Preface; Contents; About the Author; 1 Introduction; 1.1 Introduction; 1.1.1 Elastic Blade; 1.1.2 Horizontal Force Equilibrium; 1.1.3 Boundary Conditions; 1.1.4 Initial Conditions; 1.1.5 Cantilever Beam Vibrations (Non-rotating); 1.1.6 Beam Functions; 1.1.7 Rotating Beam Vibration; 1.2 Galerkin Method; 1.3 Rayleigh
Ritz Method; 1.4 Finite Element Method; 1.4.1 Element Properties; 1.4.2 Energy Expressions; 1.4.3 Assembly of Elements; 1.4.4 Cantilever; 2 Stiff String Basis Functions; 2.1 Stiff String Equation; 2.2 Stiff String Basis Functions; 2.3 Uniform Rotating Beam

2.4 Tapered Rotating Beam2.5 Hybrid Basis Functions; 2.6 Finite Element; 2.6.1 Uniform Rotating Beam; 2.7 Tapered Rotating Beam; 2.8 Summary; References; 3 Rational Interpolation Functions; 3.1 Governing Differential Equation; 3.2 Hermite Shape Functions; 3.3 New Shape Functions; 3.4 Static Finite Element Analysis; 3.5 Dynamic Finite Element Analysis; 3.5.1 Uniform Beam; 3.5.2 Tapered Rotating Beam; 3.6 Summary; References; 4 Fourier-p Superelement; 4.1 Governing Equation of Rotating Beams; 4.2 Shape Functions; 4.3 Superelement Matrices; 4.4 Numerical Results; 4.4.1 Uniform Rotating Beam

4.4.2 Tapered Rotating Beam4.5 Summary; References; 5 Physics Based Basis Functions; 5.1 Basis Function; 5.2 Finite Element Analysis; 5.3 Numerical Results; 5.3.1 Uniform Beam; 5.3.2 Tapered Beam; 5.3.3 Beams with Hub Offset; 5.4 Summary; References; 6 Collocation Approach; 6.1 Governing Differential Equation; 6.2 Point Collocation Approach; 6.2.1 Collocation Point at a Variable Location Within Beam Element; 6.2.2 Collocation Point Near the Left Node of Beam Element; 6.2.3 Collocation Point at the Midpoint of Beam Element; 6.2.4 Collocation Point Near the Right Node of Beam Element

6.2.5 Two Point Collocation6.2.6 Analysis of Shape Functions; 6.3 Finite Element Formulation; 6.4 Numerical Results; 6.4.1 Uniform Rotating Beam; 6.4.2 Tapered Rotating Beam; 6.5 Summary; References; 7 Rotor Blade Finite Element; 7.1 Energy Expressions; 7.2 Governing Differential Equations; 7.3 Derivation of the Shape Functions; 7.3.1 Shape Functions for Flapwise Bending; 7.3.2 Shape Functions for Lead-Lag Bending; 7.3.3 Shape Functions for Axial Deflection; 7.3.4 Shape Functions for Torsion; 7.4 Finite Element Method; 7.5 Numerical Results; 7.5.1 Analysis of Shape Functions

7.5.2 Validation Study7.6 Convergence Study of New FEM Element and Polynomials; 7.7 Summary; References; 8 Spectral Finite Element Method; 8.1 Governing Differential Equation; 8.2 Spectral Finite Element Formulation; 8.2.1 Interpolating Function for SFER; 8.2.2 Interpolating Function for SFEN; 8.2.3 Dynamic Stiffness Matrix in Frequency Domain; 8.3 Free Vibration Results; 8.3.1 Uniform Beam; 8.3.2 Tapered Beam 1-Linear Mass and Cubic Flexural Stiffness Variation; 8.3.3 Tapered Beam 2-Linear Mass and Flexural Stiffness Variation; 8.4 Wave Propagation Study; 8.4.1 Convergence Study