| Description |
1 online resource |
| Series |
Foundations of engineering mechanics |
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Foundations of engineering mechanics.
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| Contents |
Preface -- Contents -- About the Authors -- List of Figures -- List of Tables -- 1 Introduction -- 1.1 Free Vibration of a Single-Degree-of-Freedom System -- 1.2 Free Vibration of a Damped, Single-Degree-of-Freedom System -- 1.3 Forced Vibration of a Single-Degree-of-Freedom System -- 1.4 Forced Vibration of a Damped, Single-Degree-of-Freedom System -- 1.5 Two-Degrees-of-Freedom System -- 1.6 Free Vibration of a Continuous System -- 1.7 Hamiltonâ#x80;#x99;s Principle -- 1.8 Diagonalization of a Symmetric Matrix -- 1.9 Transformation of Coordinates |
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1.10 Momentum Theory for Axial Flight1.11 Momentum Theory for Forward Flight -- 1.12 Newtonâ#x80;#x93;Raphson Method -- 1.13 Blade Element Theory -- 1.14 Derivation of Equation of Motion of Flapping Rigid Blade -- 1.15 Derivation of Elastic Rotor Blade Equation -- 2 Finite Element Analysis in Space -- 2.1 Introduction -- 2.2 Finite Element in Space -- 2.3 Strong Form of the Equation -- 2.4 Weak Form of the Equation -- 2.5 Galerkinâ#x80;#x99;s Method -- 2.6 Shape Function in 1 Dimension -- 2.7 Shape Function Formulation for Beam Element |
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2.8 Properties of Shape Function in 1D2.9 Finite Element Formulation of Rotating Beam -- 2.10 Centrifugal Force -- 2.11 Shape Function Formulation for Two Elements -- 2.12 FEM Formulation of Rotating Beam with Only One Shape Function (for Free Vibration) -- 2.13 Calculation of Mode Shapes and Frequencies -- 2.14 FEM Formulation of Aerodynamic Force for Rotor Problem -- 3 Finite Element in Time -- 3.1 Introduction -- 3.2 Selection of Shape Function in Time -- 3.3 Finite Element in Time Example |
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3.4 Solution of Coupled Differential Equations with Finite Element in Time3.5 Enforcing Periodicity in the System -- 3.6 Advantage of Choosing an Element from (0 to 2Ï#x80;), p-Version of Finite Element in Time -- 3.7 Selection of Number of Nodes -- 3.8 Effect of Forcing Term in Finite Element in Time -- 3.9 Finite Difference Method (Rungeâ#x80;#x93;Kutta Fourth Order) -- 4 Stability Analysis -- 4.1 Introduction -- 4.2 Stability Analysis of Equations with Constant Coefficients -- 4.3 Stability Analysis of a Coupled Differential Equations with Constant Coefficients |
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4.4 Stability Analysis of the Equation with Periodic Coefficients, Floquet Theory4.5 Analytical Solution with the Floquet Theory -- 4.6 Numerical Method to Evaluate a Transition Matrix -- 4.7 Stability Analysis for Rotor Problem -- 5 Helicopter Rotor Results -- 5.1 Inputs -- 5.2 Result 1 (Mode Shapes and Frequencies of the Rotating Beam) -- 5.3 Result 2 (Response of the Rotor Blade with the Uniform Inflow Model, Using Three Different Cases) -- 5.4 Result 3 (Response of the Rotor Blade with the Linear Inflow Model, Using Three Different Cases) |
| Summary |
The book addresses computational methods for solving the problem of vibration, response, loads and stability of a helicopter rotor blade modeled as a rotating beam with flap or out-of-plane bending. The focus is on explaining the implementation of the finite element method in the space and time domain for the free vibration, aeroelastic response and stability problems. The use of Floquet analysis for the aeroelastic stability analysis of rotor blades is also shown. The contents of the book will be useful to researchers in aerodynamics and applied mechanics, and will also serve well professionals working in the aerospace industry |
| Bibliography |
Includes bibliographical references |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed October 19, 2017) |
| Subject |
Rotors (Helicopters) -- Aerodynamics.
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Rotational motion (Rigid dynamics)
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TECHNOLOGY & ENGINEERING -- Engineering (General)
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SCIENCE -- Mechanics -- Aerodynamics.
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Rotational motion (Rigid dynamics)
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Rotors (Helicopters) -- Aerodynamics
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| Form |
Electronic book
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| Author |
Panchore, Vijay, author
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| ISBN |
9789811060984 |
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9811060983 |
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