Accession Number : ADA266770


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


Descriptive Note : Final rept. 15 Sep 89-31 Mar 93,


Corporate Author : AUBURN UNIV AL DEPT OF MECHANICAL ENGINEERING


Personal Author(s) : Sinha, Subbash C


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a266770.pdf


Report Date : 28 May 1993


Pagination or Media Count : 9


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.


Descriptors :   *STABILITY , *VIBRATION , *HELICOPTER ROTORS , *ROTOR BLADES , ALGORITHMS , CONTROL SYSTEMS , STRATEGY , EXCITATION , TIME , CASE STUDIES , CHEBYSHEV POLYNOMIALS , TRANSFORMATIONS , DETERMINATION , NONLINEAR ANALYSIS , TRANSITIONS , CONVERGENCE , POLYNOMIALS , RESPONSE , HELICOPTERS , NONLINEAR SYSTEMS , REDUCTION , ACCURACY , DYNAMICS , SYSTEMS ENGINEERING , CONTROL , ORBITS


Subject Categories : Helicopters
      Mechanics


Distribution Statement : APPROVED FOR PUBLIC RELEASE