The problems associated with the prohibitive number of possible system modes for a fluttering compressor or turbine blade row are eliminated by the development that comprises the present report. The existence and uniqueness of extremely simple system flutter modes are proved for blade rows consisting of identical blades equally spaced about a common rotor. These simple system modes, if properly interpreted, have the effect of reducing by a factor of n the number of degrees of freedom necessary to analyze an w-bladed configuration. Stated differently, the system of n blades may be considered, with no loss of generality whatsoever, in terms of a single "equivalent blade." The proof holds under any type of flow and any and all types of interblade coupling, so long as a linear analysis is permissible. Moreover, since it is the flutter-inception point that is of interest in predicting critical velocity or rotational speed, it may well be that the conclusions developed apply even to the onset of stall flutter. Practical application of the method to stall-flutter calculations would, of course, require the availability of aerodynamic stallflutter coefficients. The development is carried out first under the assumption of infinite rotor inertia or, in other words, constant rotor velocity. This restriction is then relaxed, and the treatment is expanded to permit torsional oscillations of the rotor itself. I t is proved that under certain conditions the assumption of infinite rotor inertia introduces no error whatsoever.

System Mode Shapes in the Flutter of Compressor Blade Rows

Filtering and parameter estimation in a simple linear system driven by a fractional Brownian motion

We derive an arbitrage‐free pricing dynamics for claims on temperature, where the temperature follows a fractional Ornstein–Uhlenbeck process. Using a fractional white noise calculus, one can express the dynamics as a special type of conditional expectation not coinciding with the classical one. Using a Fourier transformation technique, explicit expressions are derived for claims of European and average type, and it is shown that these pricing formulas are solutions of certain Black and Scholes partial differential equations. Our results partly confirm a conjecture made by Brody, Syroka and Zervos.

/pdf/on-arbitrage-free-pricing-of-weather-derivatives-based-on-1xidz0xqoz.pdf

On arbitrage‐free pricing of weather derivatives based on fractional Brownian motion

acting on functions x (4) of class L ~ (-0% oo) is a unitary symmetric operator on the Hilbert space L ~ (-~ , oo) E9]. (The integral here is to be i n t e rp r e t ed as a Cauchy principal value at # =4.) We shall .refer to the operator H ~s the Hilbert transformation. The spectrum of the operator H consists just of the points • t. Under the application of the Fourier-Plancherel transformation

Spectral representations for finite Hilbert transformations

1. The problem. It has been shown [1] that if Xi, + X2, … are independent random variables each of density then (1.1)

The Distribution of the Maximum of Partial Sums of Independent Random Variables

/pdf/boundary-value-problems-in-aerodynamics-of-lifting-surfaces-3479105flo.pdf

Boundary value problems in aerodynamics of lifting surfaces in non-uniform motion

The symbol $ indicates that the principal value of the integral is to be taken and the coefficients cn are given constants. The special case of all cn = 0 has been dealt with extensively, for instance by Glauert [ l ] , Fuchs [2], Hamel [3], Schroeder [4] and Sohngen [S]. The values of the coefficients cn might be determined by the condition that a given kernel i£(£—#), for instance i£ = l /sinh (£—#), is approximated as nearly as possible by the kernel of equation (1). The purpose of the present note is to derive the solution of (1) for a finite number of non vanishing cn. The method of solution is an extension of the method applicable when all cn = 0. Equation (1) is first transformed by the substitutions (2) x = cos #, £ = cos 0, (3) g(*)=G( ), f(Q=F(fi) into

/pdf/solution-of-a-class-of-singular-integral-equations-4iq7r52hrx.pdf

Eric Reissner

Papers

Boundary value problems in aerodynamics of lifting surfaces in non-uniform motion

Solution of a class of singular integral equations