Static Aeroelasticity Using High Fidelity Aerodynamics in a Staggered Coupled and ROM Scheme
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2.161 Signal Processing: Continuous and Discrete Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 2.161 Signal Processing: Continuous and Discrete Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Massachusetts Institute of Technology Department of Mechanical Engineering 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 1 Lecture 1 Reading: • Class handout: The Dirac Delta and Unit-Step Functions 1 Introduction to Signal Processing In this class we will primarily deal with processing time-based functions, but the methods will also be applicable to spatial functions, for example image processing. We will deal with (a) Signal processing of continuous waveforms f(t), using continuous LTI systems (filters). a LTI dy nam ical system input ou t pu t f(t) Continuous Signal y(t) Processor and (b) Discrete-time (digital) signal processing of data sequences {fn} that might be samples of real continuous experimental data, such as recorded through an analog-digital converter (ADC), or implicitly discrete in nature. a LTI dis crete algorithm inp u t se q u e n c e ou t pu t seq u e n c e f Di screte Si gnal y { n } { n } Pr ocessor Some typical applications that we look at will include (a) Data analysis, for example estimation of spectral characteristics, delay estimation in echolocation systems, extraction of signal statistics. (b) Signal enhancement. Suppose a waveform has been contaminated by additive “noise”, for example 60Hz interference from the ac supply in the laboratory. 1copyright c D.Rowell 2008 1–1 inp u t ou t p u t ft + ( ) Fi lte r y( t) + n( t) ad d it ive no is e The task is to design a filter that will minimize the effect of the interference while not destroying information from the experiment. -
Lecture 2 LSI Systems and Convolution in 1D
Lecture 2 LSI systems and convolution in 1D 2.1 Learning Objectives Understand the concept of a linear system. • Understand the concept of a shift-invariant system. • Recognize that systems that are both linear and shift-invariant can be described • simply as a convolution with a certain “impulse response” function. 2.2 Linear Systems Figure 2.1: Example system H, which takes in an input signal f(x)andproducesan output g(x). AsystemH takes an input signal x and produces an output signal y,whichwecan express as H : f(x) g(x). This very general definition encompasses a vast array of di↵erent possible systems.! A subset of systems of particular relevance to signal processing are linear systems, where if f (x) g (x)andf (x) g (x), then: 1 ! 1 2 ! 2 a f + a f a g + a g 1 · 1 2 · 2 ! 1 · 1 2 · 2 for any input signals f1 and f2 and scalars a1 and a2. In other words, for a linear system, if we feed it a linear combination of inputs, we get the corresponding linear combination of outputs. Question: Why do we care about linear systems? 13 14 LECTURE 2. LSI SYSTEMS AND CONVOLUTION IN 1D Question: Can you think of examples of linear systems? Question: Can you think of examples of non-linear systems? 2.3 Shift-Invariant Systems Another subset of systems we care about are shift-invariant systems, where if f1 g1 and f (x)=f (x x )(ie:f is a shifted version of f ), then: ! 2 1 − 0 2 1 f (x) g (x)=g (x x ) 2 ! 2 1 − 0 for any input signals f1 and shift x0. -
Introduction to Aircraft Aeroelasticity and Loads
JWBK209-FM-I JWBK209-Wright November 14, 2007 2:58 Char Count= 0 Introduction to Aircraft Aeroelasticity and Loads Jan R. Wright University of Manchester and J2W Consulting Ltd, UK Jonathan E. Cooper University of Liverpool, UK iii JWBK209-FM-I JWBK209-Wright November 14, 2007 2:58 Char Count= 0 Introduction to Aircraft Aeroelasticity and Loads i JWBK209-FM-I JWBK209-Wright November 14, 2007 2:58 Char Count= 0 ii JWBK209-FM-I JWBK209-Wright November 14, 2007 2:58 Char Count= 0 Introduction to Aircraft Aeroelasticity and Loads Jan R. Wright University of Manchester and J2W Consulting Ltd, UK Jonathan E. Cooper University of Liverpool, UK iii JWBK209-FM-I JWBK209-Wright November 14, 2007 2:58 Char Count= 0 Copyright C 2007 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (+44) 1243 779777 Email (for orders and customer service enquiries): [email protected] Visit our Home Page on www.wileyeurope.com or www.wiley.com All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher. Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed to [email protected], or faxed to (+44) 1243 770620. -
Linear System Theory
Chapter 2 Linear System Theory In this course, we will be dealing primarily with linear systems, a special class of sys- tems for which a great deal is known. During the first half of the twentieth century, linear systems were analyzed using frequency domain (e.g., Laplace and z-transform) based approaches in an effort to deal with issues such as noise and bandwidth issues in communication systems. While they provided a great deal of intuition and were suf- ficient to establish some fundamental results, frequency domain approaches presented various drawbacks when control scientists started studying more complicated systems (containing multiple inputs and outputs, nonlinearities, noise, and so forth). Starting in the 1950’s (around the time of the space race), control engineers and scientists started turning to state-space models of control systems in order to address some of these issues. These time-domain approaches are able to effectively represent concepts such as the in- ternal state of the system, and also present a method to introduce optimality conditions into the controller design procedure. We will be using the state-space (or “modern”) approach to control almost exclusively in this course, and the purpose of this chapter is to review some of the essential concepts in this area. 2.1 Discrete-Time Signals Given a field F,asignal is a mapping from a set of numbers to F; in other words, signals are simply functions of the set of numbers that they operate on. More specifically: • A discrete-time signal f is a mapping from the set of integers Z to F, and is denoted by f[k]fork ∈ Z.Eachinstantk is also known as a time-step. -
Digital Image Processing Lectures 3 & 4
2-D Signals and Systems 2-D Fourier Transform Digital Image Processing Lectures 3 & 4 M.R. Azimi, Professor Department of Electrical and Computer Engineering Colorado State University Spring 2017 M.R. Azimi Digital Image Processing 2-D Signals and Systems 2-D Fourier Transform Definitions and Extensions: 2-D Signals: A continuous image is represented by a function of two variables e.g. x(u; v) where (u; v) are called spatial coordinates and x is the intensity. A sampled image is represented by x(m; n). If pixel intensity is also quantized (digital images) then each pixel is represented by B bits (typically B = 8 bits/pixel). 2-D Delta Functions: They are separable 2-D functions i.e. 1 (u; v) = (0; 0) Dirac: δ(u; v) = δ(u) δ(v) = 0 Otherwise 1 (m; n) = (0; 0) Kronecker: δ(m; n) = δ(m) δ(n) = 0 Otherwise M.R. Azimi Digital Image Processing 2-D Signals and Systems 2-D Fourier Transform Properties: For 2-D Dirac delta: 1 1- R R x(u0; v0)δ(u − u0; v − v0)du0dv0 = x(u; v) −∞ 2- R R δ(u; v)du dv = 1 8 > 0 − For 2-D Kronecker delta: 1 1 1- x(m; n) = P P x(m0; n0)δ(m − m0; n − n0) m0=−∞ n0=−∞ 1 2- P P δ(m; n) = 1 m;n=−∞ Periodic Signals: Consider an image x(m; n) which satisfies x(m; n + N) = x(m; n) x(m + M; n) = x(m; n) This signal is said to be doubly periodic with horizontal and vertical periods M and N, respectively. -
CHAPTER TWO - Static Aeroelasticity – Unswept Wing Structural Loads and Performance 21 2.1 Background
Static aeroelasticity – structural loads and performance CHAPTER TWO - Static Aeroelasticity – Unswept wing structural loads and performance 21 2.1 Background ........................................................................................................................... 21 2.1.2 Scope and purpose ....................................................................................................................... 21 2.1.2 The structures enterprise and its relation to aeroelasticity ............................................................ 22 2.1.3 The evolution of aircraft wing structures-form follows function ................................................ 24 2.2 Analytical modeling............................................................................................................... 30 2.2.1 The typical section, the flying door and Rayleigh-Ritz idealizations ................................................ 31 2.2.2 – Functional diagrams and operators – modeling the aeroelastic feedback process ....................... 33 2.3 Matrix structural analysis – stiffness matrices and strain energy .......................................... 34 2.4 An example - Construction of a structural stiffness matrix – the shear center concept ........ 38 2.5 Subsonic aerodynamics - fundamentals ................................................................................ 40 2.5.1 Reference points – the center of pressure..................................................................................... 44 2.5.2 A different -
Introduction to Aeroelasticity.Pdf
Aeroelasticity Dr. Ugur GUVEN Aerospace Engineer (P.hD) Nuclear Science and Technology Engineer (M.Sc) What is Aeroelasticity • Aeroelasticity is broadly defined as the interaction between the aerodynamic forces and the structural forces causing a deformation in the structure of the aerospace craft as well as in its control mechanism or in its propulsion systems. Importance of Aeroelasticity • Aeroelasticity has become a very important force especially after the 1950’s. • The interaction between aerodynamic loads and structural deformations have gained great importance in view of factors related to the design of aircraft as well as missiles. • Aeroelasticity plays at least some part on fuel sloshing as well as on the reentry of spacecraft in astronautics. Trends in Technology • Due to the advancements in technology, it has become quite common to see the slenderness ratio (ratio of length of wing span to thickness at the root) increase. • The wing span area as well as the length of aircrafts have increased causing aircraft to become much more susceptible to interaction between structural loads and aerodynamic loads Slenderness Ratio Effect of Aerodynamic Loads • The forces of lift and drag as well as torsion moment will have some sort of effect on the structural integrity of the spacecraft. • In many cases, some parts of aircraft or spacecraft may bend or ripple slightly due to these loads. • The frequency of these loads and effects can also cause the aircraft’s structure to suffer from metal fatigue in the long run. Scope of Aeroelasticity Vibration • One of the ways in which aerodynamic and structural forces collide with each other is through vibration. -
AAE556-Aeroelasticity
AIRCRAFT AEROELASTIC DESIGN AND ANALYSIS An introduction to fundamental concepts of static and dynamic aeroelasticity - with simple idealized models and mathematics to describe the essential features of aeroelastic problems. These notes are intended for the use of Purdue University students enrolled in AAE556. They are not for sale or intended for distribution to others, but may be used for educational purposes, with prior permission of the author. Terry A. Weisshaar Purdue University © 1995 (Second edition -2009) Introduction - page 1 Preface to Second Edition – The purpose and scope These notes are the result of three decades of experiences teaching a course in aeroelasticity to seniors and first or second year graduate students. During this time I have presented lectures and developed homework problems with the objective of introducing students to the complexities of a field in which several major disciplines intersect to produce major problems for high speed flight. These problems affect structural and flight stability problems, re-distribution of external aerodynamic loads and a host of other problems described in the notes. This three decade effort has been challenging, but more than anything, it has been fun. My students have had fun and have been contributors to this teaching effort. Some of them have even gone on to surpass my skills in this area and to be recognized practitioners in this area. First of all, let me emphasize what these notes are not. They are not notes on advanced methods of analysis. They are not a “how to” book describing advanced methods of analysis required to analyze complex configurations. If your job is to compute the flutter speed of a Boeing 787, you will have to learn that skill elsewhere. -
A Historical Overview of Flight Flutter Testing
tV - "J -_ r -.,..3 NASA Technical Memorandum 4720 /_ _<--> A Historical Overview of Flight Flutter Testing Michael W. Kehoe October 1995 (NASA-TN-4?20) A HISTORICAL N96-14084 OVEnVIEW OF FLIGHT FLUTTER TESTING (NASA. Oryden Flight Research Center) ZO Unclas H1/05 0075823 NASA Technical Memorandum 4720 A Historical Overview of Flight Flutter Testing Michael W. Kehoe Dryden Flight Research Center Edwards, California National Aeronautics and Space Administration Office of Management Scientific and Technical Information Program 1995 SUMMARY m i This paper reviews the test techniques developed over the last several decades for flight flutter testing of aircraft. Structural excitation systems, instrumentation systems, Maximum digital data preprocessing, and parameter identification response algorithms (for frequency and damping estimates from the amplltude response data) are described. Practical experiences and example test programs illustrate the combined, integrated effectiveness of the various approaches used. Finally, com- i ments regarding the direction of future developments and Ii needs are presented. 0 Vflutte r Airspeed _c_7_ INTRODUCTION Figure 1. Von Schlippe's flight flutter test method. Aeroelastic flutter involves the unfavorable interaction of aerodynamic, elastic, and inertia forces on structures to and response data analysis. Flutter testing, however, is still produce an unstable oscillation that often results in struc- a hazardous test for several reasons. First, one still must fly tural failure. High-speed aircraft are most susceptible to close to actual flutter speeds before imminent instabilities flutter although flutter has occurred at speeds of 55 mph on can be detected. Second, subcritical damping trends can- home-built aircraft. In fact, no speed regime is truly not be accurately extrapolated to predict stability at higher immune from flutter. -
Wing Shape Multidisciplinary Design Optimization
Faculty of Aerospace Engineering Wing Shape Multidisciplinary Design Optimization Jan Mariens August 2, 2012 Wing Shape Multidisciplinary Design Optimization Master of Science Thesis For obtaining the degree of Master of Science in Aerospace Engineering at Delft University of Technology Jan Mariens August 2, 2012 Faculty of Aerospace Engineering Delft University of Technology · Delft University of Technology Copyright c Jan Mariens All rights reserved. Delft University Of Technology Department Of Flight Performance and Propulsion The undersigned hereby certify that they have read and recommend to the Faculty of Aerospace En- gineering for acceptance a thesis entitled “Wing Shape Multidisciplinary Design Optimization” by Jan Mariens in partial fulfillment of the requirements for the degree of Master of Science. Dated: August 2, 2012 Head of Department: Dr. ir. Dries Visser Supervisor: Ali Elham, MSc. Reader one: Prof. dr. ir. Egbert Torenbeek Reader two: Dr. ir. Roelof Vos Summary Multidisciplinary design optimizations have shown great benefits for aerospace applications in the past. Especially in the last decades with the advent of high speed computing. Still computational time limits the desire for models with high level of fidelity cannot be always fulfilled. As a conse- quence, fidelity is often sacrificed in order to keep the computing time of the optimization within limits. There is always a compromise required to select proper tools for an optimization problem. In this final thesis work, the differences between existing weight modeling techniques are investi- gated. Secondly, the results of using different weight modeling techniques in multidisciplinary design optimization of aircraft wings is compared. The aircraft maximum take-off weight was selected as the objective function. -
Aeroelasticity
1 Matthew Moraguez Aeroelasticity What is Aeroelasticity? An airplane’s wing generates an upward AEROELASTICITY, NOUN force, known as lift, when it passes through air. Although lift is needed for a plane to fly, A term used in the field of aerospace its effect on the structure of the plane can be engineering to describe the interaction harmful. Aeroelasticity refers to the between a structure and a moving fluid [1]. deformation of an airplane’s wing in response to aerodynamic forces, such as lift. [1] Static vs. Dynamic Aeroelasticity Aeroelastic effects are classified as either static or dynamic. While static effects reach an equilibrium, dynamic effects are defined by oscillations [2]. Static Aeroelasticity: Aeroelasticity applies to Divergence refers to a process in which the lift a wing produces causes the wing itself to twist. This twisting any situation in which a leads to greater lift, which causes more twisting. The fluid (gas or liquid) flows process continues until equilibrium is reached [1]. In around a structure [3]. order to prevent divergence, a wing must be stiff enough to prevent twisting. If the wing is too flexible or the force of lift is too strong, divergence will occur [2]. DID YOU KNOW? Aileron reversal occurs when wing twisting causes the plane’s response to the pilot’s commands to be Aeroelasticity affects airplane reversed from the expected. In other words, when a stability, bridge design, and even blood flow through the body! [3] pilot tries to turn left, the plane will turn right [2]. Dynamic Aeroelasticity: Above a critical wind speed, a wing experiences flutter instability, which causes the wing to oscillate. -
Aeroelasticity and Structural Dynamics
Aeroelasticity and Structural Dynamics Aeroelasticity and Structural Dynamics he fourteenth issue of AerospaceLab Journal is dedicated to aeroelasticity and T structural dynamics. Aeroelasticity can be briefly defined as the study of the low frequency dynamic behavior of a structure (aircraft, turbomachine, helicopter rotor, etc.) in an aerodynamic flow. It focuses on the interactions between, on the one hand, the static or vibrational deformations of the structure and, on the Cédric LIAUZUN other hand, the modifications or fluctuations of the aerodynamic flow field. (ONERA) Senior Scientist Aeroelastic phenomena have a strong influence on stability and therefore on the integrity of aeronautical structures, as well as on their performance and durability. In the current context, in which a reduction of the footprint of aeronautics on the environment is sought, in particular by reducing the mass and fuel consumption of aircraft, aeroelasticity problems must be taken into account as early as possible in the design of such structures, whether they are conventional or innovative concepts. It is therefore necessary to develop increasingly efficient and accurate numerical and experimental methods and tools, allowing additional complex physical phenomena to be taken into account. On the other hand, the development of larger and lighter aeronautical structures entails the need to determine the dynamic characteristics of such Nicolas PIET-LAHANIER highly flexible structures, taking into account their possibly non-linear behavior (large (ONERA) displacements, for example), and optimizing them by, for example, taking advantage Senior Scientist of the particular properties of new materials (in particular, composite materials). DOI: 10.12762/2018.AL14-00 This issue of AerospaceLab Journal presents the current situation regarding numerical calculation and simulation methods specific to aeroelasticity and structural dynamics for several applications: fan damping computation and flutter prediction, static and dynamic aeroelasticity of aircraft and gust response.