Technical Notes: The Effect of Hidden Dynamic States on Floquet Eigenvalues

Peters, David A.; Su, Ay

doi:10.4050/jahs.35.72

Cited by 5 publications

(4 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A great deal of effort was devoted to describing unsteady flow in a rather parallel manner by many at the time, and Refs 7 and 8 introduce the concise history of the development of the theory. The most extensive work has been done by Peters and his co-workers (1)(2)(3)(4)8,9) during the last two decades and now the most popular equation of the dynamic inflow model is often referred to Pitt and Peters model, which is to be introduced in the next section. While the dynamic inflow model is now regarded highly useful for helicopters under normal powered flight conditions, few attempts have been made so far to apply the model to an autorotating rotor, and the applicability has not been examined adequately, although the mathematical essence holds the same both for a powered and an autorotating rotor.…”

Section: Introductionmentioning

confidence: 99%

“…1. Due to this closed form, the dynamic inflow model can also be applied to Floquet eigenvalue analysis in the stability of the flow (1) . Open loop models including free-wake and prescribedwake models, which are effective at time-marching problems, are usually not well-matched with this sort of stability analysis.…”

Section: Introductionmentioning

confidence: 99%

“…This means that Equation (9) can be used for a rotor both in normal working and windmill-brake states without any change in the general form of Equation (1). Each element in the matrices in Equation 1is determined regardless of those signs, and it can be, therefore, ascertained that the dynamic inflow model holds the same form of Equation (1) both for normal working and windmill-brake states.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamic inflow modelling for autorotating rotors

Murakami

Houston

2008

Aeronaut. j.

View full text Add to dashboard Cite

A linearised model system matrix B linearised model control matrix C L aerodynamic perturbation in roll moment C M aerodynamic perturbation in pitch moment C T aerodynamic perturbation in thrust p,q,r perturbed angular velocity components along airframe axes, rad/s r radial position on rotor disc, m R rotor radius, m U perturbation velocity vector, U = (u,v,w), dimensionless on ΩR t non-dimensional time u,v,w perturbed velocity components along airframe axes, dimensionless on ΩR u control vector v 0 component of induced velocity, mean, ms -1 v c1 component of induced velocity, longitudinal, ms -1 v s1 component of induced velocity, lateral, ms -1 v m wake mass flow velocity, ms -1 V general mass-flow parameter, dimensionless on ΩR V m mass-flow parameter, V m /ΩR V m+ mass-flow parameter for normal working state, dimensionless on ΩR V m-mass-flow parameter for windmill-brake state, dimensionless on ΩR V T non-dimensional total flow at rotor disc, dimensionless on ΩR ABSTRACTThe dynamic inflow model is a powerful tool for predicting the induced velocity distribution over a rotor disc. On account of its closed form and simplicity, the model is especially practical for studying flight mechanics or for designing control systems for helicopters. Scant attention has, however, been paid so far in utilising the dynamic inflow model to analyse an autorotating rotor, which is different from a powered rotor in the geometric relation between the direction of the inflow and the rotor disc. Autorotation is an abnormal condition for helicopters, but for gyroplanes it is the normal mode of operation. Therefore the theoretical discussion on an autorotating rotor is of importance not only to improve the understanding of present gyroplanes, but also in the development of new gyroplanes and to analyse the windmill-brake state of helicopters. Dynamic inflow modelling is reviewed from first principles, and this identifies a modification to the mass flow parameter. A qualitative assessment of this change indicates that it is likely to have a negligible impact on the trim state of rotorcraft in autorotation, but a significant effect on the dynamic inflow modes in certain flight conditions. This is confirmed by numerical simulation, although considerable differences only become apparent for steep descents with low forward speed. It is concluded that while modification of the mass flow parameter is perhaps mathematically accurate, for practical purposes it is required only in a limited area of the flight envelope of autorotating rotorcraft.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamic inflow modelling for autorotating rotors

Murakami

Houston

2008

Aeronaut. j.

View full text Add to dashboard Cite

show abstract

“…Shi, Law and Li recently expanded upon that work applying the algorithm to simulated measurements from various systems [20]. Peters and Wang [21] independently arrived at related methodology that sought to more accurately and efficiently generate the state transition matrix of an analytical LTP system [21] and to allow one to characterize the effects of hidden aerodynamic states [22]. They subsequently applied their technique to find the Floquet multipliers of a laboratory helicopter rotor [23,24].…”

Section: Introductionmentioning

confidence: 99%

Frequency-Domain Identification of Linear Time-Periodic Systems Using LTI Techniques

Allen

2009

Journal of Computational and Nonlinear Dynamics

View full text Add to dashboard Cite

A variety of systems can be faithfully modeled as linear with coefficients that vary periodically with time or Linear Time-Periodic (LTP). Examples include anisotropic rotor-bearing systems, wind turbines and nonlinear systems linearized about a periodic trajectory; all of these have been treated analytically in the literature. However, few methods exist for experimentally characterizing LTP systems. This paper presents a set of tools that can be used to experimentally characterize an LTP system, using a frequency domain approach and utilizing existing algorithms to perform parameter identification. One of the approaches is based on lifting the response to obtain an equivalent Linear Time-Invariant (LTI) form and the other based on Fourier series expansion. The development focuses on the pre-processing steps needed to apply LTI identification to the measurements, the post-processing needed to reconstruct the LTP model from the identification results and the interpretation of the measurements. This approach elucidates the similarities between LTP and LTI identification, allowing the experimentalist to transfer insight from time-invariant systems to the LTP identification problem. The approach determines the model order of the system, and post processing reveals the shapes of the time-periodic functions comprising the LTP model. Further post-processing is also presented that allows one to generate the full state transition matrix and the time-varying state matrix of the system from the parametric model if the measurement set is adequate. The experimental techniques are demonstrated on simulated measurements from a Jeffcott rotor mounted on an anisotropic, flexible shaft, supported by anisotropic bearings. INTRODUCTIONMany important dynamic systems can be modeled as Linear Time-Periodic (LTP). When a system has periodically varying parameters, it is exceedingly important to discover and accurately model this character since it can lead to parametric resonances which are not present for a Linear TimeInvariant (LTI) approximation to the system. Floquet initiated the study of LTP systems in the 1800's [1], and modern Floquet theory has been applied to a variety of mechanical systems such as helicopters [ [10][11][12]. Linear time-periodic system models are also frequently encountered in analysis of nonlinear systems, as it often proves beneficial to linearize the nonlinear system about a periodic trajectory to study its stability.Much progress has been made in the past twenty years towards analysis and control of linear and nonlinear time-periodic systems, as many concepts for LTI systems are readily extended to LTP systems [5,13]. On the other hand, experimental techniques are well developed for LTI systems, but LTP system identification has received relatively little attention. Experimental methods are needed in a number of applications, for example when it is impossible to determine the parameters or periodic functions comprising the LTP model for a system from first principles. They may also be useful to ...

show abstract

An integrated airloads-inflow model for use in rotor aeroelasticity and control analysis

Peters

Barwey

1994

Mathematical and Computer Modelling

View full text Add to dashboard Cite

Technical Notes: The Effect of Hidden Dynamic States on Floquet Eigenvalues

Cited by 5 publications

References 4 publications

Dynamic inflow modelling for autorotating rotors

Dynamic inflow modelling for autorotating rotors

Frequency-Domain Identification of Linear Time-Periodic Systems Using LTI Techniques

An integrated airloads-inflow model for use in rotor aeroelasticity and control analysis

Contact Info

Product

Resources

About