• Structural Engineering and Mechanics
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• 제64권5호
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• pp.611-620
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• 2017

A new theory of weightless sagging planer elasto-flexible cables under point loads is developed earlier by the authors and used for predicting the nonlinear dynamic response of cable-suspended linear elastic beams. However, this theory is not valid for nonlinear elastic cracked concrete beams possessing different positive and negative flexural rigidity. In the present paper, the flexural response of simply supported cracked concrete beams suspended from cables by two hangers is presented. Following a procedure established earlier, rate-type constitutive equations and third order nonlinear differential equations of motion for the structures undergoing small elastic displacements are derived. Upon general quasi-static loading, negative nodal forces, moments and support reactions may be introduced in the cable-suspended concrete beams and linear modal frequencies may abruptly change. Subharmonic resonances are predicted under harmonic loading. Uncoupling of the nodal response is proposed as a more general criterion of crossover phenomenon. Significance of the bilinearity ratio of the concrete beam and elasto-configurational displacements of the cable for the structural response is brought out. The relevance of the proposed theory for the analysis and the design of the cable-suspended bridges is critically evaluated.

• Structural Engineering and Mechanics
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• 제51권1호
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• pp.111-130
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• 2014

The aim of this study is to investigate the effects of the beam aspect ratio(L/h), hole diameter, hole location and stacking layer sequence ($[0/45/-45/90]_s$, $[45/0/-45/90]_s$ and $[90/45/-45/0]_s$) on natural frequencies of glass/epoxy perforated beams under room and high (40, 60, 80, and $100^{\circ}C$) temperatures for the common clamped-free boundary conditions (cantilever beam). The first three out of plane bending free vibration of symmetric laminated beams is studied by Timoshenko's first order shear deformation theory. For the numerical analyses, ANSYS 13.0 software package is utilized. The results show that the hole diameter, stacking layer sequence and hole location have important effect especially on the second and third mode natural frequency values for the short beams and the high temperatures affects the natural frequency values significantly. The results are presented in tabular and graphical form.

• Steel and Composite Structures
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• 제48권4호
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• pp.419-428
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• 2023

In this paper, dynamic and static bending of ball modelled by nanocomposite microbeam by nanoparticles seeing agglomeration is presented. The structural damping is considered by Kelvin-Voigt model. The agglomeration effects are assumed using Mori-Tanaka model. The football ball is modeled by third order shear deformation theory (TSDT). The motion equations are derived by principle of Hamilton's and energy method assuming size effects on the basis of Eringen theory. Using differential quadrature method (DQM) and Newmark method, the static and dynamic deflections of the structure are obtained. The effects of agglomeration and CNTs volume percent, damping of structure, nonlocal parameter, length and thickness of micro-beam are presented on the static and dynamic deflections of the nanocomposite structure. Results show that with increasing CNTs volume percent, the maximum dimensionless dynamic deflection is reduced about 17%. In addition, assuming CNTs agglomeration increases the dimensionless dynamic deflection about 14%. It is also found that with increasing the CNTs volume percent from 0 to 0.15, the static deflection is decreased about 3 times due to the enhance in the stiffness of the structure. In addition, with enhancing the nonlocal parameters, the dynamic deflection is increased about 3.1 times.

• Structural Engineering and Mechanics
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• 제87권6호
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• pp.529-540
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• 2023

A novel laminated-hybrid-composite-beam (LHCB) of glass-epoxy infused with flyash and graphene is constructed for this study. The conventional mixture-rule and constitutive-relationship are modified to incorporate filler and lamina orientation. Eringen's non-local-theory is used to include the filler effect. Hamilton's principle based on fifth-order-layer-wise-shear-deformation-theory is applied to formulate the equation of motion. The analogous shear-spring-models for LHCB with multiple-cracks are employed in finite-element-analysis (FEA). Modal-experimentations are conducted (B&K-analyser) and the findings are compared with theoretical and FEA results. In terms of dimensionless relative-natural-frequencies (RNF), the dynamic-response in cantilevered support is investigated for various relative-crack-severities (RCSs) and relative-crack-positions (RCPs). The increase of RCS increases local-flexibility in LHCB thus reductions in RNFs are observed. RCP is found to play an important role, cracks present near the end-support cause an abrupt drop in RNFs. Further, multiple cracks are observed to enhance the nonlinearity of LHCB strength. Introduction of the first to third crack in an intact LHCB results drop of RNFs by 8%, 10%, and 11.5% correspondingly. Also, it is demonstrated that the RNF varies because of the lamina-orientation, and filler addition. For 0° lamina-orientation the RNF is maximum. Similarly, it is studied that the addition of graphene reduces weight and increases the stiffness of LHCB in contrast to the addition of flyash. Additionally, the response of LHCB to moving mass is accessed by appropriately modifying the numerical programs, and it is noted that the successive introduction of the first to ninth crack results in an approximately 40% to 120% increase in the dynamic-amplitude-ratio.

• Structural Engineering and Mechanics
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• 제30권6호
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• pp.733-761
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• 2008

The failure of reinforced concrete structures in recent earthquakes caused concern about the performance of beam column joints. Confinement of joint is one of the ways to improve the performance of beam column joints during earthquakes. This paper describes an experimental study of exterior beam-column joints with two non-conventional reinforcement arrangements. One exterior beam-column joint of a six story building in seismic zone III of India was designed for earthquake loading. The transverse reinforcement of the joint assemblages were detailed as per IS 13920:1993 and IS 456:2000 respectively. The proposed nonconventional reinforcement was provided in the form of diagonal reinforcement on the faces of the joint, as a replacement of stirrups in the joint region for joints detailed as per IS 13920 and as additional reinforcement for joints detailed as per IS 456. These newly proposed detailing have the basic advantage of reducing the reinforcement congestion at the joint region. In order to study and compare the performance of joint with different detailing, four types of one-third scale specimens were cast (two numbers in each type). The main objective of the present study is to investigate the effectiveness of the proposed reinforcement detailing. All the specimens were tested under reverse cyclic loading, with appropriate axial load. From the test results, it was found that the beam-column joint having confining reinforcement as per IS: 456 with nonconventional detailing performed well. Test results indicate that the non-conventionally detailed specimens, Type 2 and Type 4 have an improvement in average ductility of 16% and 119% than their conventionally detailed counter parts (Type1 and Type 3). Further, the joint shear capacity of the Type 2 and Type 4 specimens are improved by 8.4% and 15.6% than the corresponding specimens of Type 1 and Type 3 respectively. The present study proposes a closed form expression to compute the yield and ultimate load of the system. This is accomplished using the theory of statics and the failure pattern observed during testing. Good correlation is found between the theoretical and experimental results.

• 한국재료학회지
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• 제31권7호
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• pp.382-385
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• 2021

Well-crystallized vanadium pentoxide V₂O₅ thin films are fabricated on MgO single crystal substrates by using pulsed-laser deposition technique. The linear optical transmission spectra are measured and found to be in a wavelength range from 300 to 800 nm; the data are used to determine the linear refractive index of the V₂O₅ films. The value of linear refractive index decreases with increasing wavelength, and the relationship can be well explained by Wemple's theory. The third-order nonlinear optical properties of the films are determined by a single beam z-scan method at a wavelength of 532 nm. The results show that the prepared V₂O₅ films exhibit a fast third-order nonlinear optical response with nonlinear absorption coefficient and nonlinear refractive index of 2.13 × 10^-10 m/W and 2.07 × 10^-15 cm²/kW, respectively. The real and imaginary parts of the nonlinear susceptibility are determined to be 3.03 × 10^-11 esu and 1.12 × 10^-11 esu, respectively. The enhancement of the nonlinear optical properties is discussed.

• 한국공간구조학회논문집
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• 제3권2호
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• pp.85-90
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• 2003

If we use a third order approximation for the displacement function of beam element in finite element methods, finite element solutions of beams yield nodal displacement values matching to beam theory results to have no connection with the number increasing of elements of beams. It is assumed that, as the member displacement value at beam nodes are correct, the calculation procedure of beam element stiffness matrix have no numerical errors. A the member forces are calculated by the equations of $\frac{-M}{EI}=\frac{{d^2}{\omega}}{dx^2}\;and\;\frac{dM}{dx}=V$, the member forces at nodes of beams have errors in a moment and a shear magnitudes in the case of smaller number of element. The nodal displacement value of plate subject to the lateral load converge to the exact values according to the increase of the number of the element. So it is assumed that the procedures of plate element stiffness matrix calculations has a error in the fundamental assumptions. The beam methods for the high accuracy ratio solution Is also applied to the plate analysis. The method of reducing a error ratio of member forces and element stiffness matrix in the finite element methods is studied. Results of study were as follows. 1. The matrixes of EI[B] and [K] in the equations of M(x)=EI[B]{q} and M(x) = [K]{q}+{Q} of beams are same. 2. The equations of $\frac{-M}{EI}=\frac{{d^2}{\omega}}{dx^2}\;and\;\frac{dM}{dx}=V$ for the member forces have a error ratio in a finite element method of uniformly loaded structures, so equilibrium node loads {Q} must be substituted in the equation of member forces as the numerical examples of this paper revealed.

• 정보과학회지
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• 제1권1호
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• pp.72-74
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• 1983

Traditionally, polynomials have been used to approximte functions with prescribed values at a number of points(called the knots) on a given interal on the real line. The method of splines recently developed is more flexible. It approximates a function in a piece-wise fashion, by means of a different polynomial in each subinterval. The cubic spline gas ets origins in beam theory. It possessed continuous first and second deriatives at the knots and is characterised by a minimum curvature property which es rdlated to the physical feature of minimum potential energy of the supported beam. Translated into mathematical terms, this means that between successive knots the approximation yields a third-order polynomial sith its first derivatives continuous at the knots. The minimum curvature property holds good for each subinterval as well as for the whole region of approximation This means that the integral of the square of the second derivative over the entire interval, and also over each subinterval, es to be minimized. Thus, the task of determining the spline lffers itself as a textbook problem in discrete computer programming, since the integral of ghe square of the second derivative can be obviously recognized as the criterion function whicg gas to be minimized. Starting with the initial value of the function and assuming an initial solpe of the curve, the minimum norm property of the curvature makes sequential decision of the slope at successive knots (points) feasible. It is the aim of this paper to derive the cubic spline by the methods of computer programming and show that the results which is computed the all the alues in each subinterval of the spline approximations.

• Advances in nano research
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• 제14권5호
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• pp.421-433
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• 2023

In the present paper, the influences of the variation of exponent of volume fraction of carbon nanotubes (CNTs) on the natural frequencies (NFs) of the carbon nanotube-reinforced composite (CNTRC) beams under four different boundary conditions (BCs) are investigated. The single-walled carbon nanotubes (SWCNTs) are assumed to be aligned and dispersed in a polymeric matrix with various reinforcing patterns, according to the variation of exponent of volume fraction of CNTs for functionally graded (FG) reinforcements. Besides, uniform distribution (UD) of reinforcement is also considered to analyze the influence of the non-linear (NL) variation of the reinforcement of CNTs. Using Hamilton's principle and third-order shear deformation theory (TSDT), the equations of motion of the CNTRC beam are derived. Under four different BCs, the resulting equations are solved analytically. To verify the present formulation, comparison investigations are conducted. To examine the impacts of several factors on the NFs of the CNTRC beams, numerical examples and some benchmark results are presented.

• Steel and Composite Structures
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• 제42권6호
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• pp.805-826
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• 2022

The free and live load-forced vibration behaviour of porous functionally graded (PFG) higher order nanobeams in the thermal and magnetic fields is investigated comprehensively through this work in the framework of nonlocal strain gradient theory (NLSGT). The porosity effects on the dynamic behaviour of FG nanobeams is investigated using four different porosity distribution models. These models are exploited; uniform, symmetrical, condensed upward, and condensed downward distributions. The material characteristics gradation in the thickness direction is estimated using the power-law. The magnetic field effect is incorporated using Maxwell's equations. The third order shear deformation beam theory is adopted to incorporate the shear deformation effect. The Hamilton principle is adopted to derive the coupled thermomagnetic dynamic equations of motion of the whole system and the associated boundary conditions. Navier method is used to derive the analytical solution of the governing equations. The developed methodology is verified and compared with the available results in the literature and good agreement is observed. Parametric studies are conducted to show effects of porosity parameter; porosity distribution, temperature rise, magnetic field intensity, material gradation index, non-classical parameters, and the applied moving load velocity on the vibration behavior of nanobeams. It has been showed that all the analyzed conditions have significant effects on the dynamic behavior of the nanobeams. Additionally, it has been observed that the negative effects of moving load, porosity and thermal load on the nanobeam dynamics can be reduced by the effect of the force induced from the directed magnetic field or can be kept within certain desired design limits by controlling the intensity of the magnetic field.