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CONTENTS
Volume 28, Number 6, April20 2008
 

Abstract
An application is presented of a modified Vlasov model to the free vibration analysis of plates resting on elastic foundations. The effects of the subsoil depth, the ratio of the plate dimensions,
the ratio of the subsoil depth to the plate dimension in the longer direction, and the value of the vertical deformation parameter within the subsoil on the frequency parameters of plates on an elastic foundation are investigated. This analysis has been caried out by the aid of a computer program. The first ten frequency parameters are presented in tabular and the graphical forms to evaluate the effects of the parameters considered in this study. Then mode shapes corresponding to the first six of the frequency parameters are given in graphs. It is concluded that the effect of the subsoil depth on the frequency parameters of the plates on an elastic foundation is generally larger than those of the other parameters considered in this study.

Key Words
modified Vlasov model; plates; elastic foundation; free vibration; parametric analysis.

Address
Yusuf Ayvaz: Dept. of Civil Engineering, Karadeniz Technical University, 61080 Trabzon, Turkey
Celal Burak Oguzhan: 12th Regional Directorate of State Hydraulic Works, 38060 Kayseri, Turkey

Abstract
The reports regarding the free vibration analysis of uniform beams carrying single or multiple spring-mass systems are plenty, however, among which, those with inertia effect of the helical spring(s) considered are limited. In this paper, by taking the mass of the helical spring into consideration, the stiffness and mass matrices of a spring-mass system and an equivalent mass that may be used to replace the effect of a spring-mass system are derived. By means of the last element stiffness and mass matrices, the natural frequencies and mode shapes for a uniform cantilever beam carrying any number of springmass
systems (or loaded beam) are determined using the conventional finite element method (FEM). Similarly, by means of the last equivalent mass, the natural frequencies and mode shapes of the same loaded beam are also determined using the presented equivalent mass method (EMM), where the cantilever beam elastically mounted by a number of lumped masses is replaced by the same beam rigidly attached by the same number of equivalent masses. Good agreement between the numerical results of FEM and those of EMM and/or those of the existing literature confirms the reliability of the presented approaches.

Key Words
mass of spring; cantilever beam; spring-mass system; equivalent mass; natural frequency; mode shape.

Address
Jia-Jang Wu: Dept. of Marine Engineering, National Kaohsiung Marine University, No. 142, Hai-Chuan Road,
Nan-Tzu, Kaohsiung 811, Taiwan, Republic of China

Abstract
A vibration power minimization model is developed, based on the mobility matrix method, for a vibration isolation system consisting of a vibrating source placed on an elastic support structure through multiple resilient mounts. This model is applied to investigate the design optimization of an X-Y motion stage-based vibration isolation system used in semiconductor wire-bonding equipment. By varying
the stiffness coefficients of the resilient mounts while constraining the dynamic displacement amplitudes of the X-Y motion stage, the total power flow from the X-Y motion stage (the vibrating source) to the equipment table (the elastic support structure) is minimized at each frequency interval in the concerned frequency range for different stiffnesses of the equipment table. The results show that when the equipment table is relatively flexible, the optimal design based on the proposed vibration power minimization model gives significantly little power flow than that obtained using a conventional vibration force minimization model at some critical frequencies. When the equipment table is rigid enough, both models provide almost the same predictions on the total power flow.

Key Words
design optimization; elastic support structure; power flow; vibration isolation.

Address
Shilin Xie, Siu Wing Or and Helen Lai Wa Chan: Dept. of Applied Physics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
Ping Kong Choy and Peter Chou Kee Liu: ASM Assembly Automation Ltd., 3/F., Watson Centre, 16 Kung Yip Street, Kwai Chung, New Territories, Hong Kong

Abstract
The aim of this contribution is to present a new link/beam finite element suitable for electrothermo-structural analysis of uni-axially graded materials. Continuous polynomial variation of geometry and material properties will be considered. The element matrix and relations for solution of Joule?s heat (and its distribution to the element nodes) have been established in the sense of a sequence method of a
coupled problem solution. The expression for the solution of nodal forces caused by a continuously distributed temperature field has also been derived. The theoretical part of this contribution is completed
by numerical validation, which proves the high accuracy and effectiveness of the proposed element. The results of the performed experiments are compared with those obtained using the more expensive
multiphysical link element and solid element of the FEM program Ansys. The proposed finite element could be used not only in the multiphysical analysis of the current paths and actuators but also in analysis
of other 1D construction parts made of composite or uni-axially graded materials.

Key Words
FEM; uni-axially graded materials; coupled problems.

Address
J. Murin, V. Kutis and M. Masny: Slovak University of Technology, Faculty of Electrical Engineering and Information Technology, Department of Mechanics, Bratislava 812 19 Slovak Republic

Abstract
New types of armor, including space armor, multiple-layered armor, composite armor and modular armor have been successfully developed and installed on the armored vehicles of several nations. The protective capability of armor against penetration is established. Of developed composite armor, space armor has a simple structure and is easy to produce and can be produced at low cost. This study uses the
finite element package DYTRAN and the pre and post processor PNTRAN to elucidate the ballistic resistance and penetration of space armor. Factors such as armor thickness, space between armors and
projectile profile are considered. A technique for simulating the protection afforded by armor and supporting the design of space armor is developed.

Key Words
Anti-penetration; space armor; DYTRAN.

Address
Tso-Liang Teng: Dept. of Mechanical and automation Engineering, Da-Yeh University, 112 Shan-Jiau Rd.,
Dah-Tsuen, Chang-hua, Taiwan 515, R.O.C.
Ta-Ming Shih and Cheng-Chung Lu: Dept. of Weapon System Engineering, Chung Cheng Institute of Technology, National Defense University, Taiwan, R.O.C.

Abstract
In the framework of the SPEAR (Seismic PErformance Assessment and Rehabilitation) research Project, an under-designed three storey RC frame structure, designed to sustain only gravity loads, was subjected, in three different configurations ?as-built?, Fiber Reinforced Polymer (FRP) retrofitted and rehabilitated by reinforced concrete (RC) jacketing, to a series of bi-directional pseudodynamic
(PsD) tests under different values of peak ground acceleration (PGA) (from a minimum of 0.20g to a maximum of 0.30g). The seismic deficiencies exhibited by the ?as-built? structure after the test at
PGA level of 0.20g were confirmed by a post - test assessment of the structural seismic capacity performed by a nonlinear static pushover analysis implemented on the structure lumped plasticity model.
To improve the seismic performance of the ?as-built? structure?, two rehabilitation interventions by using either FRP laminates or RC jacketing were designed. Assumptions for the analytical modeling, design criteria and calculation procedures along with local and global intervention measures and their installation details are herein presented and discussed. Nonlinear static pushover analyses for the assessment of the theoretical seismic capacity of the structure in each retrofitted configuration were performed and compared with the experimental outcomes.

Key Words
full-scale; RC; seismic retrofit; GFRP; concrete jacketing; biaxial bending; nonlinear pushover analysis.

Address
M. Di Ludovico, A. Balsamo, A. Prota and G. Manfredi:
Dept. of Structural Engineering, University of Naples Federico II, 80125, Naples, Italy

Abstract
Free axisymmetric vibrations of layered cylindrical shells of variable thickness are studied using spline function approximation techniques. Three different types of thickness variations are considered namely linear, exponential and sinusoidal. The equations of axisymmetric motion of layered cylindrical shells, on the longitudinal and transverse displacement components are obtained using Love?s first approximation theory. A system of coupled differential equations on displacement functions are obtained by assuming the displacements in a separable form. Then the displacements are approximated using Bickley-spline approximation. The vibrations of two-layered cylindrical shells, made up of several types of layered materials and different boundary conditions are considered. Parametric studies have been made on the variation of frequency parameter with respect to the relative layer thickness, length ratio and type of thickness variation parameter.

Key Words
free vibration; cylindrical shell; spline method; variable thickness; eigenvalues.

Address
K.K. Viswanathan, Kyung Su Kim, Jang Hyun Lee, Chang Hyun Lee and Jae Beom Lee: Impact & Fatigue Fracture Lab., Department of Naval Architecture& Ocean Engineering, Inha University, #253, Yonghyun-dong, Nam-gu, Incheon 402-751, Korea

Abstract
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Key Words
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Address
S. Rajendran: School of Mechanical and Aerospace Engineering, Nanyang Technological University,
Singapore 639798

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