This paper presents an implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for a quasi 1-D Euler CFD code. Given uncertainties in statistically independent, random, normally distributed input variables, a first-and second-order statistical moment matching procedure is performed to approximate the uncertainty in the CFD output. Efficient calculation of both first-and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, the moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving firstorder sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

Introductionhas been proven an effective tool for extracting aerody-namlc SDs from these modern CFD codes" . The present study will essentially build on earlier studies" m an effort to exploit the full potential of the latest version of ADIFOR 3107 fol_ obtaining SDs from CFD codes. and Eq. (3) One objective of this particular development of the AV method for aerodynamic SDs is to ensure that the relationship given by Eq. (8) is clearly understood. The I-I method for solving the forward-mode, FO SD Eq. (4) iswhere superscript M is the FO SD iteration index, andWith the I-I methodology, the CFD flow solution operator Pint is also used to solve the SD equations; this operator in Eq. (12) is evaluated and fixed using the steady-state solution for the nonlinear flow. The requisite terms of Eq. (13) are constructed either by hand differentiation (i.e., the HDII method, which is very tedious and time consuming to complete with accuracy for advanced CFD codes) or by AD, which is the forward-mode ADII method of previous studies.In contrast with the ADII method, a straightforward BB application of AD to the CFD code, which is the ADBB method, is represented symbolically asClearly ADII (Eq. (12) and (13)) and ADBB (Eq. (14)) yield the same result at steady-state convergence of each (recall Eq. (2) Second-Order Sensitivity DerivativesThe SO SD methods are presented subsequently using the index notation and beginning with the following preliminary definitions:_= r°_

Introductionhas been proven an effective tool for extracting aerody-namlc SDs from these modern CFD codes" . The present study will essentially build on earlier studies" m an effort to exploit the full potential of the latest version of ADIFOR 3107 fol_ obtaining SDs from CFD codes. and Eq. (3) One objective of this particular development of the AV method for aerodynamic SDs is to ensure that the relationship given by Eq. (8) is clearly understood. The I-I method for solving the forward-mode, FO SD Eq. (4) iswhere superscript M is the FO SD iteration index, andWith the I-I methodology, the CFD flow solution operator Pint is also used to solve the SD equations; this operator in Eq. (12) is evaluated and fixed using the steady-state solution for the nonlinear flow. The requisite terms of Eq. (13) are constructed either by hand differentiation (i.e., the HDII method, which is very tedious and time consuming to complete with accuracy for advanced CFD codes) or by AD, which is the forward-mode ADII method of previous studies.In contrast with the ADII method, a straightforward BB application of AD to the CFD code, which is the ADBB method, is represented symbolically asClearly ADII (Eq. (12) and (13)) and ADBB (Eq. (14)) yield the same result at steady-state convergence of each (recall Eq. (2) Second-Order Sensitivity DerivativesThe SO SD methods are presented subsequently using the index notation and beginning with the following preliminary definitions:_= r°_

For the purposes of stability analyses, it is necessary to describe the dynamic equilibrium state of a rotor blade in forward flight in terms of a Fourier series. Typically, this is assumed to consist of constant and sinusoidal terms that are integer multiples of the rotor speed. Such an approach neglects potentially important dynamics associated with subsynchronous, supersynchronous, and aperiodic responses. The current work investigates the occurrence of such behavior and discusses some conditions where it may be important. Simulation studies are conducted using a simplified nonlinear rotor blade model in forward flight. This model consists of a rigid blade with effective hinges at the root to simulate a hingeless rotor blade. Quasi-steady linear strip theory is used to provide aerodynamic forcing in the model. The nonlinear terms arise from geometrical effects in the structural and aerodynamic modeling procedure. The resulting system of equations is studied using direct numerical integration and harmonic balancing. Nonsynchronous and aperiodic responses are observed for several realistic parameter configurations.

The representation of females in the engineering world has grown considerably in recent decades. The message heard nation wide is that femles are fully capable of studying, practicing, and teaching engineering. Yet an issue that is rarely addressed in a public forum is that of combining a career in engineering with motherhood. It is a subject female engineers hesitate to discuss in their quest to be accepted in the male-dominated profession of engineering. The distinct roles of a mother and an engineer are viewed by many to be incongruous. As a mother, and an engineering educator, I wish to share my experiences and thoughts related to my dual role. This paper will discuss personal experiences and issues related to choosing both engineering and motherhood. "Equality" ?Although many opinions and stereotypes still exist in our society, I dare to say that I, as an engineering educator, have equal status and salary compared to any male who has worked in my position. I pay homage to the trailblazers, who bonded together decades ago and developed a powerful women's movement that made it possible for me to claim "equality." As a woman with a career, I am free from the "oppression" of a life dedicated to, and solely revolving around, a husband and children. Yet, I cannot help but notice that I am not "equal" to my co-workers; I am a mother. Although I am free of the prewomen's movement "oppression" associated with motherhood, I am not free of strong maternal