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CONTENTS
Volume 29, Number 5, July30 2008
 

Abstract
Finite element methods have often been used for structural analyses of various mechanical problems. When finite element analyses are utilized to resolve mechanical systems, numerical uncertainties
in the initial data such as structural parameters and loading conditions may result in uncertainties in the structural responses. Therefore the initial data have to be as accurate as possible in order to obtain reliable structural analysis results. The typical finite element method may not properly represent discrete systems when using uncertain data, since all input data of material properties and applied loads are defined by nominal values. An interval finite element analysis, which uses the interval arithmetic as introduced by Moore (1966) is proposed as a non-stochastic method in this study and serves a new numerical tool for evaluating the uncertainties of the initial data in structural analyses. According to this method, the element stiffness matrix includes interval terms of the lower and upper bounds of the structural parameters, and interval change functions are devised. Numerical uncertainties in the initial data are described as a tolerance error and tree graphs of uncertain data are constructed by numerical uncertainty combinations of each parameter. The structural responses calculated by all uncertainty cases can be easily estimated so that structural safety can be included in the design. Numerical applications of truss and frame structures demonstrate the efficiency of the present method with respect to numerical analyses of structural uncertainties.

Key Words
non-stochastic; interval arithmetic; finite element method; structural uncertainty; initial data; interval change function; tolerance error.

Address
Dongkyu Lee: Architectural Engineering Research Department, Steel Structure Research Laboratory, Research Institute of Industrial Science & Technology, Korea
Sungsoo Park and Soomi Shin: Department of Architectural Engineering, Pusan National University, Busan, Korea

Abstract
In piezoelectric flexible structures, the contribution of vibration modes to the dynamic response of system may change with the location of piezoelectric actuator patches, which means that the
ability of actuators to control vibration modes should be taken into account in the development of modal reduction model. The spatial H2 norm of modes, which serves as a measure of the intensity of modes to
system dynamical response, is used to pick up the modes included in the reduction model. Based on the reduction model, the paper develops the state-space representation for uncertain flexible structures with
piezoelectric material as non-collocated actuators/sensors in the modal space, taking into account uncertainties due to modal parameters variation and unmodeled residual modes. In order to suppress the vibration of the structure, a dynamic output feedback control law is designed by simultaneously considering the conflicting performance specifications, such as robust stability, transient response requirement, disturbance rejection, actuator saturation constraints. Based on linear matrix inequality, the vibration control design is converted into a linear convex optimization problem. The simulation results show how the influence of vibration modes on the dynamical response of structure varies with the location of piezoelectric actuators, why the uncertainties should be considered in the reductiom model to avoid exciting high-frequency modes in the non-collcated vibration control, and the possiblity that the conflicting performance specifications are dealt with simultaneously.

Key Words
spatial norm of modes; uncertain flexible structures; vibration control.

Address
Xu Yalan and Chen Jianjun: School of Electronic & Mechanical Engineering, Xidian University, Xi?an 710071, P.R. China

Abstract
This paper proposes the application of active multiple tuned mass dampers (AMTMD) for translational and torsional response control of a simplified two-degree-of-freedom (2DOF) structure, able to represent the dynamic characteristics of general asymmetric structures, under the ground acceleration. This 2DOF structure is a generalized 2DOF system of an asymmetric structure with predominant translational and torsional responses under earthquake excitations using the mode reduced-order method. Depending on the ratio of the torsional to the translational eigenfrequency, i.e. the torsional to translational frequency ratio (TTFR), of asymmetric structures, the following three cases can be distinguished: (1) torsionally flexible structures (TTFR < 1.0), (2) torsionally intermediate stiff structures (TTFR = 1.0), and (3) torsionally stiff structures (TTFR > 1.0). The even distribution of the AMTMD within the whole width and half width of the asymmetric structure, thus leading to three cases of installing the AMTMD (referred to as the AMTMD of case 1, AMTMD of case 2, AMTMD of case 3, respectively), is taken into account. In the present study, the criterion for searching the optimum parameters of the AMTMD is defined as the minimization of the minimum values of the maximum translational and torsional displacement dynamic magnification factors (DMF) of an asymmetric structure with the AMTMD. The criterion used for assessing the effectiveness of the AMTMD is selected as the ratio of the minimization of the minimum values of the maximum translational and torsional displacement DMF of the asymmetric structure with the AMTMD to the maximum translational and torsional displacement DMF of the asymmetric structure without the AMTMD. By resorting to these two criteria, a
careful examination of the effects of the normalized eccentricity ratio (NER) on the effectiveness and robustness of the AMTMD are carried out in the mitigation of both the translational and torsional
responses of the asymmetric structure. Likewise, the effectiveness of a single ATMD with the optimum positions is presented and compared with that of the AMTMD.

Key Words
vibration control; damping; active multiple tuned mass dampers (AMTMD); asymmetric structures; ground acceleration; torsional to translational frequency ratio (TTFR); normalized eccentricity ratio (NER).

Address
Chunxiang Li: Dept. of Civil Engineering, Shanghai University, No.149 Yanchang Rd., Shanghai 200072, P. R. China
Xueyu Xiong: College of Civil Engineering, Tongji University, No. 1239 Si Ping Rd., Shanghai 200092, P. R. China

Abstract
This paper adopts the numerical assembly method (NAM) to determine the exact solutions of natural frequencies and mode shapes of a multi-span and multi-step beam carrying a number of various concentrated elements including point masses, rotary inertias, linear springs, rotational springs and springmass systems. First, the coefficient matrix for an intermediate station with various concentrated elements, cross-section change and/or pinned support and the ones for the left-end and right-end supports of a beam are derived. Next, the overall coefficient matrix for the entire beam is obtained using the numerical assembly technique of the conventional finite element method (FEM). Finally, the exact solutions for the natural frequencies of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and the associated mode shapes are obtained by substituting the corresponding values of integration constants into the associated eigenfunctions.

Key Words
multi-step beam; exact solution; natural frequency; mode shape.

Address
Hsien-Yuan Lin: Dept. of Mechanical Engineering, Cheng Shiu University, Kaohsiung 833, Taiwan, Republic of China

Abstract
Transient solution of asymmetric mechanical and thermal stresses for hollow cylinders made of functionally graded material is presented. Temperature distribution, as function of radial and
circumferential directions and time, is analytically obtained, using the method of separation of variables and generalized Bessel function. A direct method is used to solve the Navier equations, using the Euler
equation and complex Fourier series.

Key Words
transient; thermoelasticity; functionally graded material; hollow cylinder.

Address
M. Jabbari and A.R. Vaghari: Postgraduate School, Tehran South Branch, Azad University, Tehran, Iran
A. Bahtui: Department of System Engineering, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK
M.R. Eslami: Distinguished Center of Thermoelasticity, Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran

Abstract
To gain understanding of the applicability of CFRP cables in super long-span cable-stayed bridges, by taking a 1400 m cable-stayed bridge as example, mechanics performance including the static behavior under service load, dynamic behavior, wind stability and seismic behavior of the bridge using either steel or CFRP cables are investigated numerically and compared. The results show that viewed from the aspect of mechanics performance, the use of CFRP cables in super long-span cable-stayed bridges is feasible, and the cross-sectional areas of CFRP cables should be determined by the principle of
equivalent axial stiffness.

Key Words
cable-stayed bridges; CFRP cable; mechanics performance.

Address
Xin-Jun Zhang: College of Civil Engineering and Architecture, Zhejiang University of Technology, Hangzhou 310014, China

Abstract
In this paper, the double displacement coupled statics and dynamics of the electromechanical integrated electrostatic harmonic drive are developed. The linearization of the nonlinear dynamic equations is completed. Based on natural frequency and mode function, the double displacement coupled forced response of the drive system to voltage excitation are obtained. Changes of the forced response along with the system parameters are investigated. The voltage excitation can cause the radial and tangent coupled forced responses of the flexible ring. The flexible ring radius, ring thickness and clearance between the ring and stator have obvious influences on the double displacement coupled forced responses.

Key Words
electromechanical integrated; Harmonic drive; forced response; voltage excitation.

Address
Lizhong Xu, Cuirong Zhu and Lei Qin: Mechanical engineering institute, Yanshan University, Qinhuangdao 066004, China

Abstract
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Key Words
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Address
R.E. Rossi: Institute of Applied Mechanics, Department of Engineering, Universidad Nacional del Sur, Av.Alem 1253, B8000CPB Bahia Blanca, Argentina


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