C. E. Hammond

Bio: C. E. Hammond is an academic researcher. The author has contributed to research in topics: Damper & Floquet theory. The author has an hindex of 1, co-authored 1 publications receiving 37 citations.

Efficient numerical treatment of periodic systems with application to stability problems

Abstract: Two efficient numerical methods for dealing with the stability of linear periodic systems are presented. Both methods combine the use of multivariable Floquet-Liapunov theory with an efficient numerical scheme for computing the transition matrix at the end of one period. The numerical properties of these methods are illustrated by applying them to the simple parametric excitation problem of a fixed end column. The practical value of these methods is shown by applying them to some helicopter rotor blade aeroelastic and structural dynamics problems. It is concluded that these methods are numerically efficient, general and practical for dealing with the stability of large periodic systems.

Helicopter rotor dynamics by finite element time approximation

Abstract: Starting from a variational formulation, based on Hamilton's principle, the paper exploits the finite element technique in the time domain in order to generate, by an automated procedure, a numerical approximation of the nonlinear periodic equations peculiar to the dynamics of helicopter rotors. With this method, a unified approach is developed, which can be used to solve both the response and stability problem. Two simple examples are presented that show how the method can be used to study the trimmed response of a fully articulated rigid blade and the mechanical instability analysis of a four-bladed rotor.

Rotary wing aeroelasticity - A historical perspective

Abstract: This paper provides a historical perspective of the fundamental developments that have played a central role in rotary-wing dynamics and aeroelasticity and have had a major impact on the design of rotary-wing aircraft. The paper describes a historical progression starting with the classical flap-pitch problem that emulated fixed-wing behavior and describes the evolution of the dynamic and aeroelastic problems into those that are unique to rotoreraft, such as the flap-lag problem, the lag-pitch problem, and the coupled flap-lag-torsional problem. Subsequently, the coupled rotor/fuselage aeromechanical problems such as ground and air resonance are considered. A description of the evolution of the methodology used in the formulation and solution of these types of problems is also provided, emphasizing the structural and aerodynamic models required for their effective formulation and solution. The mathematical techniques used for solving the rotary-wing aeroelastic problems in hover and forward flight are also described. The primary emphasis of the paper is on aeroelastic stability, and aeroelastic response is only treated briefly. The paper focuses on contributions that have historical value because they represent landmark treatments. Because of the large amount of material available, an all-inclusive treatment of the research done in this field is impractical, and the paper has unavoidable omissions.

Numerical methods for determining the stability and response of periodic systems with applications to helicopter rotor dynamics and aeroelasticity

Abstract: This paper reviews and extends some recently developed numerical techniques for analyzing the stability, linear response and nonlinear response of periodic systems, which are governed by ordinary differential equations with periodic coefficients. The main emphasis is on applications aimed at rotor blade aeroelastic stability and response calculations in forward flight. First Floquer theory is br4iefly reviewed and numerically efficient methods for evaluating the transition matrix at the end of one period are described. Next the numerical treatment of the linear response problem is discussed. Finally the numerical solution of the nonlinear response problem is treated using quasilinearization and periodic shooting. Applications illustrating numerical properties of the methods are described.