Solution and sensitivity analysis of a complex transcendental eigenproblem with pairs of real eigenvalues

This paper considers complex transcendental eigenvalue problems where one is interested in pairs of eigenvalues that are restricted to take real values only. Such eigenvalue problems arise in dynamic stability analysis of nonconservative physical systems, i.e., flutter analysis of aeroelastic systems. Some available solution methods are discussed and a new method is presented. Two computational approaches are described for analytical evaluation of the sensitivities of these eigenvalues when they are dependent on other parameters. The algorithms presented are illustrated through examples

Experimental investigation of propfan aeroelastic response in off-axis flow with mistuning

Measured vibratory strain amplitudes from off-axis flow are compared for the blades of two, 8-bladed propfan model rotors with mistuning. One rotor had inherent mistuning. The other was intentionally mistuned by replacing every other blade of the first rotor with a blade of same geometry but different frequencies and mode shapes. The data shows that the intentional mistuning had a beneficial effect on the aeroelastic response of the propfan motors for a wide range of off-axis flow angles, blade pitch angles, and rotational speeds. Statistical trends of blade strain amplitudes are compared for both the rotors in terms of the ratio of the maximum to the mean and the coefficient of variation

Stochastic sensitivity measure for mistuned high-performance turbines

A stochastic measure of sensitivity is developed in order to predict the effects of small random blade mistuning on the dynamic aeroelastic response of turbomachinery blade assemblies. This sensitivity measure is based solely on the nominal system design (i.e., on tuned system information), which makes it extremely easy and inexpensive to calculate. The measure has the potential to become a valuable design tool that will enable designers to evaluate mistuning effects at a preliminary design stage and thus assess the need for a full mistuned rotor analysis. The predictive capability of the sensitivity measure is illustrated by examining the effects of mistuning on the aeroelastic modes of the first stage of the oxidizer turbopump in the Space Shuttle Main Engine. Results from a full analysis mistuned systems confirm that the simple stochastic sensitivity measure predicts consistently the drastic changes due to misturning and the localization of aeroelastic vibration to a few blades

Concurrent processing adaptation of aeroplastic analysis of propfans

Discussed here is a study involving the adaptation of an advanced aeroelastic analysis program to run concurrently on a shared memory multiple processor computer. The program uses a three-dimensional compressible unsteady aerodynamic model and blade normal modes to calculate aeroelastic stability and response of propfan blades. The identification of the computational parallelism within the sequential code and the scheduling of the concurrent subtasks to minimize processor idle time are discussed. Processor idle time in the calculation of the unsteady aerodynamic coefficients was reduced by the simple strategy of appropriately ordering the computations. Speedup and efficiency results are presented for the calculation of the matched flutter point of an experimental propfan model. The results show that efficiencies above 70 percent can be obtained using the present implementation with 7 processors. The parallel computational strategy described here is also applicable to other aeroelastic analysis procedures based on panel methods

Efficient computation of aerodynamic influence coefficients for aeroelastic analysis on a transputer network

Aeroelastic analysis is multi-disciplinary and computationally expensive. Hence, it can greatly benefit from parallel processing. As part of an effort to develop an aeroelastic capability on a distributed memory transputer network, a parallel algorithm for the computation of aerodynamic influence coefficients is implemented on a network of 32 transputers. The aerodynamic influence coefficients are calculated using a 3-D unsteady aerodynamic model and a parallel discretization. Efficiencies up to 85 percent were demonstrated using 32 processors. The effect of subtask ordering, problem size, and network topology are presented. A comparison to results on a shared memory computer indicates that higher speedup is achieved on the distributed memory system

A computational procedure for automated flutter analysis

A direct solution procedure for computing the flutter Mach number and the flutter frequency is applied to the aeroelastic analysis of propfans using a finite element structural model and an unsteady aerodynamic model based on a three-dimensional subsonic compressible lifting surface theory. An approximation to the Jacobian matrix that improves the efficiency of the iterative process is presented. The Jacobian matrix is indirectly approximated from approximate derivatives of the flutter matrix. Examples are used to illustrate the convergence properties. The direct solution procedure facilitates the automated flutter analysis in addition to contributing to the efficient use of computer time as well as the analyst's time

Aeroelastic dynamics of mistuned blade assemblies with closely spaced blade modes

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76999/1/AIAA-1993-1628-443.pd

Localization of aeroelastic modes in mistuned high-energy turbines

The effects of blade mistuning on the aerodynamic characteristics of a class of bladed-disk assemblies, namely high energy turbines, are discussed. The specific rotor analyzed is the first stage of turbine blades of the oxidizer turbopump in the Space Shuttle Main Engine. The common occurrence of fatigue cracks for these turbine blades indicates the possibility of high dynamic loading. Since mistuning under conditions of weak interblade coupling has been shown to increase blade response amplitudes drastically for simple structural models of blade assemblies, it provides a plausible explanation for the occurrence of cracks. The focus here is on the effects of frequency mistuning on the aeroelastic stability of the assembly and on the aeroelastic mode shapes

A semianalytical technique for sensitivity analysis of unsteady aerodynamic computations

A semianalytical approach is developed for the sensitivity analysis of linear unsteady aerodynamic loads. The semianalytical approach is easier to implement than the analytical approach. It is also computationally less expensive than the finite difference approach when used with panel methods, which require a large number of panels. The semianalytical approach is applied to an isolated airfoil in a 2-D flow and rotating propfan blades in 3-D flow. Sensitivity coefficients with respect to non-shape-dependent variables are shown for some cases. It is expected that the semianalytical approach will be useful in aeroelastic design procedures particularly when mistuning is present, and that it is potentially useful for shape sensitivity analysis of linear unsteady aerodynamics

Aeroelastic modal characteristics of mistuned blade assemblies - Mode localization and loss of eigenstructure

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76142/1/AIAA-1991-1218-735.pd