Techno Press


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CONTENTS
Volume 39, Number 1, July10 2011
 

Abstract
This study investigates the feasibility of detecting structural damage using the HHT method. A damage detection index, the ratio of bandwidth (RB) is proposed. This index is highly correlated or approximately equal to the change of equivalent damping ratio for an intact structure incurring damage from strong ground motions. Based on an analysis of shaking table test data from benchmark models subjected to adjusted Kobe and El Centro earthquakes, the damage detection index is evaluated using the Hilbert-Huang Transform (HHT) and the Fast Fourier Transform (FFT) methods, respectively. Results indicate that, when the response of the structure is in the elastic region, the RB value only slightly changes in both the HHT and the FFT spectra. Additionally, RB values estimated from the HHT spectra vs. the PGA values change incrementally when the structure response is nonlinear i.e., member yielding occurs, but not in the RB curve from the FFT spectra. Moreover, the RB value of the top floor changes more than those from the other floors. Furthermore, structural damage is detected only when using the acceleration response data from the top floor. Therefore, the ratio of bandwidth RB estimated from the smoothed HHT spectra is an effective and sensitive damage index for detecting structural damage. Results of this study also demonstrate that the HHT is a powerful method in analyzing the nonlinear responses of steel structures to strong ground motions.

Key Words
damage detection index; HHT; inter-story drift; half-power bandwidth

Address
Dung-Jiang Chiou, Wen-Ko Hsu: Department of Civil Engineering, National Central University Jhung-li, Taoyuan, Taiwan, R.O.C.
Cheng-Wu Chen: Institute of Maritime Information and Technology, National Kaohsiung Marine University,
Kaohsiung 80543, Taiwan, R.O.C.; Global Earth Observation and Data Analysis Center, National Cheng Kung University,
Tainan, Taiwan 701, R.O.C.
Chih-Min Hsieh: Institute of Maritime Information and Technology, National Kaohsiung Marine University, Kaohsiung 80543, Taiwan, R.O.C.
Jhy-Pyng Tang and Wei-Ling Chiang: Department of Civil Engineering, National Central University Jhung-li, Taoyuan, Taiwan, R.O.C.

Abstract
The natural frequencies of continuous systems depend on the governing partial differential equation and can be numerically estimated using the finite element method. The accuracy and convergence of the finite element method depends on the choice of basis functions. A basis function will generally perform better if it is closely linked to the problem physics. The stiffness matrix is the same for either static or dynamic loading, hence the basis function can be chosen such that it satisfies the static part of the governing differential equation. However, in the case of a rotating beam, an exact closed form solution for the static part of the governing differential equation is not known. In this paper, we try to find an approximate solution for the static part of the governing differential equation for an uniform rotating beam. The error resulting from the approximation is minimized to generate relations between the constants assumed in the solution. This new function is used as a basis function which gives rise to shape functions which depend on position of the element in the beam, material, geometric properties and rotational speed of the beam. The results of finite element analysis with the new basis functions are verified with published literature for uniform and tapered rotating beams under different boundary conditions. Numerical results clearly show the advantage of the current approach at high rotation speeds with a reduction of 10 to 33% in the degrees of freedom required for convergence of the first five modes to four decimal places for an uniform rotating cantilever beam.

Key Words
rotating beam; finite element method; basis functions; shape function; turbine blade

Address
R. Ganesh and Ranjan Ganguli: Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, India

Abstract
An accurate substructural synthesis method including random responses synthesis, frequencyresponse functions synthesis and mid-order modes synthesis is developed based on rigorous substructure description, dynamic condensation and coupling. An entire structure can firstly be divided into several substructures according to different functions, geometric and dynamic characteristics. Substructural displacements are expressed exactly by retained mid-order fixed-interfacial normal modes and residual constraint modes. Substructural interfacial degree-of-freedoms are eliminated by interfacial displacements compatibility and forces equilibrium between adjacent substructures. Then substructural mode vibration equations are coupled to form an exact-condensed synthesized structure equation, from which structural mid-order modes are calculated accurately. Furthermore, substructural frequency-response function equations are coupled to yield an exact-condensed synthesized structure vibration equation in frequency domain, from which the generalized structural frequency-response functions are obtained. Substructural frequency-response functions are calculated separately by using the generalized frequency-response functions, which can be assembled into an entire-structural frequency-response function matrix. Substructural power spectral density functions are expressed by the exact-synthesized substructural frequency-response functions, and substructural random responses such as correlation functions and meansquare responses can be calculated separately. The accuracy and capacity of the proposed substructure synthesis method is verified by numerical examples.

Key Words
substructural synthesis; fixed interface substructure; random response; frequency-response function; mid-order mode

Address
Z.G. Ying and W.Q. Zhu: Department of Mechanics, School of Aeronautics and Astronautics, Zhejiang University,
Hangzhou 310027, P.R. China
S.Q. Ye and Y.Q. Ni: Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong

Abstract
A simply structural damage detection software is developed to identification damage in beams. According to linear fracture mechanics theory, the localized additional flexibility in damage vicinity can be represented by a lumped parameter element. The damaged beam is modeled by waveletbased elements to gain the first three frequencies precisely. The first three frequencies influencing functions of damage location and depth are approximated by means of surface-fitting techniques to gain damage detection database of forward problem. Then the first three measured natural frequencies are employed as inputs to solve inverse problem and the intersection of the three frequencies contour lines predict the damage location and depth. The DLL (Dynamic Linkable Library) file of damage detection method is coded by C++ and the corresponding interface of software is coded by virtual instrument software LabVIEW. Finally, the software is tested on beams and shafts in engineering. It is shown that the presented software can be used in actual engineering structures.

Key Words
damage detection; wavelet finite element method; LabVIEW; software

Address
Jiawei Xiang: School of Mechanical and Electrical Engineering, Guilin University of Electronic Technology, Guilin, 541004, P.R. China; State Key Laboratory for Manufacturing Systems Engineering, Xi\'an Jiaotong University, Xi\'an 710049, P.R. China
Zhansi Jiang and Yanxue Wang: School of Mechanical and Electrical Engineering, Guilin University of Electronic Technology, Guilin, 541004, P.R. China
Xuefeng Chen: State Key Laboratory for Manufacturing Systems Engineering, Xi\'an Jiaotong University, Xi\'an 710049, P.R. China


Abstract
The explicit nonlinear dynamic relaxation method (DRM) is applied to the nonlinear geodesic shape finding analysis by introducing fictional tensioned \'strings\' along the desired seams with a three or four-node membrane element. A number of results from the numerical example for the nonlinear geodesic shape finding and patterning analysis are obtained by the proposed method to demonstrate the accuracy and efficiency of the developed method. Therefore, the proposed geodesic shape finding algorithm may improve the applicability of a four-node membrane element to membrane structural engineering and design analysis simultaneously for the shape finding, stress, and patterning analysis.

Key Words
tension membrane structures; patterning; geodesic element; shape finding algorithm; dynamic relaxation method; kinetic damping

Address
K.S. Lee and S.E. Han: Department of Architectural Engineering, School of Architecture, Inha University, 253 Yonghyundong, Nam-gu, Incheon 402-751, Korea

Abstract
The present work deals with obtaining the critical buckling load and the natural frequencies of clamped, orthotropic, rectangular thin plates subjected to different linear distributed in-plane forces. An analytical solution is proposed. Using the Ritz method, the dependence between in-plane forces and natural frequencies are estimated for various plate sizes, and some results are compared with finite element solutions and where possible, comparison is made with previously published results. Beam functions are used as admissible functions in the Ritz method.

Key Words
critical buckling; vibration; orthotropic plate; in-plane force; rectangular, clamped; Ritz method

Address
D.H. Felix: Department of Engineering, Institute of Applied Mechanics (IMA), Universidad Nacional del Sur, Av. Alem 1253, Bahia Blanca (B8000CPB), Argentina
D.V. Bambill: Department of Engineering, Institute of Applied Mechanics (IMA), Universidad Nacional del Sur, Av. Alem 1253, Bahia Blanca (B8000CPB), Argentina; Comision Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Argentina
C.A. Rossit: Department of Engineering, Institute of Applied Mechanics (IMA), Universidad Nacional del Sur, Av. Alem 1253, Bahia Blanca (B8000CPB), Argentina; Comision Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Argentina

Abstract
Pushover analysis has gained significant popularity as an analytical tool for realistic determination of the inelastic behaviour of RC structures. Though significant work has been done to evaluate the demands realistically, the evaluation of capacity and realistic failure modes has taken a back seat. In order to throw light on the inelastic behaviour and capacity evaluation for the RC framed structures, a 3D Reinforced concrete frame structure was tested under monotonically increasing lateral pushover loads, in a parabolic pattern, till failure. The structure consisted of three storeys and had 2 bays along the two orthogonal directions. The structure was gradually pushed in small increments of load and the corresponding displacements were monitored continuously, leading to a pushover curve for the structure as a result of the test along with other relevant information such as strains on reinforcement bars at critical locations, failure modes etc. The major failure modes were observed as flexural failure of beams and columns, torsional failure of transverse beams and joint shear failure. The analysis of the structure was by considering all these failure modes. In order to have a comparison, the analysis was performed as three different cases. In one case, only the flexural hinges were modelled for critical locations in beams and columns; in second the torsional hinges for transverse beams were included in the analysis and in the third case, joint shear hinges were also included in the analysis. It is shown that modelling and capturing all the failure modes is practically possible and such an analysis can provide the realistic insight into the behaviour of the structure.

Key Words
reinforced concrete structure; experiment; pushover analysis; failure modes; seismic response

Address
Akanshu Sharma: Reactor Safety Division, Bhabha Atomic Research Centre, Mumbai - 400085, India; Institute for Construction Materials, University of Stuttgart, Stuttgart - 70569, India
G.R. Reddy: Reactor Safety Division, Bhabha Atomic Research Centre, Mumbai - 400085, India
R. Eligehausen: Institute for Construction Materials, University of Stuttgart, Stuttgart - 70569, India
K.K. Vaze: Reactor Safety Division, Bhabha Atomic Research Centre, Mumbai - 400085, India

Abstract
To ensure safety and long term performance, structural control has rapidly matured over the past decade into a viable means of limiting structural responses to strong winds and earthquakes. Nonlinear response history analysis requires rigorous procedure to compute seismic demands. Therefore the simplified nonlinear analysis procedures are useful to determine performance of the structure. In this investigation, application of improved capacity demand diagram method in the control of structural system is presented for the first time. Developed pole assignmet method (DPAM) in structural systems control is introduced. Genetic algorithm (GA) is employed as an optimization tool for minimizing a target function that defines values of coefficient matrices providing the placement of actuators and optimal control forces. The ground acceleration is modified under induced control forces. Due to this, performance of structure based on improved nonlinear demand diagram is selected to threshold of nonlinear behavior of structure. With small energy consumption characteristics, semi-active devices are especially attractive solutions for limiting earthquake effects. To illustrate the efficiency of DPAM, a 30-story steel moment frame structure employing the semi-active control devices is applied. In comparison to the widely used linear quadratic regulation (LQR), the DPAM controller was shown to be just as effective and better in the reduction of structural responses during large earthquakes.

Key Words
developed pole assignment method (DPAM); semi-active optimal control; genetic algorithm (GA); capacity-demand diagram; nonlinear behavior; decreased ground acceleration; linear quadratic regulation (LQR)

Address
Fereidoun Amini and Kaveh Karami: Department of Civil Engineering, Iran University of Science and Technology, Narmak 16846, Tehran, Iran


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