Efficient solution of the fuzzy eigenvalue problem in structural dynamics

2014 ◽  
Vol 31 (5) ◽  
pp. 864-878 ◽  
Author(s):  
Yuying Xia ◽  
M. Friswell
Keyword(s):  
Eigenvalue Problem ◽  
Perturbation Method ◽  
Degrees Of Freedom ◽  
Eigenvalue Problems ◽  
Structural Vibration ◽  
Design Problems ◽  
Content Type ◽  
Analysis And Design ◽  
Stiffness Matrices ◽  
Fuzzy Eigenvalues

Purpose – Many analysis and design problems in engineering and science involve uncertainty to varying degrees. This paper is concerned with the structural vibration problem involving uncertain material or geometric parameters, specified as fuzzy parameters. The requirement is to propagate the parameter uncertainty to the eigenvalues of the structure, specified as fuzzy eigenvalues. However, the usual approach is to transform the fuzzy problem into several interval eigenvalue problems by using the α-cuts method. Solving the interval problem as a generalized interval eigenvalue problem in interval mathematics will produce conservative bounds on the eigenvalues. The purpose of this paper is to investigate strategies to efficiently solve the fuzzy eigenvalue problem. Design/methodology/approach – Based on the fundamental perturbation principle and vertex theory, an efficient perturbation method is proposed, that gives the exact extrema of the first-order deviation of the structural eigenvalue. The fuzzy eigenvalue approach has also been improved by reusing the interval analysis results from previous α-cuts. Findings – The proposed method was demonstrated on a simple cantilever beam with a pinned support, and produced very accurate fuzzy eigenvalues. The approach was also demonstrated on the model of a highway bridge with a large number of degrees of freedom. Originality/value – This proposed Vertex-Perturbation method is more efficient than the standard perturbation method, and more general than interval arithmetic methods requiring the non-negative decomposition of the mass and stiffness matrices. The new increment method produces highly accurate solutions, even when the membership function for the fuzzy eigenvalues is complex.

scholarly journals Vibration Analysis of Structures with Rotation and Reflection Symmetry

1996 ◽  
Vol 3 (4) ◽  
pp. 303-311
Author(s):  
Baojian Li ◽  
Xiaozhong Zheng ◽  
Jie Zhao
Keyword(s):  
Theoretical Analysis ◽  
Eigenvalue Problem ◽  
Vibration Analysis ◽  
Group Representation ◽  
Computer Time ◽  
Modal Testing ◽  
Structural Vibration ◽  
Reflection Symmetry ◽  
Analysis Method ◽  
Stiffness Matrices

The article applies group representation theory to the vibration analysis of structures with Cnvsymmetry, and presents a new structural vibration analysis method. The eigenvalue problem of the whole structure is divided into much smaller subproblems by forming the mass and stiffness matrices of one substructure and than modifying them to form mass and stiffness matrices in each irreducible subspace, resulting in the saving of computer time and memory. The modal characteristics of structures with Cnvsymmetry are derived from theoretical analysis. Computation and modal testing are used to verify the validity of the theoretical deductions.

Generalizing of Numerically Solving Methods of Eigenvalue Problems to Asymmetrical, Damping Included Case

2001 ◽  
Author(s):  
Shahram Rezaei
Keyword(s):  
Eigenvalue Problem ◽  
Eigenvalue Problems ◽  
Lanczos Method ◽  
Subspace Method ◽  
Damping Matrix ◽  
Stiffness Matrices

Abstract In this paper, “Subspace” method is generalized to asymmetrical case. In the new algorithm described here, “Lanczos” method is used to find the first subspace and to solve the eigenvalue problem resulted in generalized subspace method. To solve the standard eigenvalue problem developed by “Lanczos” method “Jacoby” method is used. If eigenvalue problem includes damping matrix, that will be imported in new defined mass and stiffness matrices.

On Various Eigenvalue Problem Formulations for Viscously Damped Linear Mechanical Systems

2005 ◽  
Vol 33 (3) ◽  
pp. 235-243
Author(s):  
M. Gürgöze
Keyword(s):  
Eigenvalue Problem ◽  
Degrees Of Freedom ◽  
Eigenvalue Problems ◽  
Mechanical Vibration ◽  
The State ◽  
State Space Method ◽  
Problem Formulations ◽  
Linear Mechanical System ◽  
Definition Of ◽  
Space Method

The state-space method is frequently used to obtain the eigenvalues of a viscously damped linear mechanical system. Differences in the definition of the state vector and auxiliary matrices found in the literature lead to differences in the formulation of the eigenvalue problems and this in turn can cause difficulties for students on mechanical vibration courses. In this study, various eigenvalue problem formulations in different textbooks have been examined, relationships between them have been established and results have been applied to a numerical example of a system with two degrees of freedom.

The Perturbation Method for Stability Analysis of Uncertain Structures

2013 ◽  
Vol 367 ◽  
pp. 302-307
Author(s):  
Chang Rui Ji ◽  
Zao Ni
Keyword(s):  
Stability Analysis ◽  
Eigenvalue Problem ◽  
Perturbation Method ◽  
Stability Problem ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Interval Mathematics ◽  
Stiffness Matrices ◽  
Uncertain Structure ◽  
Uncertain Structures

This paper is concerned with the structural stability problem involving uncertain-but-bounded parameters, specified as bounds on these parameters. This produces interval stand and geometry stiffness matrices, and the problem is transformed into a interval buckling eigenvalue problem in interval mathematics. The perturbation method is proposed to determine the lower and upper bounds on the buckling eigenvalues and due to uncertain-but-bounded parameters. Moreover, the critical load of the uncertain structure can be obtained. The effectiveness of the presented method was demonstrated by comparison with conventional stability theory, using a typical numerical example.

A second-order perturbation method for fuzzy eigenvalue problems

2016 ◽  
Vol 33 (2) ◽  
Author(s):  
Mengwu Guo ◽  
Hongzhi Zhong ◽  
Kuan You
Keyword(s):  
Perturbation Method ◽  
Perturbation Methods ◽  
Eigenvalue Problems ◽  
Second Order ◽  
Order Perturbation ◽  
First Order ◽  
Alpha Level ◽  
Basic Parameters ◽  
Fuzzy Eigenvalues ◽  
Derivatives Of

Purpose For eigenvalue problems containing uncertain inputs characterized by fuzzy basic parameters, first-order perturbation methods have been developed to extract eigen-solutions, but either the result accuracy or the computational efficiency of these methods is less satisfactory. This paper presents an efficient method for estimation of fuzzy eigenvalues with high accuracy. Design/methodology/approach Based on the first order derivatives of eigenvalues and modes with respect to the fuzzy basic parameters, expressions of the second order derivatives of eigenvalues are formulated. Then a second-order perturbation method is introduced to provide more accurate fuzzy eigenvalue solutions. Only one eigenvalue solution is sought for the perturbed formulation, and quadratic programming is performed to simplify the alpha-level optimization. Findings Fuzzy natural frequencies and buckling loads of some structures are estimated with good accuracy, illustrating the high computational efficiency of the proposed method. Originality/value Up to the second order derivatives of the eigenvalues with respect to the basic parameters are represented in functional forms, which are used to introduce a second-order perturbation method for treatment of fuzzy eigenvalue problems. The corresponding alpha-level optimization is thus simplified into quadratic programming. The proposed method provides much more accurate interval solutions at alpha-cuts for the membership functions of fuzzy eigenvalues. Analogously, third- and higher-order perturbation methods can be developed for more stringent accuracy demands or for the treatment of stronger nonlinearity. The present work can be applied to realistic structural analysis in civil engineering, especially for those structures made of dispersed materials such as concrete and soil.

scholarly journals Super-Exponentially Convergent Parallel Algorithm for a Fractional Eigenvalue Problem of Jacobi-Type

2018 ◽  
Vol 18 (1) ◽  
pp. 21-32 ◽  
Author(s):  
Ivan Gavrilyuk ◽  
Volodymyr Makarov ◽  
Nataliia Romaniuk
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Eigenvalue Problems ◽  
Exponential Convergence ◽  
Linear Boundary ◽  
Recursive Procedure ◽  
Content Type ◽  
Numerical Examples ◽  
Discrete Scheme ◽  
Symbolic Algorithm

AbstractA new algorithm for eigenvalue problems for the fractional Jacobi-type ODE is proposed. The algorithm is based on piecewise approximation of the coefficients of the differential equation with subsequent recursive procedure adapted from some homotopy considerations. As a result, the eigenvalue problem (which is in fact nonlinear) is replaced by a sequence of linear boundary value problems (besides the first one) with a singular linear operator called the exact functional discrete scheme (EFDS). A finite subsequence of m terms, called truncated functional discrete scheme (TFDS), is the basis for our algorithm. The approach provides super-exponential convergence rate as {m\to\infty}. The eigenpairs can be computed in parallel for all given indexes. The algorithm is based on some recurrence procedures including the basic arithmetical operations with the coefficients of some expansions only. This is an exact symbolic algorithm (ESA) for {m=\infty} and a truncated symbolic algorithm (TSA) for a finite m. Numerical examples are presented to support the theory.

scholarly journals An automated system analysis and design tool for spacecrafts ceas space journal

2021 ◽  
Author(s):  
Manfred Ehresmann ◽  
Georg Herdrich ◽  
Stefanos Fasoulas
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Degrees Of Freedom ◽  
System Analysis ◽  
Propulsion System ◽  
Optimal System ◽  
Automated System ◽  
Processing Unit ◽  
Data Set ◽  
Analysis And Design

AbstractIn this paper, a generic full-system estimation software tool is introduced and applied to a data set of actual flight missions to derive a heuristic for system composition for mass and power ratios of considered sub-systems. The capability of evolutionary algorithms to analyse and effectively design spacecraft (sub-)systems is shown. After deriving top-level estimates for each spacecraft sub-system based on heuristic heritage data, a detailed component-based system analysis follows. Various degrees of freedom exist for a hardware-based sub-system design; these are to be resolved via an evolutionary algorithm to determine an optimal system configuration. A propulsion system implementation for a small satellite test case will serve as a reference example of the implemented algorithm application. The propulsion system includes thruster, power processing unit, tank, propellant and general power supply system masses and power consumptions. Relevant performance parameters such as desired thrust, effective exhaust velocity, utilised propellant, and the propulsion type are considered as degrees of freedom. An evolutionary algorithm is applied to the propulsion system scaling model to demonstrate that such evolutionary algorithms are capable of bypassing complex multidimensional design optimisation problems. An evolutionary algorithm is an algorithm that uses a heuristic to change input parameters and a defined selection criterion (e.g., mass fraction of the system) on an optimisation function to refine solutions successively. With sufficient generations and, thereby, iterations of design points, local optima are determined. Using mitigation methods and a sufficient number of seed points, a global optimal system configurations can be found.

Workspace, dexterity and dimensional optimization of microhexapod

2015 ◽  
Vol 35 (4) ◽  
pp. 341-347 ◽  
Author(s):  
E. Rouhani ◽  
M. J. Nategh
Keyword(s):  
Degrees Of Freedom ◽  
Optimization Problem ◽  
Screw Theory ◽  
Design Parameters ◽  
Dimensional Synthesis ◽  
Content Type ◽  
Workspace Analysis ◽  
The Difference ◽  
Flexure Joints ◽  
6 Degrees Of Freedom

Purpose – The purpose of this paper is to study the workspace and dexterity of a microhexapod which is a 6-degrees of freedom (DOF) parallel compliant manipulator, and also to investigate its dimensional synthesis to maximize the workspace and the global dexterity index at the same time. Microassembly is so essential in the current industry for manufacturing complicated structures. Most of the micromanipulators suffer from their restricted workspace because of using flexure joints compared to the conventional ones. In addition, the controllability of micromanipulators inside the whole workspace is very vital. Thus, it is very important to select the design parameters in a way that not only maximize the workspace but also its global dexterity index. Design/methodology/approach – Microassembly is so essential in the current industry for manufacturing complicated structures. Most of the micromanipulators suffer from their restricted workspace because of using flexure joints compared to the conventional ones. In addition, the controllability of micromanipulators inside the whole workspace is very vital. Thus, it is very important to select the design parameters in a way that not only maximize the workspace but also its global dexterity index. Findings – It has been shown that the proposed procedure for the workspace calculation can considerably speed the required calculations. The optimization results show that a converged-diverged configuration of pods and an increase in the difference between the moving and the stationary platforms’ radii cause the global dexterity index to increase and the workspace to decrease. Originality/value – The proposed algorithm for the workspace analysis is very important, especially when it is an objective function of an optimization problem based on the search method. In addition, using screw theory can simply construct the homogeneous Jacobian matrix. The proposed methodology can be used for any other micromanipulator.

A design approach for process-based knowledge management systems

2017 ◽  
Vol 21 (4) ◽  
pp. 693-717 ◽  
Author(s):  
Surendra Sarnikar ◽  
Amit V. Deokar
Keyword(s):  
Knowledge Management ◽  
Feasibility Study ◽  
Systems Analysis ◽  
Design Theory ◽  
Systems Design ◽  
Design Approach ◽  
Content Type ◽  
Analysis And Design ◽  
Systems Analysis And Design ◽  
Design Techniques

Purpose This paper presents a design approach for process-based knowledge management (PKM) systems that can support knowledge-intensive processes where effective task execution is highly reliant on the knowledge and expertise of participants executing the tasks. The proposed design approach includes design methods and kernel theories governing the design of PKM systems and can also be easily integrated with existing systems analysis and design techniques. Design/methodology/approach The design science research methodology is used to design and develop the artifact which includes the overall PKM design approach. Information systems design theory is used as a high-level framework to develop and structure the design approach. Relevant design methods and behavioral theories are reviewed to identify kernel theories that guide the design and development of PKM systems. The design approach consists of meta-requirements for PKM systems and design processes to achieve the meta-requirements. A feasibility study is conducted to evaluate the feasibility of the proposed approach. Findings The design approach presented in this paper can guide system analysts and system developers in the design of knowledge management systems for supporting knowledge-intensive processes. The paper also includes a comprehensive design theory for PKM systems consisting of meta-requirements and a synthesis of various kernel theories into actionable design procedures. The proposed procedures include knowledge requirements modeling, knowledge flows modeling and knowledge and process performance modeling procedures. The feasibility study indicates that the PKM approach can be more useful and effective than solely using unified modeling language (UML)-based systems analysis and design techniques for the design of PKM systems. Research limitations/implications An implication to information systems design research is the feasibility of developing a specialized design approach that incorporates significant domain knowledge to solve complex information system design problems. An implication to practice is the significant potential to improve productivity and effectiveness of systems analysts and designers in developing PKM systems. A limitation is the small sample size of the feasibility study used to evaluate the ease of use and utility of the design approach. Originality/value The study makes a unique contribution by proposing a design approach that integrates business process and knowledge management considerations. The approach is particularly valuable because of the focus on integration with existing systems analysis and design techniques, thus allowing for easier adoption.

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