A New Treatment of Periodic Systems with Applications to Helicopter Rotor Blade Dynamics

Abstract

A new solution technique for general periodic systems encountered in many mechanical systems including the helicopter rotor-blade dynamics has been developed. In this technique, the state transition matrices (STM) of periodic systems are obtained in terms of the shifted Chebyshev polynomials of first and second kind. Due to the excellent convergence properties of Chebyshev polynomials, the approach is found to be super efficient in terms of the CPU time with accuracy level comparable to any higher order numerical algorithms such as Runge-Kutta, Adams-Mouton, etc., schemes. The technique is suitable for both numerical and symbolic implementations. The method can be used in a variety of applications such as stability of linear and nonlinear periodic systems, response calculations of linear and nonlinear periodic systems, design of control systems for periodic systems, direct determination of periodic orbits of nonlinear systems and nonlinear analysis of periodic systems in stable, center and unstable manifolds. Case studies corresponding to each of these applications have been reported. Apart from the above mentioned utilities, the technique has resulted in a very practical procedure in obtaining the well-known Liapunov- Floquet (L-F) Transformation matrix which allows one to design a control system in the time-invariant domain. Currently, the research efforts are directed toward utilizing the L-F transformation matrix for various other problems such as order reduction, bifurcation analysis and nonlinear control design strategies for periodic systems. In the following, a short enumeration of the achievements of the project is presented.

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Document Details

Document Type
Technical Report
Publication Date
May 28, 1993
Accession Number
ADA266770

Entities

People

  • Subbash C. Sinha

Organizations

  • Auburn University

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Case Studies
  • Chebyshev Polynomials
  • Coefficients
  • Computations
  • Control Systems
  • Dynamics
  • Engineering
  • Helicopter Rotors
  • Helicopters
  • Linear Systems
  • Mechanical Engineering
  • Nonlinear Analysis
  • Nonlinear Systems
  • Polynomials
  • Vibration

Fields of Study

  • Mathematics
  • Physics

Readers

  • Approximation Theory.
  • Control Systems Engineering.
  • Operations Research

Technology Areas

  • Space