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Finite Element Analysis of Rotating Beams: Physics Based Interpolation 1st ed. 2017 [Kõva köide]

  • Formaat: Hardback, 283 pages, kõrgus x laius: 235x155 mm, kaal: 6215 g, 19 Illustrations, color; 89 Illustrations, black and white; XII, 283 p. 108 illus., 19 illus. in color., 1 Hardback
  • Sari: Foundations of Engineering Mechanics
  • Ilmumisaeg: 17-Aug-2016
  • Kirjastus: Springer Verlag, Singapore
  • ISBN-10: 9811019010
  • ISBN-13: 9789811019012
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  • Formaat: Hardback, 283 pages, kõrgus x laius: 235x155 mm, kaal: 6215 g, 19 Illustrations, color; 89 Illustrations, black and white; XII, 283 p. 108 illus., 19 illus. in color., 1 Hardback
  • Sari: Foundations of Engineering Mechanics
  • Ilmumisaeg: 17-Aug-2016
  • Kirjastus: Springer Verlag, Singapore
  • ISBN-10: 9811019010
  • ISBN-13: 9789811019012
Teised raamatud teemal:
This book addresses the solution of rotating beam free-vibration problems using the finite element method. It provides an introduction to the governing equation of a rotating beam, before outlining the solution procedures using Rayleigh-Ritz, Galerkin and finite element methods. The possibility of improving the convergence of finite element methods through a judicious selection of interpolation functions, which are closer to the problem physics, is also addressed.
 
The book offers a valuable guide for students and researchers working on rotating beam problems – important engineering structures used in helicopter rotors, wind turbines, gas turbines, steam turbines and propellers – and their applications. It can also be used as a textbook for specialized graduate and professional courses on advanced applications of finite element analysis.

Arvustused

This book provides an introduction to finite elements for rotating beam problems. This book can be useful to engineers, graduate students and researchers working on rotating beam problems. (V. Leontiev, zbMATH 1369.74001, 2017)

1 Introduction
1(62)
1.1 Introduction
1(11)
1.1.1 Elastic Blade
1(4)
1.1.2 Horizontal Force Equilibrium
5(1)
1.1.3 Boundary Conditions
5(1)
1.1.4 Initial Conditions
5(1)
1.1.5 Cantilever Beam Vibrations (Non-rotating)
6(4)
1.1.6 Beam Functions
10(1)
1.1.7 Rotating Beam Vibration
11(1)
1.2 Galerkin Method
12(6)
1.3 Rayleigh--Ritz Method
18(21)
1.4 Finite Element Method
39(24)
1.4.1 Element Properties
40(2)
1.4.2 Energy Expressions
42(3)
1.4.3 Assembly of Elements
45(3)
1.4.4 Cantilever
48(15)
2 Stiff String Basis Functions
63(26)
2.1 Stiff String Equation
63(2)
2.2 Stiff String Basis Functions
65(3)
2.3 Uniform Rotating Beam
68(1)
2.4 Tapered Rotating Beam
69(3)
2.5 Hybrid Basis Functions
72(5)
2.6 Finite Element
77(5)
2.6.1 Uniform Rotating Beam
79(3)
2.7 Tapered Rotating Beam
82(5)
2.8 Summary
87(2)
References
88(1)
3 Rational Interpolation Functions
89(18)
3.1 Governing Differential Equation
89(2)
3.2 Hermite Shape Functions
91(2)
3.3 New Shape Functions
93(2)
3.4 Static Finite Element Analysis
95(3)
3.5 Dynamic Finite Element Analysis
98(6)
3.5.1 Uniform Beam
98(2)
3.5.2 Tapered Rotating Beam
100(4)
3.6 Summary
104(3)
References
105(2)
4 Fourier-p Superelement
107(14)
4.1 Governing Equation of Rotating Beams
108(1)
4.2 Shape Functions
109(2)
4.3 Superelement Matrices
111(1)
4.4 Numerical Results
111(7)
4.4.1 Uniform Rotating Beam
112(1)
4.4.2 Tapered Rotating Beam
112(6)
4.5 Summary
118(3)
References
118(3)
5 Physics Based Basis Functions
121(22)
5.1 Basis Function
122(7)
5.2 Finite Element Analysis
129(1)
5.3 Numerical Results
130(8)
5.3.1 Uniform Beam
130(4)
5.3.2 Tapered Beam
134(3)
5.3.3 Beams with Hub Offset
137(1)
5.4 Summary
138(5)
References
141(2)
6 Collocation Approach
143(28)
6.1 Governing Differential Equation
143(3)
6.2 Point Collocation Approach
146(14)
6.2.1 Collocation Point at a Variable Location Within Beam Element
146(3)
6.2.2 Collocation Point Near the Left Node of Beam Element
149(1)
6.2.3 Collocation Point at the Midpoint of Beam Element
150(2)
6.2.4 Collocation Point Near the Right Node of Beam Element
152(1)
6.2.5 Two Point Collocation
153(5)
6.2.6 Analysis of Shape Functions
158(2)
6.3 Finite Element Formulation
160(2)
6.4 Numerical Results
162(7)
6.4.1 Uniform Rotating Beam
162(4)
6.4.2 Tapered Rotating Beam
166(3)
6.5 Summary
169(2)
References
169(2)
7 Rotor Blade Finite Element
171(34)
7.1 Energy Expressions
173(2)
7.2 Governing Differential Equations
175(2)
7.3 Derivation of the Shape Functions
177(9)
7.3.1 Shape Functions for Flapwise Bending
179(2)
7.3.2 Shape Functions for Lead-Lag Bending
181(2)
7.3.3 Shape Functions for Axial Deflection
183(1)
7.3.4 Shape Functions for Torsion
184(2)
7.4 Finite Element Method
186(1)
7.5 Numerical Results
186(8)
7.5.1 Analysis of Shape Functions
186(8)
7.5.2 Validation Study
194(1)
7.6 Convergence Study of New FEM Element and Polynomials
194(4)
7.7 Summary
198(7)
Appendix 1
200(2)
References
202(3)
8 Spectral Finite Element Method
205(24)
8.1 Governing Differential Equation
206(1)
8.2 Spectral Finite Element Formulation
207(4)
8.2.1 Interpolating Function for SFER
208(1)
8.2.2 Interpolating Function for SFEN
208(1)
8.2.3 Dynamic Stiffness Matrix in Frequency Domain
209(2)
8.3 Free Vibration Results
211(8)
8.3.1 Uniform Beam
211(3)
8.3.2 Tapered Beam 1-Linear Mass and Cubic Flexural Stiffness Variation
214(2)
8.3.3 Tapered Beam 2-Linear Mass and Flexural Stiffness Variation
216(3)
8.4 Wave Propagation Study
219(6)
8.4.1 Convergence Study
219(2)
8.4.2 Numerical Results
221(4)
8.5 Summary
225(4)
References
226(3)
9 Violin String Shape Functions
229(22)
9.1 Timoshenko Rotating Beam and Violin String
230(4)
9.2 Violin String Shape Functions
234(6)
9.3 Results and Discussion
240(8)
9.3.1 Uniform Beam
240(2)
9.3.2 Tapered Beam
242(6)
9.4 Summary
248(3)
References
249(2)
Appendix A Stiffness Matrix 251(22)
Appendix B MATLAB Code 273(6)
Appendix C Governing Equation for Rotating Timoshenko Beam 279
Prof. Ranjan Ganguli obtained his M.S. and PhD in Aerospace Engineering from the University of Maryland, College Park, in 1991 and 1994, respectively, and his B.Tech degree in Aerospace Engineering from the Indian Institute of Technology, Kharagpur, in 1989.  Following his PhD, he worked at the Alfred Gessow Rotorcraft Center of the University of Maryland as Assistant Research Scientist until 1997 on projects on rotorcraft health monitoring and vibratory load validation for the Naval Surface Warfare Center and United Technology Research Center, respectively. He also worked at the GE Research Lab in Schenectady, New York, and at Pratt and Whitney, East Hartford, Connecticut, from 1997 to 2000. He joined the Aerospace Engineering department of the Indian Institute of Science, Bangalore, as Assistant Professor in July 2000. He was promoted to Associate Professor in 2005 and to Full Professor in 2009. He is currently the Satish Dhawan Chair Professorat the Indian Institute of Science, Bangalore. He has held visiting positions at TU Braunschweig, University of Ulm and Max Planck Institute of Metal Research, Stuttgart, in Germany; University Paul Sabatier and Institute of Mathematics, in Toulouse, France; Konkuk University in South Korea, the University of Michigan, Ann Arbor, in USA, and the Nanyang Technological University, Singapore. Prof. Ganguli's research interests are in helicopter aeromechanics, aeroelasticity, structural dynamics, composite and smart structures, design optimization, finite element methods and health monitoring. He has published 178 articles in refereed journals and over 100 conference papers.  He was awarded the American Society of Mechanical Engineers (ASME) best paper award in 2001, the Golden Jubilee award of the Aeronautical Society of India in 2002, the Alexander von Humboldt fellowship in 2007 and the Fulbright Senior Research fellowship in 2010. Prof. Ganguli is a Fellow ofthe ASME, a Fellow of the Royal Aeronautical Society, UK, a Fellow of the Indian National Academy of Engineering, a Fellow of the Aeronautical Society of India, an Associate Fellow of the American Institute of Aeronautics and Astronautics and a Senior Member of the Institute of Electrical and Electronic Engineers (IEEE).  He has taught courses on flight and space mechanics, engineering optimization, helicopter dynamics, aircraft structures, structural mechanics, aeroelasticity and navigation. He has supervised the thesis of 15 PhD and 35 Masters degree students. He has written books on Engineering Optimization and Gas Turbine Diagnostics, both published by CRC Press, New York, and books titled Structural Damage Detection using Genetic Fuzzy Systems and Smart Helicopter Rotors,  published by Springer.