A presentation of the theory behind the Rayleigh-Ritz (R-R)method, as well as a discussion of the choice of admissiblefunctions and the use of penalty methods, including recentdevelopments such as using negative inertia and bi-penaltyterms. While presenting the mathematical basis of the R-Rmethod, the authors also give simple explanations and analogies tomake it easier to understand. Examples include calculation ofnatural frequencies and critical loads of structures and structuralcomponents, such as beams, plates, shells and solids. MATLAB codesfor some common problems are also supplied.
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978-1-118-98443-7 (9781118984437)
Schweitzer Klassifikation
PREFACE xi
INTRODUCTION AND HISTORICAL NOTES xiii
CHAPTER 1. PRINCIPLE OF CONSERVATION OF ENERGY ANDRAYLEIGH'S PRINCIPLE 1
CHAPTER 2. RAYLEIGH'S PRINCIPLE AND ITS IMPLICATIONS11
CHAPTER 3. THE RAYLEIGH-RITZ METHOD AND SIMPLEAPPLICATIONS 21
CHAPTER 4. LAGRANGIAN MULTIPLIER METHOD 33
CHAPTER 5. COURANT'S PENALTY METHOD INCLUDING NEGATIVESTIFFNESS AND MASS TERMS 39
CHAPTER 6. SOME USEFUL MATHEMATICAL DERIVATIONS AND APPLICATIONS55
CHAPTER 7. THE THEOREM OF SEPARATION AND ASYMPTOTIC MODELINGTHEOREMS 67
CHAPTER 8. ADMISSIBLE FUNCTIONS 81
CHAPTER 9. NATURAL FREQUENCIES AND MODES OF BEAMS 89
CHAPTER 10. NATURAL FREQUENCIES AND MODES OF PLATES OFRECTANGULAR PLANFORM 113
CHAPTER 11. NATURAL FREQUENCIES AND MODES OF SHALLOW SHELLS OFRECTANGULAR PLANFORM 133
CHAPTER 12. NATURAL FREQUENCIES AND MODES OF THREE-DIMENSIONALBODIES 149
CHAPTER 13. VIBRATION OF AXIALLY LOADED BEAMS AND GEOMETRICSTIFFNESS 161
CHAPTER 14. THE RRM IN FINITE ELEMENTS METHOD 181
BIBLIOGRAPHY 197
APPENDIX 203
INDEX 229
