurukshetra University, Kurukshetra, India
Kulwinder Singh: Department of Mathematics, Lovely Professional University, Phagwara, India (I.K. Gujral Punjab Technical University, Jalandhar, India)
D.S. Pathania: Department of Mathematics, GNDEC, Ludhiana, India

Abstract
In this study, the nonlinear vibration analysis of the composite nanoplate is studied. The composite nanoplate is fabricated by the functional graded (FG) core and lipid face sheets. The material properties in the FG core vary in three directions. The Kelvin-Voigt model is used to study the viscoelastic effect of the lipid layers. By using the Von-Karman assumptions, the nonlinear differential equation of the vibration analysis of the composite nanoplate is obtained. The foundation of the system is modeled by the nonlinear Pasternak foundation. The Bubnov-Galerkin method and the multiple scale method are used to solve the nonlinear differential equation of the composite nanoplate. The free and force vibration analysis of the composite nanoplate are studied. A comparison between the presented results and the reported results is done and good achievement is obtained. The reported results are verified by the results which are obtained by the Runge-Kutta method. The effects of different parameters on the nonlinear vibration frequencies, the primary, the super harmonic and subharmonic resonance cases are investigated. This work will be useful to design the nanosensors with high biocompatibility.

Key Words
three dimensional FG; nonlinear vibration frequency; lipid layers; composite nanoplate

Address
M. Mohammadi and A. Rastgoo: School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

Abstract
Modified couple stress formulation and first order shear deformation theory are used for magneto-electro-elastic bending analysis of three-layered curved size-dependent beam subjected to mechanical, magnetic and electrical loads. The governing equations are derived using a displacement field including radial and transverse displacements of middle surface and a rotation component. Size dependency is accounted based on modified couple stress theory by employing a small scale parameter. The numerical results are presented to study the influence of small scale parameter, initial electric and magnetic potentials and opening angle on the magneto-electro-elastic bending results of curved micro beam.

Key Words
modified couple stress; initial electric and magnetic potentials; bending results; radial and transverse displacements

Address
M. Arefi: Department of Solid Mechanic, Faculty of Mechanical Engineering, University of Kashan, Kashan 87317-51167, Iran

Abstract
It is very common to find an empirical formulation in an earthquake design code to calculate fundamental vibration period of a structural system. Fundamental vibration period or frequency is a key parameter to provide adequate information pertinent to dynamic characteristics and performance assessment of a structure. This parameter enables to assess seismic demand of a structure. It is possible to find an empirical formulation related to reinforced concrete structures, masonry towers and slender masonry structures. Calculated natural vibration frequencies suggested by empirical formulation in the literatures has not suits in a high accuracy to the case of rest of the historical masonry bridges due to different construction techniques and wide variety of material properties. For the listed reasons, estimation of fundamental frequency gets harder. This paper aims to present an empirical formulation through Mean Square Error study to find ambient vibration frequency of historical masonry bridges by using a non-linear regression model. For this purpose, a series of data collected from literature especially focused on the finite element models of historical masonry bridges modelled in a full scale to get first global natural frequency, unit weight and elasticity modulus of used dominant material based on homogenization approach, length, height and width of the masonry bridge and main span length were considered to predict natural vibration frequency. An empirical formulation is proposed with 81% accuracy. Also, this study draw attention that this accuracy decreases to 35%, if the modulus of elasticity and unit weight are ignored.

Key Words
empirical formulation; fundamental frequency; finite element method; historical masonry bridges

Address
Onur Onat: Department of Civil Engineering, Munzur Univeristy, 62000 Aktuluk Campus, Tunceli, Turkey

Abstract
Structural deterioration arises due to aging, environmental effects, deficiencies during design and construction phase, and overloading. Experimental and numerical investigations are carried out in this study to evaluate the performance of control and flexural deficient reinforced concrete (RC) beams under monotonic loading. Three levels of flexural deficiency are considered in this study. After confirming load carrying capacities of control and flexural deficient beams, the flexural deficient RC beams are strengthened with carbon fibre reinforced polymer (CFRP) fabric. CFRP strengthened RC beams are tested under monotonic loading and compared with the performance of control specimen. Further, non-linear finite element analyses are also carried out to evaluate the flexural performance of control, deficient and CFRP strengthened flexural deficient RC beams. There is good correlation between results of experimental and numerical investigations. Numerical approach presented in this study can be adopted for assessing the adequacy of CFRP retrofit measure.

Key Words
flexural deficient; monotonic loading; CFRP strengthening; experimental investigation; numerical simulation

Address
Nawal Kishor Banjara and K. Ramanjaneyulu:
1) Academy of Scientific and Innovative Research, CSIR Campus, Taramani, Chennai-600113, India
2) CSIR-Structural Engineering Research Centre, CSIR Campus, Taramani, Chennai-600113, India

Abstract
The local topography has a significant effect on the characteristics of seismic ground motion. This paper investigates the influence of topographic effects on the seismic response of a train-bridge system. A 3-D finite element model with local absorbing boundary conditions is established for the local site. The time histories of seismic ground motion are converted into equivalent loads on the artificial boundary, to obtain the seismic input at the bridge supports. The analysis of the train-bridge system subjected to multi-support seismic excitations is performed, by applying the displacement time histories of the seismic ground motion to the bridge supports. In a case study considering a bridge with a span of 466 m crossing a valley, the seismic response of the train-bridge system is analyzed. The results show that the local topography and the incident angle of seismic waves have a significant effect on the seismic response of the train-bridge system. Leaving these effects out of consideration may lead to unsafe analysis results.

Key Words
train-bridge system; seismic analysis; topographic effect; viscous-spring artificial boundary; incident angle; azimuth

Address
Hong Qiao:
1) School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture,
15 Yongyuan Rd, Beijing 102616, China
2) School of Civil Engineering, Beijing Jiaotong University, Shangyuancun No.3, Beijing 100044, China
3) Department of Civil Engineering, KU Leuven, Kasteelpark Arenberg 40, Leuven B-3001, Belgium
Xianting Du and He Xia: School of Civil Engineering, Beijing Jiaotong University, Shangyuancun No.3, Beijing 100044, China
Guido De Roeck and Geert Lombaert: Department of Civil Engineering, KU Leuven, Kasteelpark Arenberg 40, Leuven B-3001, Belgium
Peiheng Long: School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, 15 Yongyuan Rd, Beijing 102616, China

Abstract
This paper presents results from experimental and numerical studies on the response of steel-concrete composite box bridge girders under certain localized fire exposure conditions. Two composite box bridge girders, a simply supported girder and a continuous girder respectively, were tested under simultaneous loading and fire exposure. The simply supported girder was exposed to fire over 40% of its span length in the middle zone, and the two-span continuous girder was exposed to fire over 38% of its length of the first span and full length of the second span. A measurement method based on comparative rate of deflection was provided to predict the failure time in the hogging moment zone of continuous composite box bridge girders under certain localized fire exposure condition. Parameters including transverse and longitudinal stiffeners and fire scenarios were introduced to investigate fire resistance of the composite box bridge girders. Test results show that failure of the simply supported girder is governed by the deflection limit state, whereas failure of the continuous girder occurs through bending buckling of the web and bottom slab in the hogging moment zone. Deflection based criterion may not be reliable in evaluating failure of continuous composite box bridge girder under certain fire exposure condition. The fire resistance (failure time) of the continuous girder is higher than that of the simply supported girder. Data from fire tests is successfully utilized to validate a finite element based numerical model for further investigating the response of composite box bridge girders exposed to localized fire. Results from numerical analysis show that fire resistance of composite box bridge girders can be highly influenced by the spacing of longitudinal stiffeners and fire severity. The continuous composite box bridge girder with closer longitudinal stiffeners has better fire resistance than the simply composite box bridge girder. It is concluded that the fire resistance of continuous composite box bridge girders can be significantly enhanced by preventing the hogging moment zone from exposure to fire. Longitudinal stiffeners with closer spacing can enhance fire resistance of composite box bridge girders. The increase of transverse stiffeners has no significant effect on fire resistance of composite box bridge girders.

Key Words
bridge fires; fire resistance; steel-concrete composite box girders; fire tests; finite element analysis; bridge girders

Address
Gang Zhang: School of Highway, Chang\'an University, Xi\'an, Shaanxi 710064, China
Venkatesh Kodur: Department of Civil and Environmental Engineering, Michigan State University, East Lansing, MI 48864, USA
Weifa Yao and Qiao Huang: School of Transportation, Southeast University, Nanjing, JiangSu 210096, China

Abstract
This paper analyzes nonlinear free vibration of the circular nano-tubes made of functionally graded materials in the framework of nonlocal strain gradient theory in conjunction with a refined higher order shear deformation beam model. The effective material properties of the tube related to the change of temperature are assumed to vary along the radius of tube based on the power law. The refined beam model is introduced which not only contains transverse shear deformation but also satisfies the stress boundary conditions where shear stress cancels each other out on the inner and outer surfaces. Moreover, it can degenerate the Euler beam model, the Timoshenko beam model and the Reddy beam model. By incorporating this model with Hamilton\'s principle, the nonlinear vibration equations are established. The equations, including a material length scale parameter as well as a nonlocal parameter, can describe the size-dependent in linear and nonlinear vibration of FGM nanotubes. Analytical solution is obtained by using a two-steps perturbation method. Several comparisons are performed to validate the present analysis. Eventually, the effects of various physical parameters on nonlinear and linear natural frequencies of FGM nanotubes are analyzed, such as inner radius, temperature, nonlocal parameter, strain gradient parameter, scale parameter ratio, slenderness ratio, volume indexes, different beam models.

Key Words
functionally graded material; nonlinear vibration; nonlocal strain gradient theory; nanotubes

Address
Yang Gao and Wan-Shen Xiao:
1) State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China
2) College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China
Haiping Zhu: School of Computing, Engineering and Mathematics, Western Sydney University, Locked, Bag 1797, Penrith, NSW 2751, Australia

Abstract
In this paper, shear behavior of non-persistent joint surrounded in concrete and gypsum layers has been investigated using experimental test and numerical simulation. Two types of mixture were prepared for this study. The first type consists of water and gypsum that were mixed with a ratio of water/gypsum of 0.6. The second type of mixture, water, sand and cement were mixed with a ratio of 27%, 33% and 40% by weight. Shear behavior of a non-persistent joint embedded in these specimens is studied. Physical models consisting of two edge concrete layers with dimensions of 160 mm by 130 mm by 60 mm and one internal gypsum layer with the dimension of 16 mm by 13 mm by 6 mm were made. Two horizontal edge joints were embedded in concrete beams and one angled joint was created in gypsum layer. Several analyses with joints with angles of 0o, 30o, and 60o degree were conducted. The central fault places in 3 different positions. Along the edge joints, 1.5 cm vertically far from the edge joint face and 3 cm vertically far from the edge joint face. All samples were tested in compression using a universal loading machine and the shear load was induced because of the specimen geometry. Concurrent with the experiments, the extended finite element method (XFEM) was employed to analyze the fracture processes occurring in a non-persistent joint embedded in concrete and gypsum layers using Abaqus, a finite element software platform. The failure pattern of non-persistent cracks (faults) was found to be affected mostly by the central crack and its configuration and the shear strength was found to be related to the failure pattern. Comparison between experimental and corresponding numerical results showed a great agreement. XFEM was found as a capable tool for investigating the fracturing mechanism of rock specimens with non-persistent joint.

Key Words
non-persistent joints; uniaxial test; shear behaviour; experimental and numerical approaches

Address
Hadi Haeri and Zheming Zhu: MOE Key Laboratory of Deep Underground Science and Engineering, School of Architecture and Environment, Sichuan University, Chengdu 610065, China
V. Sarfarazi: Department of Mining Engineering, Hamedan University of Technology, Hamedan Iran
N. Nohekhan Hokmabadi and MR. Moshrefifar: Geology Department, Yazd University, Yazd, Iran
A. Hedayat: Department of Civil and Environmental Engineering, Colorado School of Mines, Golden, CO 8040, USA

Abstract
In this paper, a new higher order shear deformation model is developed for static and free vibration analysis of functionally graded beams with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. Different patterns of porosity distributions (including even and uneven distribution patterns, and the logarithmic-uneven pattern) are considered. In addition, the effect of different micromechanical models on the bending and free vibration response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams whose properties vary continuously across the thickness according to a simple power law. Based on the present higher-order shear deformation model, the equations of motion are derived from Hamilton\'s principle. Navier type solution method was used to obtain displacement, stresses and frequencies, and the numerical results are compared with those available in the literature. A comprehensive parametric study is carried out to assess the effects of volume fraction index, porosity fraction index, micromechanical models, mode numbers, and geometry on the bending and natural frequencies of imperfect FG beams.

Key Words
functionally graded materials; bending; free vibration; micromechanical models; porosity

Address
Lazreg Hadji:
1) Laboratory of Geomatics and Sustainable Development, Ibn Khaldoun University of Tiaret, Algeria
2) Department of Civil Engineering, Ibn Khaldoun University, BP 78 Zaaroura, 14000 Tiaret, Algeria
Nafissa Zouatnia:
1) Department of Civil Engineering, Laboratory of Structures, Geotechnics and Risks (LSGR), Hassiba Benbouali University of Chlef, BP 151, Hay Essalam, UHB Chlef, Chlef (02000), Algeria
2) Department of Civil Engineering, Ibn Khaldoun University, BP 78 Zaaroura, 14000 Tiaret, Algeria
Fabrice Bernard: University of Rennes, INSA Rennes, Laboratory of Civil Engineering and Mechanical Engineering, France


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