Finite Element Analysis of Rotating Beams


Book Description

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.










Finite Element Analysis of Beam-to-Beam Contact


Book Description

Phenomena occurring during a contact of two bodies are encountered in everyday life. In reality almost every type of motion is related to frictional contact between a moving body and a ground. Moreover, modeling of simple and more complex processes as nailing, cutting, vacuum pressing, movement of machines and their elements, rolling or, finally, a numerical simulation of car crash tests, requires taking contact into account. Therefore, its analysis has been a subject of many research efforts for a long time now. However, it is author’s opinion that there are relatively few efforts related to contact between structural elements, like beams, plates or shells. The purpose of this work is to fill this gap. It concerns the beam-to-beam contact as a specific case of the 3D solids contact. A numerical formulation of frictional contact for beams with two shapes of cross-section is derived. Further, a couple of effective methods for modeling of smooth curves representing beam axes are presented. A part of the book is also devoted to analyze some aspects of thermo-electro-mechanical coupling in contact of thermal and electric conductors. Analyses in every chapter are illustrated with numerical examples showing the performance of derived contact finite elements.




The Rotating Beam Problem in Helicopter Dynamics


Book Description

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.







Vibration Analysis of Rotating Curved Beams with Variable Cross-section


Book Description

In this study, in-plane free vibration characteristics of rotating curved beams are investigated by Finite Difference Method and Finite Element Method since the mathematical model of the present problem is based on the differential eigenvalue problem with variable coefficients. A computer program regarding the titled problem is developed in Mathematica and this program is verified by using results available in the literature. The effects of taper parameters of the curved beam and rotation speed on natural frequencies are investigated.










TEXTBOOK OF FINITE ELEMENT ANALYSIS


Book Description

Designed for a one-semester course in Finite Element Method, this compact and well-organized text presents FEM as a tool to find approximate solutions to differential equations. This provides the student a better perspective on the technique and its wide range of applications. This approach reflects the current trend as the present-day applications range from structures to biomechanics to electromagnetics, unlike in conventional texts that view FEM primarily as an extension of matrix methods of structural analysis. After an introduction and a review of mathematical preliminaries, the book gives a detailed discussion on FEM as a technique for solving differential equations and variational formulation of FEM. This is followed by a lucid presentation of one-dimensional and two-dimensional finite elements and finite element formulation for dynamics. The book concludes with some case studies that focus on industrial problems and Appendices that include mini-project topics based on near-real-life problems. Postgraduate/Senior undergraduate students of civil, mechanical and aeronautical engineering will find this text extremely useful; it will also appeal to the practising engineers and the teaching community.