V. R. Murthy

Dynamic characteristics of stiffened rings by transfer matrix approach

Natural frequencies and mode shapes of circular rings on rigid and elastic supports are determined for in-plane vibration by using a transfer matrix approach. The transfer matrices are obtained by numerical integration of differential equations of the elements For the class of problems considered in this paper, the characteristic determinant is of the order 2×2 irrespective of the number of supports.

Dynamic characteristics of rotor blades

Abstract The transmission matrix method is used to determine the dynamic characteristics (natural frequencies and the associated mode shapes) of rotor blades. The problems treated are combined flapwise bending, chordwise bending, and torsion of twisted non-uniform blades and its special subcases. The orthogonality relations that exist between the natural modes are derived. The method is appealing because of its simplicity for programming for digital computer calculations and also the inputs are generated very easily since they are merely the coefficients of the differential equations of motion.

Determination of vibration characteristics of multiple-load-path blades by a modified Galerkin's method

Abstract A modified Galerkins method is developed to determine the natural vibration characteristics of multiple-load-path rotor blades. The development follows parallel to the CAMRAD program procedure for a single load-path-blade. Two types of finite series expansion functions are utilized: exact transcendental solutions to nonrotating uniform beam problems, and polynomial functions. A computer program based on this method is developed to determine the free vibration characteristics of multiple-load-path blades undergoing coupled flapwise bending, chordwise bending, twisting and extensional motions. Numerical results are obtained for two rotors. The first has constant properties along the span and the second is modelled from a nonuniform experimental rotor with discontinuous properties. Natural frequencies compare well with those predicted using a finite element approach, and with the experimental results for the second rotor.

Dynamics of helicopter rotor blades

Abstract A rotating blade finite element with coupled bending, torsion and axial stretching degrees-of-freedom is developed. APL is used for symbolic manipulations required for the development of the element. The element is implemented in MSC/NASTRAN to generate the numerical results. The results are compared with the experimental and other published numerical results and are found to be accurate. There are several immediate potential applications. The implementation of the element in the existing finite element software greatly enhances their utility for helicopter applications.

Static and dynamic analysis of airships

Consideration of geometric nonlinearities is important in the static and dynamic design of nonrigid airships. The finite-element method, using MSC/NASTRAN, is applied to perform linear and nonlinear static analyses and to determine the free vibration characteristics of such airships. It is found that the solutions obtained using the linear plus differential stiffness matrix may be quite adequate for airship structural analysis. A procedure to design a wrinkle-free catenary curtain is presented. The necessary solution sequence alterations used to determine the natural vibration characteristics of airships using MSC/NASTRAN are presented.

Solution bounds for varying geometry beams

Abstract The theory of differential and integral inequalities is applied to obtain upper and lower bounds to the transfer matrix for beams with varying geometry. Various techniques of generating and refining these bounds are investigated. Numerical results indicate that these bounds can be refined to produce numerical agreement of the upper and the lower bound to a given number of significant digits. Proceeding from bounds on the transfer matrix elements a theory is developed for determining upper and lower bounds on the natural frequencies and mode shapes and on the solution state vector for static loading of such beams. This procedure is then extended to the analysis of multispan beams with varying geometry. Numerical results are presented for various configurations.

Optimal Controller for an Autonomous Helicopter in Hovering and Forward Flight

In this paper, an optimal controller is investigate d based on the Linear Quadratic Control method. The controller simulation is execut ed based on a small-scale autonomous model helicopter, Yamaha R-50. Genetic algorithms are employed to generate weighting matrices by optimizing the performance index of the control system. As a result, this method produces optimal weighting matrices which further improve the Linear Quadratic Controller. A full state feedback approach is used in the control design process. A Kalman observer is integrated into the controller to predi ct full state variables, since only a limited number of state variables are measured. Finally, th e performance of the controller is evaluated in the time domain with and without disturbances when the model helicopter is in hovering flight and forward flight. I. Introduction utonomous helicopters offer special advantages for major operations in both civilian and military sect ors, particularly in cases that are considered either in accessible or dangerous for human beings, due to th eir vertical take-off and landing (VTOL) capabilities. The contr ol system of autonomous helicopters plays a key rol e in its ability to carry out the assigned task effectively. This has lead to a growing interest in the design and analysis of the control system of autonomous helicopters. In 1990s, classic control theory was widely used for autonom ous helicopter control systems, which is mainly a succe ssive loop closure approach. The control gains are selected separately using tools such as Root locus, Bode and Nyquist plots. The controller parameters are usual ly tuned based on the controller performance measured either in ti me domain or in frequency domain. This design procedure becomes increasingly difficult as more and more loo ps are added, specifically, when the dynamics invol ve multiple inputs, multiple outputs, or multiple feedback loop s with complex performance criteria. To control an autonomous helicopter modeled as a complex Multiple Input Multiple Output (MIMO) system, the performance criteria can not be easily met by the approach based on classis cont rol theory. Several researchers have developed a number of diff erent ways for the control system design of autonom ous helicopters in the literature. Shim et al 1 presented three different control methods using li near robust, fuzzy logic, and nonlinear tracking controls, for an autonomous helicopter in hover and low speed flight. Johnson a nd Kannan 2

Sensitivity analysis of discrete periodic systems with applications to helicopter rotor dynamics

We present a sensitivity formulation for periodic systems and a theoretical model for a helicopter rotor in forward flight. The formulation and the rotor model are validated by a few comparisons with other available methods and experimental values. The greatest advantage of the present sensitivity analysis is that the order of the Floquet matrix is independent of the number parameters to be investigated. This yields substantial savings in computation times over the existing methods.

Optimal flight path planner for an unmanned helicopter by evolutionary algorithms

This paper presents an evolutionary method to develop an optimal flight path planner for an unmanned helicopter with initial, fi nal states, and waypoint constraints under certain prescribed operational en vironment. The operational environment consists of concave and non-concave obstacles which are represented by different geometric shapes and their combinations. The minimum flight time is considered as the objective function in the optimiz ation process. The stochastic universal sampling selection technique, mutation and crossover operators are implemented in the evolutionary method. Finally, the method is validated by applying to optimal flight path problems in highly constrained operational environments.

Sensitivity Derivatives of Eigendata of One-Dimensional Structural Systems

A general formulation based on the transfer matrix is presented to calculate the sensitivity derivatives of eigenvalue problems of one-dimensional structural systems. The method is equally applicable to any discrete or distributed system of one variable. The formulation is applied to determine the sensitivity derivatives of eigendata of a rotating helicopter blade and also to an optimization problem of a cantilever beam with frequency constraints. It is found that the computational efe ciency of the present method is superior to those of the existing methods by an order of magnitude and that this efe cacy improves with increasing numbers of design parameters and degrees of freedom.