Search results for: Fully fuzzy linear equations

Authors: Bainian Li, Kongsheng Zhang, Jian Xu

Abstract:

In this paper we study the fuzzy c-mean clustering algorithm combined with principal components method. Demonstratively analysis indicate that the new clustering method is well rather than some clustering algorithms. We also consider the validity of clustering method.

Keywords: FCM algorithm, Principal Components Analysis, Clustervalidity

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Authors: S. Suwannasri, R. Sirovetnukul

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The effective machine-job assignment of injection molding machines is very important for industry because it is not only directly affects the quality of the product but also the performance and lifetime of the machine as well. The phase of machine selection was mostly done by professionals or experienced planners, so the possibility of matching a job with an inappropriate machine might occur when it was conducted by an inexperienced person. It could lead to an uneconomical plan and defects. This research aimed to develop a machine selection system for plastic injection machines as a tool to help in decision making of the user. This proposed system could be used both in normal times and in times of emergency. Fuzzy logic principle is applied to deal with uncertainty and mechanical factors in the selection of both quantity and quality criteria. The six criteria were obtained from a plastic manufacturer's case study to construct a system based on fuzzy logic theory using MATLAB. The results showed that the system was able to reduce the defects of Short Shot and Sink Mark to 24.0% and 8.0% and the total defects was reduced around 8.7% per month.

Keywords: Injection molding machine, machine selection, fuzzy logic, defects in injection molding, matlab.

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Authors: Mohammad Hasan Raouf, Ebrahim Rasooli Anarmarzi, Hamid Lesani, Javad Olamaei

Abstract:

This paper proposes the application of a hierarchical fuzzy system (HFS) based on multi-input power system stabilizer (MPSS) and also Static Var Compensator (SVC) in multi-machine environment.The number of rules grows exponentially with the number of variables in a conventional fuzzy logic system. The proposed HFS method is developed to solve this problem. To reduce the number of rules the HFS consists of a number of low-dimensional fuzzy systems in a hierarchical structure. In fact, by using HFS the total number of involved rules increases only linearly with the number of input variables. In the MPSS, to have better efficiency an auxiliary signal of reactive power deviation (ΔQ) is added with ΔP+ Δω input type Power system stabilizer (PSS). Phasor model of SVC is described and used in this paper. The performances of MPSS, Conventional power system stabilizer (CPSS), hierarchical Fuzzy Multi-input Power System Stabilizer (HFMPSS) and the proposed method in damping inter-area mode of oscillation are examined in response to disturbances. By using digital simulations the comparative study is illustrated. It can be seen that the proposed PSS is performing satisfactorily within the whole range of disturbances.

Keywords: Power system stabilizer (PSS), hierarchical fuzzysystem (HFS), Static VAR compensator (SVC)

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Authors: Hirofumi Miyajima, Kazuya Kishida, Noritaka Shigei, Hiromi Miyajima

Abstract:

Most of self-tuning fuzzy systems, which are automatically constructed from learning data, are based on the steepest descent method (SDM). However, this approach often requires a large convergence time and gets stuck into a shallow local minimum. One of its solutions is to use fuzzy rule modules with a small number of inputs such as DIRMs (Double-Input Rule Modules) and SIRMs (Single-Input Rule Modules). In this paper, we consider a (generalized) DIRMs model composed of double and single-input rule modules. Further, in order to reduce the redundant modules for the (generalized) DIRMs model, pruning and generative learning algorithms for the model are suggested. In order to show the effectiveness of them, numerical simulations for function approximation, Box-Jenkins and obstacle avoidance problems are performed.

Keywords: Box-Jenkins’s problem, Double-input rule module, Fuzzy inference model, Obstacle avoidance, Single-input rule module.

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Authors: Camelia Frigioiu, Katica (Stevanovic) Hedrih, Iulian Gabriel Birsan

Abstract:

In this paper we study the rheonomic mechanical systems from the point of view of Lagrange geometry, by means of its canonical semispray. We present an example of the constraint motion of a material point, in the rheonomic case.

Keywords: Lagrange's equations, mechanical system, non-linear connection, rheonomic Lagrange space.

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Authors: Thi T. Nguyen, Lee N. Gordon-Brown

Abstract:

A new deployment of the multiple criteria decision making (MCDM) techniques: the Simple Additive Weighting (SAW), and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for portfolio allocation, is demonstrated in this paper. Rather than exclusive reference to mean and variance as in the traditional mean-variance method, the criteria used in this demonstration are the first four moments of the portfolio distribution. Each asset is evaluated based on its marginal impacts to portfolio higher moments that are characterized by trapezoidal fuzzy numbers. Then centroid-based defuzzification is applied to convert fuzzy numbers to the crisp numbers by which SAW and TOPSIS can be deployed. Experimental results suggest the similar efficiency of these MCDM approaches to selecting dominant assets for an optimal portfolio under higher moments. The proposed approaches allow investors flexibly adjust their risk preferences regarding higher moments via different schemes adapting to various (from conservative to risky) kinds of investors. The other significant advantage is that, compared to the mean-variance analysis, the portfolio weights obtained by SAW and TOPSIS are consistently well-diversified.

Keywords: Fuzzy numbers, SAW, TOPSIS, portfolio optimization, higher moments, risk management.

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Authors: Wudhichai Assawinchaichote, Sing Kiong Nguang

Abstract:

This paper investigates the problem of designing a robust state-feedback controller for a class of uncertain Markovian jump nonlinear systems that guarantees the L2-gain from an exogenous input to a regulated output is less than or equal to a prescribed value. First, we approximate this class of uncertain Markovian jump nonlinear systems by a class of uncertain Takagi-Sugeno fuzzy models with Markovian jumps. Then, based on an LMI approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear systems to have an H performance are derived. An illustrative example is used to illustrate the effectiveness of the proposed design techniques.

Keywords: Robust H, Fuzzy Control, Markovian Jump Systems, LMI.

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Authors: Tao Zhao, Xin Wang

Abstract:

With the increasing complexity of engineering problems, the traditional, single-objective and deterministic optimization method can not meet people-s requirements. A multi-objective fuzzy optimization model of resource input is built for M chlor-alkali chemical eco-industrial park in this paper. First, the model is changed into the form that can be solved by genetic algorithm using fuzzy theory. And then, a fitness function is constructed for genetic algorithm. Finally, a numerical example is presented to show that the method compared with traditional single-objective optimization method is more practical and efficient.

Keywords: Fitness function, genetic algorithm, multi-objectivefuzzy optimization, satisfaction degree membership function.

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Authors: G. M. Arun Prasath, N. Arthi

Abstract:

This work proposed a multi-objective mathematical programming approach to select the appropriate supply network elements. The multi-item multi-objective production-distribution inventory model is formulated with possible constraints under fuzzy environment. The unit cost has taken under fuzzy environment. The inventory model and warehouse location model has combined to formulate the production-distribution inventory model. Warehouse location is important in supply chain network. Particularly, if a company maintains more selling stores it cannot maintain individual secondary warehouse near to each selling store. Hence, maintaining the optimum number of secondary warehouses is important. Hence, the combined mathematical model is formulated to reduce the total expenditure of the organization by arranging the network of minimum number of secondary warehouses. Numerical example has been taken to illustrate the proposed model.

Keywords: Fuzzy inventory model, warehouse location model, triangular fuzzy number, secondary warehouse, LINGO software.

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Authors: H. Zarei, M. H. Fazel Zarandi, M. Karbasian

Abstract:

A Decision Support System/Expert System for stock portfolio selection presented where at first step, both technical and fundamental data used to estimate technical and fundamental return and risk (1st phase); Then, the estimated values are aggregated with the investor preferences (2nd phase) to produce convenient stock portfolio. In the 1st phase, there are two expert systems, each of which is responsible for technical or fundamental estimation. In the technical expert system, for each stock, twenty seven candidates are identified and with using rough sets-based clustering method (RC) the effective variables have been selected. Next, for each stock two fuzzy rulebases are developed with fuzzy C-Mean method and Takai-Sugeno- Kang (TSK) approach; one for return estimation and the other for risk. Thereafter, the parameters of the rule-bases are tuned with backpropagation method. In parallel, for fundamental expert systems, fuzzy rule-bases have been identified in the form of “IF-THEN" rules through brainstorming with the stock market experts and the input data have been derived from financial statements; as a result two fuzzy rule-bases have been generated for all the stocks, one for return and the other for risk. In the 2nd phase, user preferences represented by four criteria and are obtained by questionnaire. Using an expert system, four estimated values of return and risk have been aggregated with the respective values of user preference. At last, a fuzzy rule base having four rules, treats these values and produce a ranking score for each stock which will lead to a satisfactory portfolio for the user. The stocks of six manufacturing companies and the period of 2003-2006 selected for data gathering.

Keywords: Stock Portfolio Selection, Fuzzy Rule-Base ExpertSystems, Financial Decision Support Systems, Technical Analysis, Fundamental Analysis.

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Authors: C. Ardil

Abstract:

The decision to select an unmanned combat aircraft is complicated since several options and conflicting criteria must be considered at simultaneously. When making multiple criteria decision, it is important to consider the selected evaluation criteria, including priceability, payloadability, stealthability, speedability , and survivability. The fundamental goal of the study is to select the best unmanned combat aircraft by taking these evaluation criteria into account. The optimal aircraft was chosen using the fuzzy proximity measure method, which enables decision-makers to designate preferences as standard fuzzy set numbers during the multiple criteria decision-making process. To assess the applicability of the proposed approach, a numerical example is provided. Finally, by comparing determined unmanned combat aircraft, the proposed method produced a successful application, and the best aircraft was selected.

Keywords: standard fuzzy sets (SFS), unmanned combat aircraft selection, multiple criteria decision making (MCDM), multiple criteria group decision making (MCGDM), proximity measure method (PMM)

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Authors: Omid Heydarnia, Akbar Allahverdizadeh, Behnam Dadashzadeh, M. R. Sayyed Noorani

Abstract:

Underactuated biped robots control is one of the interesting topics in robotics. The main difficulties are its highly nonlinear dynamics, open-loop instability, and discrete event at the end of the gait. One of the methods to control underactuated systems is the partial feedback linearization, but it is not robust against uncertainties and disturbances that restrict its performance to control biped walking and running. In this paper, fuzzy partial feedback linearization is presented to overcome its drawback. Numerical simulations verify the effectiveness of the proposed method to generate stable and robust biped walking and running gaits.

Keywords: Underactuated system, biped robot, fuzzy control, partial feedback linearization.

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Authors: Guangbin Wang, Ning Zhang, Fuping Tan

Abstract:

In this paper, we present parallel alternating two-stage methods for solving linear system Ax = b, where A is a monotone matrix or an H-matrix. And we give some convergence results of these methods for nonsingular linear system.

Keywords: Parallel, alternating two-stage, convergence, linear system.

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Authors: A. Ghaffari, A. Meghdari, D. Naderi, S. Eslami

Abstract:

In this paper an algorithm based on the adaptive neuro-fuzzy controller is provided to enhance the tipover stability of mobile manipulators when they are subjected to predefined trajectories for the end-effector and the vehicle. The controller creates proper configurations for the manipulator to prevent the robot from being overturned. The optimal configuration and thus the most favorable control are obtained through soft computing approaches including a combination of genetic algorithm, neural networks, and fuzzy logic. The proposed algorithm, in this paper, is that a look-up table is designed by employing the obtained values from the genetic algorithm in order to minimize the performance index and by using this data base, rule bases are designed for the ANFIS controller and will be exerted on the actuators to enhance the tipover stability of the mobile manipulator. A numerical example is presented to demonstrate the effectiveness of the proposed algorithm.

Keywords: Mobile Manipulator, Tipover Stability Enhancement, Adaptive Neuro-Fuzzy Inference Controller System, Soft Computing.

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Authors: R. Tur, A. Yardımcı

Abstract:

Imperfect knowledge cannot be avoided all the time. Imperfections may have several forms; uncertainties, imprecision and incompleteness. When we look to classification of methods for the management of imperfect knowledge we see fuzzy set-based techniques. The choice of a method to process data is linked to the choice of knowledge representation, which can be numerical, symbolic, logical or semantic and it depends on the nature of the problem to be solved for example decision support, which will be mentioned in our study. Fuzzy Logic is used for its ability to manage imprecise knowledge, but it can take advantage of the ability of neural networks to learn coefficients or functions. Such an association of methods is typical of so-called soft computing. In this study a new method was used for the management of imprecision for collected knowledge which related to economic analysis of construction industry in Turkey. Because of sudden changes occurring in economic factors decrease competition strength of construction companies. The better evaluation of these changes in economical factors in view of construction industry will made positive influence on company-s decisions which are dealing construction.

Keywords: Fuzzy logic, decision support systems, construction industry.

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Authors: Mohd Ariff Admon, Abdul Rahman Mohd Kasim, Sharidan Shafie

Abstract:

This paper considers the effect of heat generation proportional l to (T - T∞ )p , where T is the local temperature and T∞ is the ambient temperature, in unsteady free convection flow near the stagnation point region of a three-dimensional body. The fluid is considered in an ambient fluid under the assumption of a step change in the surface temperature of the body. The non-linear coupled partial differential equations governing the free convection flow are solved numerically using an implicit finite-difference method for different values of the governing parameters entering these equations. The results for the flow and heat characteristics when p ≤ 2 show that the transition from the initial unsteady-state flow to the final steadystate flow takes place smoothly. The behavior of the flow is seen strongly depend on the exponent p.

Keywords: Free convection, Boundary layer flow, Stagnationpoint, Heat generation

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Authors: Xiangbin Zhu

Abstract:

EDF (Early Deadline First) algorithm is a very important scheduling algorithm for real- time systems . The EDF algorithm assigns priorities to each job according to their absolute deadlines and has good performance when the real-time system is not overloaded. When the real-time system is overloaded, many misdeadlines will be produced. But these misdeadlines are not uniformly distributed, which usually focus on some tasks. In this paper, we present an adaptive fuzzy control scheduling based on EDF algorithm. The improved algorithm can have a rectangular distribution of misdeadline ratios among all real-time tasks when the system is overloaded. To evaluate the effectiveness of the improved algorithm, we have done extensive simulation studies. The simulation results show that the new algorithm is superior to the old algorithm.

Keywords: Fuzzy control, real-time systems, EDF, misdeadline ratio.

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Authors: I. Kruashvili, I. Inashvili, K. Bziava, M. Lomishvili

Abstract:

Seepage capillary anomalies in the active layer of soil, related to the soil water movement, often cause variation of soil hydrophysical properties and become one of the main objectives of the hydroecology. It is necessary to mention that all existing equations for computing the seepage flow particularly from soil channels, through dams, bulkheads, and foundations of hydraulic engineering structures are preferable based on the linear seepage law. Regarding the existing beliefs, anomalous seepage is based on postulates according to which the fluid in free volume is characterized by resistance against shear deformation and is presented in the form of initial gradient. According to the above-mentioned information, we have determined: Equation to calculate seepage coefficient when the velocity of transition flow is equal to seepage flow velocity; by means of power function, equations for the calculation of average and maximum velocities of seepage flow have been derived; taking into consideration the fluid continuity condition, average velocity for calculation of average velocity in capillary tube has been received.

Keywords: Seepage, soil, velocity, water.

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Authors: Masrour Dowlatabadi, Jalil Shirazi

Abstract:

In this paper, an improved edge detection algorithm based on fuzzy combination of mathematical morphology and wavelet transform is proposed. The combined method is proposed to overcome the limitation of wavelet based edge detection and mathematical morphology based edge detection in noisy images. Experimental results show superiority of the proposed method, as compared to the traditional Prewitt, wavelet based and morphology based edge detection methods. The proposed method is an effective edge detection method for noisy image and keeps clear and continuous edges.

Keywords: Edge detection, Wavelet transform, Mathematical morphology, Fuzzy logic.

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Authors: V. V. Zozulya

Abstract:

New theory for functionally graded (FG) shell based on expansion of the equations of elasticity for functionally graded materials (GFMs) into Legendre polynomials series has been developed. Stress and strain tensors, vectors of displacements, traction and body forces have been expanded into Legendre polynomials series in a thickness coordinate. In the same way functions that describe functionally graded relations has been also expanded. Thereby all equations of elasticity including Hook-s law have been transformed to corresponding equations for Fourier coefficients. Then system of differential equations in term of displacements and boundary conditions for Fourier coefficients has been obtained. Cases of the first and second approximations have been considered in more details. For obtained boundary-value problems solution finite element (FE) has been used of Numerical calculations have been done with Comsol Multiphysics and Matlab.

Keywords: Shell, FEM, FGM, legendre polynomial.

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Authors: Dursun M., Koc F., Ozbay H.

Abstract:

In this study, a double-sided linear switched reluctance motor (LSRM) drive was investigated as an alternative actuator for vertical linear transportation applications such as a linear elevator door, hospital and subway doors which move linearly and where accurate position control and rapid response is requested. A prototype sliding elevator door that is focused on a home elevator with LSRMs is designed. The motor has 6/4 poles, 3 phases, 8A, 24V, 250 W and 250 N pull forces. Air gap between rotor and translator poles of the designed motor and phase coil-s ideal inductance profile are obtained in compliance with the geometric dimensions. Operation and switching sections as motor and generator has been determined from the inductance profile.

Keywords: Linear switched reluctance motor, sliding door, elevator door, linear motor design.

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Authors: Triloksingh G. Arora, Mohan V. Aware, Dhananjay R. Tutakne

Abstract:

Thyristor based firing angle controlled voltage regulators are extensively used for speed control of single phase induction motors. This leads to power saving but the applied voltage and current waveforms become non-sinusoidal. These non-sinusoidal waveforms increase voltage and thermal stresses which result into accelerated insulation aging, thus reducing the motor life. Life models that allow predicting the capability of insulation under such multi-stress situations tend to be very complex and somewhat impractical. This paper presents the fuzzy logic application to investigate the synergic effect of voltage and thermal stresses on intrinsic aging of induction motor insulation. A fuzzy expert system is developed to estimate the life of induction motor insulation under multiple stresses. Three insulation degradation parameters, viz. peak modification factor, wave shape modification factor and thermal loss are experimentally obtained for different firing angles. Fuzzy expert system consists of fuzzyfication of the insulation degradation parameters, algorithms based on inverse power law to estimate the life and defuzzyficaton process to output the life. An electro-thermal life model is developed from the results of fuzzy expert system. This fuzzy logic based electro-thermal life model can be used for life estimation of induction motors operated with non-sinusoidal voltage and current waveforms.

Keywords: Aging, Dielectric losses, Insulation and Life Estimation.

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Authors: Bo-Wei Song, Yun-Jung Lee

Abstract:

This paper presents an intention interface and controller for a wire-driven heavy object lifting system that assists the operator with moving a heavy object. The handler is designed to allow a comfortable working posture for the operator. Plus, as a human assistive system, the operator is involved in the control loop, where a fuzzy control system is used to consider the human control characteristics. The effectiveness and performance of the proposed system are proved by experiments.

Keywords: Fuzzy controller, Handler design, Heavy object lifting system, Human-assistive device, Human-in-the-loop system.

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Authors: Devdutt

Abstract:

An active quarter car model with three degrees of freedom is presented for vibration reduction of passenger seat. The designed Fuzzy Logic Controller (FLC) and Self-Tuning Fuzzy Logic Controller (STFLC) are applied in seat suspension. Vibration control performance of active and passive quarter car systems are determined using simulation work. Simulation results in terms of passenger seat acceleration and displacement responses are compared for controlled and uncontrolled cases. Simulation results showed the improved results of both FLC and STFLC controllers in improving passenger ride comfort compared to uncontrolled case. Furthermore, the best performance in simulation studies is achieved by STFLC controlled suspension system compared to FLC controlled and uncontrolled cases.

Keywords: Active suspension system, quarter car model, passenger ride comfort, self-tuning fuzzy logic controller.

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Authors: Shuenn-Yih Chang, Chiu-Li Huang

Abstract:

Three structure-dependent integration methods have been developed for solving equations of motion, which are second-order ordinary differential equations, for structural dynamics and earthquake engineering applications. Although they generally have the same numerical properties, such as explicit formulation, unconditional stability and second-order accuracy, a different performance is found in solving the free vibration response to either linear elastic or nonlinear systems with high frequency modes. The root cause of this different performance in the free vibration responses is analytically explored herein. As a result, it is verified that a weak instability is responsible for the different performance of the integration methods. In general, a weak instability will result in an inaccurate solution or even numerical instability in the free vibration responses of high frequency modes. As a result, a weak instability must be prohibited for time integration methods.

Keywords: Dynamic analysis, high frequency, integration method, overshoot, weak instability.

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Authors: Anupma Bansal

Abstract:

We seek exact solutions of the coupled Klein-Gordon-Schrödinger equation with variable coefficients with the aid of Lie classical approach. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of coupled Klein-Gordon-Schrödinger equations involving some special functions such as Airy wave functions, Bessel functions, Mathieu functions etc.

Keywords: Klein-Gordon-Schödinger Equation, Lie Classical Method, Exact Solutions

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Authors: Suraiya Jabin, Kamal K. Bharadwaj

Abstract:

This research presents a system for post processing of data that takes mined flat rules as input and discovers crisp as well as fuzzy hierarchical structures using Learning Classifier System approach. Learning Classifier System (LCS) is basically a machine learning technique that combines evolutionary computing, reinforcement learning, supervised or unsupervised learning and heuristics to produce adaptive systems. A LCS learns by interacting with an environment from which it receives feedback in the form of numerical reward. Learning is achieved by trying to maximize the amount of reward received. Crisp description for a concept usually cannot represent human knowledge completely and practically. In the proposed Learning Classifier System initial population is constructed as a random collection of HPR–trees (related production rules) and crisp / fuzzy hierarchies are evolved. A fuzzy subsumption relation is suggested for the proposed system and based on Subsumption Matrix (SM), a suitable fitness function is proposed. Suitable genetic operators are proposed for the chosen chromosome representation method. For implementing reinforcement a suitable reward and punishment scheme is also proposed. Experimental results are presented to demonstrate the performance of the proposed system.

Keywords: Hierarchical Production Rule, Data Mining, Learning Classifier System, Fuzzy Subsumption Relation, Subsumption matrix, Reinforcement Learning.

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Authors: G. Büyüközkan , O. Feyzioglu, Z. Vardaloglu

Abstract:

Collaborative planning, forecasting and replenishment (CPFR) coordinates the various supply chain management activities including production and purchase planning, demand forecasting and inventory replenishment between supply chain trading partners. This study proposes a systematic way of analyzing CPFR supporting factors using fuzzy cognitive map (FCM) approach. FCMs have proven particularly useful for solving problems in which a number of decision variables and uncontrollable variables are causally interrelated. Hence the FCMs of CPFR are created to show the relationships between the factors that influence on effective implementation of CPFR in the supply chain.

Keywords: Collaborative planning, forecasting and replenishment, fuzzy cognitive map, information sharing, decision synchronization, incentive alignment.

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Authors: M. S. Osman, A. A. Tharwat, I. A. El-Khodary, A. G. Chalabi

Abstract:

In this paper, we propose a multiple objective optimization model with respect to portfolio selection problem for investors looking forward to diversify their equity investments in a number of equity markets. Based on Markowitz-s M-V model we developed a Fuzzy Mixed Integer Multi-Objective Nonlinear Programming Problem (FMIMONLP) to maximize the investors- future gains on equity markets, reach the optimal proportion of the budget to be invested in different equities. A numerical example with a comprehensive analysis on artificial data from several equity markets is presented in order to illustrate the proposed model and its solution method. The model performed well compared with the deterministic version of the model.

Keywords: Equity Markets, Future Scenarios, PortfolioSelection, Multiple Criteria Fuzzy Optimization

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Authors: T. Yamaguchi, Y. Kurosawa, S. Maruyama, K. Tobita, Y. Hirano, K. Yokouchi, K. Kihara, T. Sunaga

Abstract:

This paper describes dynamic analysis using proposed fast finite element method for a shock absorbing structure including a sponge. The structure is supported by nonlinear concentrated springs. The restoring force of the spring has cubic nonlinearity and linear hysteresis damping. To calculate damping properties for the structures including elastic body and porous body, displacement vectors as common unknown variable are solved under coupled condition. Under small amplitude, we apply asymptotic method to complex eigenvalue problem of this system to obtain modal parameters. And then expressions of modal loss factor are derived approximately. This approach was proposed by one of the authors previously. We call this method as Modal Strain and Kinetic Energy Method (MSKE method). Further, using the modal loss factors, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled equations using normal coordinate corresponding to linear natural modes. This transformation yields computation efficiency. As a numerical example of a shock absorbing structures, we adopt double skins with a sponge. The double skins are supported by nonlinear concentrated springs. We clarify influences of amplitude of the input force on nonlinear and chaotic responses.

Keywords: Dynamic response, Nonlinear and chaotic motions, Finite Element analysis, Numerical analysis.

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