The Dynamics of Slender Beams. Helicopter Rotor Study i


Book Description

The purpose of the study is to formulate a non-linear exact theory for large amplitude flap-wise vibration of helicopter rotors. Previous linear beam theories, employing the assumption of small displacement, are limited in their treatment of the rotor problem. Some nonlinear theories have been developed. But these investigations, in one way or another, suffer from questionable assumptions and the true nature of the dynamics of a slender beam is not clearly understood. Beam equations for large amplitude vibration are formulated to include axial forces, shear deformation and rotatory inertia effects. (Author).




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.







Nonlinear Vibrations of Cantilever Beams and Plates


Book Description

Many engineering problems can be solved using a linear approximation. In the Finite Element Analysis (FEA) the set of equations, describing the structural behaviour is then linear K d = F (1.1) In this matrix equation, K is the stiffness matrix of the structure, d is the nodal displacements vector and F is the external nodal force vector. Characteristics of linear problems is that the displacements are proportional to the loads, the stiffness of the structure is independent on the value of the load level. Though behaviour of real structures is nonlinear, e.g. displacements are not proportional to the loads; nonlinearities are usually unimportant and may be neglected in most practical problems.




Statics and Rotational Dynamics of Composite Beams


Book Description

This book presents a comprehensive study of the nonlinear statics and dynamics of composite beams and consists of solutions with and without active elements embedded in the beams. The static solution provides the initial conditions for the dynamic analysis. The dynamic problems considered include the analyses of clamped (hingeless) and articulated (hinged) accelerating rotating beams. Two independent numerical solutions for the steady state and the transient responses are presented. The author illustrates that the transient solution of the nonlinear formulation of accelerating rotating beam converges to the steady state solution obtained by the shooting method. Other key areas considered include calculation of the effect of perturbing the steady state solution, coupled nonlinear flap-lag dynamics of a rotating articulated beam with hinge offset and aerodynamic damping, and static and dynamic responses of nonlinear composite beams with embedded anisotropic piezo-composite actuators. The book is intended as a thorough study of nonlinear elasticity of slender beams and is targeted to researchers, graduate students, and practicing engineers in the fields of structural dynamics, aerospace structures, and mechanical engineering.




Linear and Non-Linear Deformations of Elastic Solids


Book Description

Linear and Non-Linear Deformations of Elastic Solids aims to compile the advances in the field of linear and non-linear elasticity through discussion of advanced topics. Broadly classified into two parts, it includes crack, contact, scattering and wave propagation in linear elastic solids and bending vibration, stability in non-linear elastic solids supported by MATLAB examples. This book is aimed at graduate students and researchers in applied mathematics, solid mechanics, applied mechanics, structural mechanics and includes comprehensive discussion of related analytical/numerical methods.







A Study of Helicopter Rotor Dynamics and Modeling Methods


Book Description

The rotor system is the primary source of vibratory forces on a helicopter. Vibratory forces result from the rotor system response to dynamic and aerodynamic loading. This thesis discusses sources of excitation, and investigates rotor system modeling methods. Computer models based on finite element and Mykiestad methods are developed and compared for the free and forced vibration cases of a nniform rotor blade. The modeling assumptions and the effects of non-iniform physical parameters are discussed. The Myklestad based computer model is expanded to include coupling effects isherent in modern rotor blades. This rotor modeling program is incorporated into the Dynamics section of the Joint Army/Navy Rotorcraft Analysis and Design (JANRAD) program currenfly used by the Naval Postgraduate School?s helicopter design course (AA43O6) for preliminary helicopter design and analysis. Computer programs are developed as tools to investigate the stabffity of a rotor system for the specfflc cases of rotor flapping and ground/air resonance. A rotor flapping stability model, based upon Floquet theory, provides a means of analyzing the effect of increasing advance ratio on the flapping stability of a rotor system. The ground/air resonance model uses a constant coefficient approximation of the rotor system to allow analysis of the effects of coupling between rotor lag motion and airframe motion.







Dynamics of Civil Structures, Volume 2


Book Description

Dynamics of Civil Structures, Volume 2: Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics, 2022, the second volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of the Dynamics of Civil Structures, including papers on: Structural Vibration Humans & Structures Innovative Measurement for Structural Applications Smart Structures and Automation Modal Identification of Structural Systems Bridges and Novel Vibration Analysis Sensors and Control