한국지진공학회 추계학술발표회 IMPROVED SENSITIVITY METHOD FOR NATURAL FREQUENCY AND MODE SHAPE OF DAMPED SYSTEM Hong-Ki Jo1), *Man-Gi Ko2) and In-Won Lee3) 1) Graduate.

Slides:

Advertisements

Similar presentations

1 Department of Civil and Environmental Engineering Sungkyunkwan University 비대칭 박벽보의 개선된 해석이론 및 방법 An Improved Theory and Analysis Procedures of Nonsymmetric.

Advertisements

MDOF SYSTEMS WITH DAMPING General case Saeed Ziaei Rad.

Sensitivity of Eigenproblems Review of properties of vibration and buckling modes. What is nice about them? Sensitivities of eigenvalues are really cheap!

Multi-degree-of-freedom System Shock Response Spectrum

Mar Numerical approach for large-scale Eigenvalue problems 1 Definition Why do we study it ? Is the Behavior system based or nodal based? What are.

M M S S V V 0 Free vibration analysis of a circular plate with multiple circular holes by using addition theorem and direct BIEM Wei-Ming Lee 1, Jeng-Tzong.

Unit 6: Structural vibration An Introduction to Mechanical Engineering: Part Two Structural vibration Learning summary By the end of this chapter you should.

1 Adjoint Method in Network Analysis Dr. Janusz A. Starzyk.

TWO DEGREE OF FREEDOM SYSTEM. INTRODUCTION Systems that require two independent coordinates to describe their motion; Two masses in the system X two possible.

1 Assessment of Imprecise Reliability Using Efficient Probabilistic Reanalysis Farizal Efstratios Nikolaidis SAE 2007 World Congress.

Differential Equations

Solution of Eigenproblem of Non-Proportional Damping Systems by Lanczos Method In-Won Lee, Professor, PE In-Won Lee, Professor, PE Structural Dynamics.

Yeong-Jong Moon*: Graduate Student, KAIST, Korea Kang-Min Choi: Graduate Student, KAIST, Korea Hyun-Woo Lim: Graduate Student, KAIST, Korea Jong-Heon Lee:

Algorithms for a large sparse nonlinear eigenvalue problem Yusaku Yamamoto Dept. of Computational Science & Engineering Nagoya University.

1 PSSC Mode Localization in Multispan Beams with Massive and Stiff Couplers on Supports Dong-Ok Kim and In-Won Lee Department of Civil Engineering.

1 SIMULATION OF VIBROACOUSTIC PROBLEM USING COUPLED FE / FE FORMULATION AND MODAL ANALYSIS Ahlem ALIA presented by Nicolas AQUELET Laboratoire de Mécanique.

1 Efficient Mode Superposition Methods for Non-Classically Damped System Sang-Won Cho, Graduate Student, KAIST, Korea Ju-Won Oh, Professor, Hannam University,

In-Won Lee, Professor, PE In-Won Lee, Professor, PE Structural Dynamics & Vibration Control Lab. Structural Dynamics & Vibration Control Lab. Korea Advanced.

© 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the.

Structural Dynamics & Vibration Control Lab. 1 Kang-Min Choi, Ph.D. Candidate, KAIST, Korea Jung-Hyun Hong, Graduate Student, KAIST, Korea Ji-Seong Jo,

Progress in identification of damping: Energy-based method with incomplete and noisy data Marco Prandina University of Liverpool.

MECH 391 Instrumentation Lab 9 Vibration Analysis of an Aluminum Cantilever Beam Performed: 03/15/04 Sinan Ozcan : I believe I performed 100% of this lab.

Professor Walter W. Olson Department of Mechanical, Industrial and Manufacturing Engineering University of Toledo System Solutions y(t) t +++++… 11 22.

1 MODELING MATTER AT NANOSCALES 4. Introduction to quantum treatments The variational method.

Diagonalization and Similar Matrices In Section 4.2 we showed how to compute eigenpairs (,p) of a matrix A by determining the roots of the characteristic.

* 김 만철, 정 형조, 박 선규, 이 인원 * 김 만철, 정 형조, 박 선규, 이 인원 구조동역학 및 진동제어 연구실 구조동역학 및 진동제어 연구실 한국과학기술원 토목공학과 중복 또는 근접 고유치를 갖는 비비례 감쇠 구조물의 자유진동 해석 1998 한국전산구조공학회 가을.

Computational Structural Engineering Institute Autumn Conference 2002 Oct , 2002 VIBRATION CONTROL OF BRIDGE FOR SERVICEABILITY Jun-Sik Ha 1),

ECE 576 – Power System Dynamics and Stability Prof. Tom Overbye University of Illinois at Urbana-Champaign 1 Lecture 26: Modal Analysis,

What is the determinant of What is the determinant of

Hong-Ki Jo 1), Man-Gi Ko 2) and * In-Won Lee 3) 1) Graduate Student, Dept. of Civil Engineering, KAIST 2) Professor, Dept. of Civil Engineering, Kongju.

HEAT TRANSFER FINITE ELEMENT FORMULATION

*Man-Cheol Kim, Hyung-Jo Jung and In-Won Lee *Man-Cheol Kim, Hyung-Jo Jung and In-Won Lee Structural Dynamics & Vibration Control Lab. Structural Dynamics.

Yeong-Jong Moon 1), Jong-Heon Lee 2) and In-Won Lee 3) 1) Graduate Student, Department of Civil Engineering, KAIST 2) Professor, Department of Civil Engineering,

ME 440 Intermediate Vibrations Th, April 16, 2009 Chapter 6: Multi-degree of Freedom (MDOF) Systems © Dan Negrut, 2009 ME440, UW-Madison Quote of the Day:

Derivatives of static response from linear finite element analysis Local search algorithms benefit from derivatives even when they are calculated by finite.

대한토목공학회 추계 학술발표회 대구 2003 년 10 월 24 일 T. X. Nguyen, 한국과학기술원 건설 및 환경공학과 박사과정 김병완, 한국과학기술원 건설 및 환경공학과 박사후연구원 정형조, 세종대학교 토목환경공학과 교수 이인원, 한국과학기술원 건설 및 환경공학과.

* In-Won Lee 1), Sun-Kyu Park 2) and Hong-Ki Jo 3) 1) Professor, Department of Civil Engineering, KAIST 2) Professor, Department of Civil Engineering,

STATIC ANALYSIS OF UNCERTAIN STRUCTURES USING INTERVAL EIGENVALUE DECOMPOSITION Mehdi Modares Tufts University Robert L. Mullen Case Western Reserve University.

모달변위를 이용한 지진하중을 받는 구조물의 능동 신경망제어 2004 년도 한국전산구조공학회 춘계 학술발표회 국민대학교 2004 년 4 월 10 일 이헌재, 한국과학기술원 건설및환경공학과 박사과정 정형조, 세종대학교 토목환경공학과 조교수 이종헌, 경일대학교 토목공학과 교수.

RELIABLE DYNAMIC ANALYSIS OF TRANSPORTATION SYSTEMS Mehdi Modares, Robert L. Mullen and Dario A. Gasparini Department of Civil Engineering Case Western.

Yeong-Jong Moon 1), Sun-Kyu Park Lee 2) and In-Won Lee 3) 1) Graduate Student, Department of Civil Engineering, KAIST 2) Professor, Department of Civil.

ECE 576 – Power System Dynamics and Stability Prof. Tom Overbye University of Illinois at Urbana-Champaign 1 Lecture 23: Small Signal.

By Dr. A. Ranjbaran, Associate Professor

Dynamic Analysis of Structures by

error-driven local adaptivity in elasto-dynamics

OSE801 Engineering System Identification Spring 2010

Dynamic Response of MDOF Structures

VIBRATION CONTROL OF STRUCTURE USING CMAC

Chapter 4 Multiple Degree of Freedom Systems

Dr-Ing Asrat Worku, AAIT

Modal Control for Seismically Excited Structures using MR Damper

Chapter 2 Interconnect Analysis

LOCATION AND IDENTIFICATION OF DAMPING PARAMETERS

1C9 Design for seismic and climate changes

A BRIDGE WITH VEHICLE LOADS

ADVANCED VIBRATION Lecture #1 Asst. Prof. Dr. Mahir Hameed Majeed ©2018.

중복근을 갖는 감쇠 시스템의 고유진동수와 모드의 고차 민감도 해석

DCT-based Processing of Dynamic Features for Robust Speech Recognition Wen-Chi LIN, Hao-Teng FAN, Jeih-Weih HUNG Wen-Yi Chu Department of Computer Science.

한국지진공학회 춘계 학술발표회 서울대학교 호암교수관 2003년 3월 14일

Structural Optimization Design ( Structural Analysis & Optimization )

SKTN 2393 Numerical Methods for Nuclear Engineers

Modelling and identification of damping in aero-structures ECERTA Project Liverpool 26 November 2007 Marco Prandina.

Modified Sturm Sequence Property for Damped Systems

ISEC-02 Second International Conference on Structural Engineering and Construction Algebraic Method for Sensitivity Analysis of Eigensystems with Repeated.

Simplified Algebraic Method

Modified Sturm Sequence Property for Damped Systems

ECE 576 POWER SYSTEM DYNAMICS AND STABILITY

Modified Modal Methods in Asymmetric Systems

MULTI DEGREE OF FREEDOM (M-DOF)

November 5, 2002 SE 180 Final Project.

Presentation transcript:

한국지진공학회 추계학술발표회 IMPROVED SENSITIVITY METHOD FOR NATURAL FREQUENCY AND MODE SHAPE OF DAMPED SYSTEM Hong-Ki Jo1), *Man-Gi Ko2) and In-Won Lee3) 1) Graduate Student, Department of Civil Engineering, KAIST 2) Professor, Department of Civil Engineering, KongJu National Univ. 3) Professor, Department of Civil Engineering, KAIST

OUTLINE INTRODUCTION PREVIOUS STUDIES PROPOSED METHOD NUMERICAL EXAMPLE CONCLUSIONS

INTODUCTION Objective of Study Applications of Sensitivity Analysis - To find the derivatives of eigenvalues and eigenvectors of damped systems with respect to design variables. Applications of Sensitivity Analysis - Determination of the sensitivity of dynamic responses - Optimization of natural frequencies and mode shapes - Optimization of structures subject to natural frequencies. - Stability of structures - Reanalysis of modified structures

Problem Definition - Eigenvalue problem of damped system (1)

- State space equation (2) - Orthonormalization condition (3)

- Objective Given: Find: * indicates derivatives with respect to design variables (length, area, moment of inertia, etc.)

PREVIOUS STUDIES Z. Zimoch, “Sensitivity Analysis of Vibrating Systems,” Journal of Sound and Vibration, Vol. 117, pp. 447-458, 1987. (4) - restricted to lumped systems with distinct eigenvalues.

Q. H. Zeng, “Highly Accurate Modal Method for Calculating Eigenvector Derivatives in Viscous Damping System,” AIAA Journal, Vol. 33, No. 4, pp. 746-751, 1995. (5) (6) - many eigenvectors are required to calculate eigenvector derivatives.

Sondipon Adhikari, “Calculation of Derivative of Complex Modes Using Classical Normal Modes,” Computer & Structures, Vol. 77, No. 6, pp. 625-633, 2000. (7) - applicable only when the elements of C are small.

I. W. Lee, D. O. Kim and G. H. Jung, “Natural Frequency and Mode Shape Sensitivities of Damped Systems: part I, Distinct Natural Frequencies,” Journal of Sound and Vibration, Vol. 223, No. 3, pp. 399-412, 1999. I. W. Lee, D. O. Kim and G. H. Jung, “Natural Frequency and Mode Shape Sensitivities of Damped Systems: part II, Multiple Natural Frequencies,” Journal of Sound and Vibration, Vol. 223, No. 3, pp. 413-424, 1999.

Lee’s method (1999) (8) (9) - eigenvalue and eigenvector derivatives are obtained separately.

PROPOSED METHOD Rewriting basic equations - Eigenvalue problem (10) - Orthonormalization condition (11)

Differentiating eq.(10) with respect to design variable (12) Differentiating eq.(11) with respect to design variable (13)

- the coefficient matrix is symmetric and non-singular. Combining eq.(12) and eq.(13) into a single matrix (14) - the coefficient matrix is symmetric and non-singular. eigenpair derivatives are obtained simultaneously. corresponding eigenpair only is required.

Numerical Stability The determinant property (15)

Then (16)

Arranging eq.(16) (17) Using the determinant property of partitioned matrix (18)

Numerical Stability is Guaranteed. Therefore (19) Numerical Stability is Guaranteed.

NUMERICAL EXAMPLE Cantilever Beam

Analysis Methods Comparisons Lee’s method (1999) Proposed method Solution time (CPU)

Eigenvalue derivative Results of Analysis (Eigenvalue) Mode Number Eigenvalue Eigenvalue derivative (Lee’s method) (Proposed method) 1 -0.001 - 2.625i -0.014 -52.496i 2 -0.001 + 2.625i -0.014 +52.496i 3 -0.014 -16.449i -5.411e-1 -3.290e+2i 4 -0.014 +16.449i -5.411e-1+3.290e+2i 5 -0.035 -26.236i 4.770e-7 -2.970e-8i 6 -0.035 +26.236i 4.770e-7 +2.970e-8i 7 -0.106 -46.056i -4.242e+0 -9.210e+2i 8 -0.106 +46.056i -4.242e+0+9.210e+2i 9 -0.407 -90.244i -1.628e+1 -1.804e+3i 10 -0.407 +90.244i -1.628e+1+1.804e+3i Same

Eigenvector derivative Results of Analysis (First eigenvector) DOF number Eigenvector Eigenvector derivative (Lee’s method) (Proposed method) 1 2 3 1.513e-05 +1.513e-05i -3.027e-04 -3.027e-04i 4 1.204e-04 +1.204e-04i -0.002 - 0.002i 5  157 158 159 0.014 + 0.014i -0.279 - 0.279i 160 0.002 + 0.002i -0.038 - 0.038i Same

CPU time for 160 Eigenpairs Method Ratio (sec) Lee’s method (1999) 223.33 1.00 Proposed method 164.89 0.74

Comparison for each operations Total Lee’s method Proposed Method Operations CPU time (sec) 33.89 61.01 47.09 81.34 223.33 53.62 40.60 70.67 164.89

CONCLUSIONS  An efficient eigensensitivity technique ! Proposed method - is simple - guarantees numerical stability - reduces the CPU time.  An efficient eigensensitivity technique !

Future works Proposed method is able to extend to asymmetric non-conservative systems - Needs for comparison with other method in CPU time

Thank you for your attention.

APPENDIX Differentiating eq.(1) with respect to design variable (20) Pre-multiplying each side of eq.(20) by gives eigenvalue derivative. (21)

Lee’s method (1999) Differentiating eq.(3) with respect to design variable (22) Combining eq.(20) and eq.(22) into a matrix gives eigenvector derivative. (23)