Active vibration control of flexible structures under aerodynamic excitation

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ACTIVE VIBRATION CONTROL OF FLEXIBLE STRUCTURES UNDER AERODYNAMIC

EXCITATION

SANJEEV SOOD

DEPARTMENT OF MECHANICAL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY DELHI

OCTOBER 2016 OCTOBER 2018

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© Indian Institute of Technology Delhi (IITD), New Delhi, 201 8

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ACTIVE VIBRATION CONTROL OF FLEXIBLE STRUCTURES UNDER AERODYNAMIC

EXCITATION

by

SANJEEV SOOD

DEPARTMENT OF MECHANICAL ENGINEERING

Submitted

in fulfillment of the requirements of the degree of Doctor of Philosophy to the

INDIAN INSTITUTE OF TECHNOLOGY DELHI OCTOBER, 2016

submitted

in the fulfilment of the requirements of the degree of Doctor of Philosophy to the

OCTOBER 2018

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This thesis is dedicated to my respected parents Smt. Surendra Sood and Sh. Om Prakash Sood, my supervisors Prof. S. P. Singh, Dr. A. K. Darpe

&

wife Nidhi Sood, son Dhruv Sood and

daughter Snigdha Sood

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i

CERTIFICATE

This is to certify that the thesis entitled ACTIVE VIBRATION CONTROL OF FLEXIBLE STRUCTURES UNDER AERODYNAMIC EXCITATION submitted by SANJEEV SOOD to the Indian Institute of Technology Delhi for the award of the degree of Doctor of Philosophy is a bonafide record of the research work carried out by him under our supervision. This thesis has been prepared in conformity with the rules and regulations of the Indian Institute of Technology Delhi. We further certify that the thesis has attained a standard required for a degree Doctor of Philosophy. The research reported and the results presented in the thesis, in full or in parts, have not been submitted to any other Institute or University for the award of any degree or diploma.

_ _

Prof. S. P. Singh Dr. A. K. Darpe

Professor Associate Professor

Department of Mechanical Engineering Department of Mechanical Engineering Indian Institute of Technology Delhi Indian Institute of Technology Delhi

New Delhi-110016, India New Delhi-110016, India

Date

_______________

Date

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ACKNOWLEDGEMENTS

First and foremost, I would like to express my deepest gratitude to my supervisors Prof. S.

P. Singh and Dr. A. K. Darpe. They always understood the intricacies involved in finding out time from my busy office schedule. I appreciate their availability during after office hours and on weekends including Sundays to discuss various research related topics with me. They always inspired me to complete my research work with utmost dedication and sincerity.

I am also very thankful to my Student Research Committee (SRC) members, Prof. K. Gupta (Chairman), Dr. Subodh V. Modak, and Dr. Suresh Bhalla. Their valuable suggestions during different review meetings of the Ph.D. made significant improvements in the quality of the research work carried out.

I am also indebted to Mr. Manik Mukherjee, ex-director of Directorate of Futuristic Technology Management, DRDO Hqrs for inspiring me to pursue Ph.D. He constantly encouraged me to complete my research work related to the doctoral program. I am also grateful to DRDO, especially Mr. MH Rahaman, Director General (Tech. Management) for providing me freedom and space to carry out the research work.

I am also thankful to Mr. K. N. Madhu, the lab in charge of the Vibration Research Laboratory (VRL) for helping me out with the experimental work. I also appreciate the friendly gestures of the research scholars of the VRL, Dr. Skylab Bhore, Dr. Apurba Mandal, Dr. Ashish Purohit, Dr. Piyush Shakya, Mr. Radhe Shyam Maurya, Mr. Asjad Mokhtar, Mr. Jaskaran Singh, Mr. Anvesh Reddy, Mr. Pradeep Kundu, Research Assistant Ms. Sintu Punnoose, NIT Suratkal

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B. Tech. intern Mr. Anmol Gaurav, IIT Delhi B. Tech. students Mr. Pushpendra Sharma and Mr.

Vasu Sharma. They made my time at VRL memorable and enjoyable.

I would also like to thank my parents, my wife Nidhi Sood, son Dhruv Sood, daughter Snigdha Sood for their constant moral support to crawl through the difficult phases of the doctoral program. They had to suffer on several occasions due to myself being occupied in the research work. This research work would not have been possible without their support. In the last, I would like to thank the God for giving me strength to complete this research work.

Sanjeev Sood

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ABSTRACT

Detailed experimental and numerical investigation of flow-induced vibration under aerodynamic loading and its systematic control are reported. The methodology is developed on a simple twodimensional model of a beam and the work has been extended in the case of the three-dimensional plate. A thin plate with a front obstacle is used as a test model. Various excitation strategies as stochastic excitation, and random excitations and aerodynamic excitation are studied and implemented in the numerical simulation. The uncontrolled and controlled responses of the cantilevered plate are simulated using Ansys workbench and a MATLAB code developed in- house. A two-way fluid-structure interaction is considered in simulation. The concept of efficient modal control has been explored by assigning weightage to states based on FFT.

Using the system identification approach, vibration control of the plate using LQR Controller is investigated. It required the information of input to the structure and the response of the structure.

Based on the pressure exerted on the plate by the fluid and its response, the equivalent state matrices are identified based on subspace iteration method. The effectiveness of a control based on the system identification approach which is derived from plate response in flow is investigated.

It is shown that the control based on the system identification approach derived from plate response with full FSI is more effective compared to the case when the structure identification is done without considering the FSI.

Under changing excitation conditions as usually happens in flow situations, an adaptive controller is experimentally explored in the modeling of the active vibration control of flexible structures.

The use of multiple patches on the plate and designing a MIMO controller for producing a control which can effectively control tonal as well as broadband excitations has been studied and reported.

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सार

वायुगतिकीय के िहि प्रवाह प्रेरिि कंपन की तवस्िृि प्रयोगात्मक औि संख्यात्मक जांच

लोत ंग औि इसके व्यवतस्िि तनयंत्रण की सूचना दी गई है। पद्धति एक सिल twodimensional पि तवकतसि तकया गया है

एक बीम का मॉ ल औि कायय तत्र-आयामी के मामले में बढा तदया गया है

प्लेट। सामने की बाधा वाली पिली प्लेट का प्रयोग पिीक्षण मॉ ल के रूप में तकया जािा है। के रूप में तवतिन्न उत्तेजना िणनीतियों

स्टोकातस्टक उत्तेजना, औि यादृतछिक उत्तेजना औि वायुगतिकीय उत्तेजना का अध्ययन तकया जािा है औि

संख्यात्मक तसमुलेशन में लागू तकया गया। अतनयंतत्रि औि तनयंतत्रि प्रतितियाओं के

cantilevered प्लेट Ansys workbench औि इनहाउस तवकतसि एक MATLAB को का उपयोग कि नकल कि िहे हैं।

तसमुलेशन में दो ििफा द्रव-संिचना पिस्पि तिया माना जािा है। कुशल की अवधािणा

एफएफटी के आधाि पि िाज्यों को वेटेज असाइन किके मॉ ल तनयंत्रण का पिा लगाया गया है।

तसस्टम पहचान दृतिकोण का उपयोग, एलक्यूआि तनयंत्रक का उपयोग कि प्लेट का कंपनतनयंत्रण है

की जााँच की। इसे संिचना में इनपुट की जानकािी औि संिचना की प्रतितिया की आवश्यकिा िी।

ििल पदािय औि इसकी प्रतितिया, समकक्ष िाज्य द्वािा प्लेट पि लगाए गए दबाव के आधाि पि

मेतिस की पहचान सबस्पेस पुनिावृतत्त तवतध के आधाि पि की जािी है। एक तनयंत्रण आधारिि की प्रिावशीलिा

प्रवाह पहचान प्लेट से प्राप्त तसस्टम पहचान दृतिकोण पि जांच की जािी है।

यह तदखाया गया है तक प्लेट प्रतितिया से प्राप्त तसस्टम पहचान दृतिकोण के आधाि पि तनयंत्रण जब संिचना पहचान की जािी है िो मामले की िुलना में पूणय एफएसआई अतधक प्रिावी होिा है

एफएसआई पि तवचाि तकए तबना।

उत्तेजना की तस्िति को बदलने के िहि आमिौि पि प्रवाह तस्ितियों में होिा है, एक अनुकूली तनयंत्रक लचीली संिचनाओं के सतिय कंपन तनयंत्रण के मॉ तलंग में प्रयोगात्मक रूप से एक्सप्लोि तकया गया है।

प्लेट पि एकातधक पैच का उपयोग औि तनयंत्रण के तनमायण के तलए एक एमआईएमओ तनयंत्रक त जाइन किना

जो टोनल के साि-साि ब्रॉ बैं उत्तेजनाओं को प्रिावी ढंग से तनयंतत्रि कि सकिा है औि अध्ययन तकया गया है

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List of Figures

Figure 1-1: A picture showing the failure of the Tacoma Narrows bridge (Fuller, Lang. and Lang,

2000) ... 1

Figure 1-2: Active cancellation and vibration isolation with feedback and feed forward for an aircraft engine mount (Luo &Young, 2013) ... 3

Figure 1-3: Interaction of Various forces in Actively controlled response of structure in Flow .... 5

Figure 1-4: LQG controller model ... 10

Figure 3-1: Plate with Piezo Patches ... 42

Figure 3-2: Model of the plate in ANSYS with Piezo sensor and actuator ... 42

Figure 3-3: Equivalent concentrated moment 𝑀 applied to piezoelectric patch ... 43

Figure 3-4: Time versus displacement for Impulse Load ... 45

Figure 3-5: FFT of displacement for Impulse Load case ... 45

Figure 3-6: Aerodynamic Load versus Time ... 46

Figure 3-7: Displacement Time response for Aerodynamic Load with 5% fluctuation. ... 47

Figure 3-8: FFT of Displacement for Aerodynamic Load case ... 47

Figure 3-9: Finite element and nodes... 50

Figure 3-10: Assembly of finite element matrices ... 52

Figure 3-11: Mode shapes ... 53

Figure 3-12: FE model of plate developed in ANSYS workbench ... 54

Figure 3-13:(a) 1st mode shape: pure bending (b) 2nd mode shape: pure torsion (c) 3rd mode shape: coupled (d) 4th mode shape: coupled (e) 5th mode shape: coupled ... 55

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Figure 3-14: LQG controller model ... 57

Figure 3-15: Flow chart of simulation in MATLAB ... 60

Figure 3-16: Schematic of simulation setup ... 64

Figure 3-17: FFT of the excitation force ... 66

Figure 3-18: Variation in maximum control moment with coefficient of R matrix ... 68

Figure 3-19: Variation in RMS with coefficient of R matrix ... 68

Figure 3-20: Simulated response of system for input weightage matrices R1 and R2 ... 69

Figure 3-21: FFT of response ... 70

Figure 3-22: Response of the plate for 4 Hz/0.2N excitation (a, b) analytical results, (c, d) Results from ANSYS Workbench ... 72

Figure 3-25: Damped response of the plate (a, b) for 4Hz/0.2N excitation (c, d) for 6Hz/0.2N excitation. ... 75

Figure 3-26: Uncontrolled and controlled response of the plate for 4Hz/0.2N excitation. ... 76

Figure 4-1: Schematic of MFX solver ... 85

Figure 4-2: Flow computational domain used in the benchmark study ... 86

Figure 4-3: Schematic of square bluff body with the trailing flexible plate, (a) 3D view, (b) 2D view. ... 89

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Figure 4-4: Flow computational domain... 89

Figure 4-5: Mesh configuration (a) unstructured mesh over the test model, b) mesh configuration in the boundary layer over the surface of the plate ... 91

Figure 4-6: Time history and frequency spectrum of the lift force at a flow velocity of 6 m/s. ... 92

Figure 4-7: Instantaneous configuration of vorticity contours of the flow filed around the vibrating plate plotted for the 40 mm upstream obstacle and 4 m/s floe velocity at different time instances. ... 95

Figure 4-8: Instantaneous configuration of pressure contours of the flow filed around the vibrating plate plotted for the 40 mm upstream obstacle and 4 m/s floe velocity at different time instances. ... 96

Figure 4-9: Instantaneous configuration of streamline pattern of the flow filed around the vibrating plate plotted for the 40 mm upstream obstacle and 4 m/s floe velocity at different time instances. ... 97

Figure 4-10: Time history and frequency response at 140mm from fixed end of the plate at 4 m/s flow velocity. ... 99

Figure 4-11: Superimposed images of plate displacement at 4 m/s flow velocity ... 99

Figure 4-12: Mean flow velocity (4 m/s) with a gust fluctuation ... 101

Figure 4-13: Response of the plate against gust flow velocity ... 102

Figure 4-14: Flow computational domain used for vertical plate simulation ... 103

Figure 4-15: (a) Vorticity contour (b) Pressure contour and (c) stream line pattern ... 104

Figure 4-16: Time history and frequency spectrum of vibration of tip of the vertical plate ... 105

Figure 5-1: Control Procedure using the identified Model ... 108

Figure 5-2: Subspace and classical methods of system identification; Overschee et al (1996) . 109 Figure 5-3: Finite element model of Flexible plate ... 110

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Figure 5-4: Schematic of plate with bluff body ahead ... 111

Figure 5-5: Simulated plate model in the wind tunnel Flow ... 112

Figure 5-6: Location of point on plate for measuring response ... 112

Figure 5-7: Pressure difference (At plate center line, 390 mm from fixed end) ... 113

Figure 5-8: Uncontrolled responses (At 390 mm from fixed end along the plate center line) ... 113

Figure 5-9: LQR Controlled system response for Varying ‘R’ (At plate center line, 390 mm from fixed end) ... 115

Figure 5-10: Zones of the Plate and Measurement Points for System Identification ... 116

Figure 5-11: Force at various locations at plate center line at different Distances from fixed end ... 116

Figure 5-12: Comparison of computed response (from identified system matrices) and simulated response (using CFX) (100 mm from fixed end...117

Figure 5-13: Comparison of computed response (from identified system matrices) and simulated response (using CFX) at plate center line, 200 mm from fixed end ... 118

Figure 5-14: Comparison of computed response (from identified system matrices) and simulated response (using CFX) at plate center line, at plate center line, 300 mm from fixed end ... 118

Figure 5-15: Comparison of computed response (from identified system matrices) and simulated response (using CFX) at plate center line, 390 mm from fixed end (location 4) ... 119

Figure 5-16: LQR Controlled system response for Varying ‘R’=1 (At plate center line –Various locations from fixed end) ... 120

Figure 5-17: LQR Controlled system response for Varying ‘R’=0.5(At plate center line –Various locations from fixed end) ... 120

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Figure 5-18: LQR Controlled system response for Varying ‘R’=0.01(At plate center line –

Various locations from fixed end) ... 121 Figure 5-19: LQR Controlled system response for Varying ‘R’=0.001 (At plate center line – Various locations from fixed end) ... 121 Figure 5-20: Simulated v/s Modeled response of Bare Plate(At plate center line –100 mm; 200 mm; 300 mm; 390 mm from fixed end)... 123 Figure 5-21: LQR Controlled bare Plate response for Varying ‘R’=0.5*I (At plate center line – 100 mm: 200 mm; 300 mm; 390 mm from fixed end) ... 125 Figure 5-22: LQR Controlled bare Plate response for Varying ‘R’=0.1*I (At plate center line – 100 mm: 200 mm; 300 mm; 390 mm from fixed end) ... 125 Figure 5-23: LQR Controlled bare Plate response for Varying R=0.01*I (At plate center line – 100 mm: 200 mm; 300mm; 390 mm from fixed end) ... 126 Figure 5-24: LQR Controlled bare Plate response for Varying ‘R’=0.001*I (At plate center line – 100 mm: 200 mm; 300 mm; 390 mm from fixed end) ... 126 Figure 5-25: Control Effectiveness: Actual gain versus Bare Plate gain ... 127 Figure 5-26: Plot Control Effectiveness: Actual Gain v/s Bare Plate Gain (Expanded) ... 127 Figure 5-27: Comparison of control force for different measurement locations for the two cases ... 128 Figure 5-28: Uncontrolled responses of plate in flow at 4m /sec. Simulated (through system identification) and (b) Actual ... 129 Figure 5-29: Uncontrolled and Controlled responses of plate in flow at 4m /sec. Q= [I]; R=0.1At position 60mm from fixed end and (b) At position 100mm from fixed end ... 130 Figure 5-30: Change in Control Force for one of the states with ‘R’ for plate in flow at 4m /sec.

LQR control applied to seven states system; Q=[I] ... 130

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Figure 6-1: Proposed overall scheme of control for modal controller of identified plate model

... 134

Figure 6-2: Schematic of the experimental structure with controller ... 135

Figure 6-3: An experimental setup of the cantilevered plate ... 136

Figure 6-4: Uncontrolled & Controlled Response with system matrices derived by random excitation under still air condition. ... 137

Figure 6-5: Control of Vibrations under air flow (a) Comparison of estimated and measured response (b) Comparison of controlled and uncontrolled response ... 140

Figure 6-6: Flexible Plate in wind Tunnel – Piezo Actuator side ... 141

Figure 6-7: Flexible plate in wind Tunnel – Piezo Sensor side ... 142

Figure 6-8: Flexible plate in wind Tunnel – View from flow exit side ... 143

Figure 6-9: Wind Tunnel set up –With instrumentation ... 143

Figure 6-10: Wind Tunnel Drive unit and control panel ... 144

Figure 6-11: Controlled and uncontrolled response at different flow velocities (a) 16.4 m/s, identification without FSI (b) 17.2 m/s Identification with FSI effects. ... 145

Figure 6-12: Uncontrolled response to external excitation for a plate under flow ... 146

Figure 6-13: Controlled response to external excitation for a plate under flow ... 147

Figure 6-14: Uncontrolled response under aerodynamic excitation ... 148

Figure 6-15: Controlled response under aerodynamic excitation ... 148

Figure 6-16: Input to the Actuator ... 149

Figure 6-17: Sensor Output ... 149

Figure 6-18: Controlled and Uncontrolled Plate response for Flow Velocity=0, under random excitation ... 150

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Figure 6-19: Frequency Spectrum of Plate Vibrations (zero flow velocity) ... 151

Figure 6-20: Input to Actuator ... 152

Figure 6-21: Sensor Output ... 153

Figure 6-22: Frequency spectrum of Sensor Outputs at speed 8.45 m/sec ... 154

Figure 6-23: Controlled and Uncontrolled plate response ... 154

Figure 6-24: Frequency spectrum of Vibration Response at flow speed of 10.89 m/sec ... 155

Figure 6-25: Random Excitation applied to Actuator 1 ... 158

Figure 6-26: Random Excitation applied to Actuator 2 ... 159

Figure 6-27: Sensor 1 Response ... 159

Figure 6-28: Sensor 2 Response ... 160

Figure 6-29: Controlled & Uncontrolled Response for Sensor 1 at 8.45 m/s velocity with System Matrix for 8.45m/s ... 163

Figure 6-30: Controlled & Uncontrolled Response for Sensor 2 at 8.45 m/s velocity with System Matrix for 8.45m/s ... 164

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List of Tables

Table 2-1: Some salient contributions for modelling of flow induced vibrations ... 19

Table 2-2: Table of literature survey on Active vibration control: Some Contributions ... 30

Table 3-1: Natural frequencies of plate ... 56

Table 3-2: Controlled response for different states weightage matrices ... 67

Table 3-3: Controlled response for different input weightage matrices R1 & R2 ... 71

Table 3-4: Summary of uncontrolled and controlled response of the plate against harmonic excitation ... 78

Table 4-1: Properties of fluid and solid structure and other parameters of study ... 87

Table 4-2: Results of FSI validation ... 87

Table 4-3: Variation of vortex shedding frequency with flow speed for rigid test model ... 92

Table 4-4: Natural frequency of the plate ... 94

Table 6-1: RMS VALUES ... 165

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Nomenclature and Abbreviations

̅ Average

β Function of roughness of surface

Φ Electric potential

𝜉 Local coordinates of the element.

𝜂 Local coordinates of the element.

𝜌 Density of plate material

ACLD Active constrained layer damping Av Overall control voltage

AVC Active vibration control

bd Width of piezo patch

𝐵_𝑜1 Indices of nodes for external random force

𝐵_𝑜2 Indices of nodes for control force

C Damping Coefficient

CARE Solution of the controller algebraic Riccati equation CFD Computational Fluid Dynamics

CWE Computational Wind Engineering

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d31 Piezoelectric transverse coefficient of Piezo patch

D Size of the cylinder

DNS Direct numerical simulation

E Young’s Modulus

E(.) Expectation operator

EIE Extraneous induced excitation EMC Efficient Modal Control

Ep Modulus of plate

f Vector of external mechanical loads

fc Control force

fe External random excitation force

fN First bending mode natural frequency of the plate f(t) Applied force

fvs Frequency of vortex shedding

FARE Estimator Algebraic Riccati equation

FFT Fast Fourier Transform

FSI Fluid-structure interactions

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gd Displacement gain

gv Derivative gain

h Half thickness of plate

H Shape function matrix

J Performance index

K Stiffness/Stiffness matrix

Kc Controller gain

Ke Estimator gain

Kuu Stiffness matrix

KuΦ Coupling matrix combining mechanical variable u and electrical variable Φ KΦΦ Matrix of electrical capacitance

LQE Linear-quadratic estimator LQG Linear-quadratic Gaussian

LQR Linear-quadratic regulator

m Number of element along the length of the plate

M Mass/Mass matrix

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M1 Concentrated moment

MFX Multi-field solver

MIE Movement induced excitation MIMO Multi input multi output

n Number of element along the width of the plate

NS Navier-Stokes

P Proportional

PD Proportional-Derivative

PID Proportional-Integral-Derivative

q Electric charge brought to the electrodes

Q Positive state weight matrix

Q1 State weight matrix

R Positive input weight matrix

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R1 Input weight matrix

R2 Input weight matrix

RANS Reynolds Averaged Navier-Stokes

Ru1u2 Cross variance function of the longitudinal velocity components u1 and u2

Sc Solution of the controller algebraic Riccati equation (CARE) Se Solution of the estimator Algebraic Riccati equation (FARE) SISO Single input single output

Sn Spectral density function SST Shear Stress Transport

St Strouhal number

t time

𝑇_𝑒 Kinetic energy

u Control force

1

u Longitudinal velocity components

2

u Longitudinal velocity components

𝑢_𝑒 Random excitation force

𝑢_𝑐 Control moment

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U Inlet flow Velocity

𝑈_𝑒 Potential energy

v Process noise

V Mean velocity of the wind

V1 Covariance of process noise (v) VIV Vortex-induced vibration

w Flexural displacement of node

w1 Measurement noise

W Width of the plate

W1 Covariance of measurement noise

x State vector

𝑥̂ Estimated state

X Flexural displacement

x(t) Exact control effort as computed by the controller in x direction

y Output being measured

y(t) Exact control effort as computed by the controller in y direction

Active vibration control of flexible structures under aerodynamic excitation

ACTIVE VIBRATION CONTROL OF FLEXIBLE STRUCTURES UNDER AERODYNAMIC

EXCITATION

SANJEEV SOOD

DEPARTMENT OF MECHANICAL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY DELHI

OCTOBER 2016 OCTOBER 2018

© Indian Institute of Technology Delhi (IITD), New Delhi, 201 8

ACTIVE VIBRATION CONTROL OF FLEXIBLE STRUCTURES UNDER AERODYNAMIC

EXCITATION

by

SANJEEV SOOD

DEPARTMENT OF MECHANICAL ENGINEERING

Submitted

in fulfillment of the requirements of the degree of Doctor of Philosophy to the

INDIAN INSTITUTE OF TECHNOLOGY DELHI OCTOBER, 2016

submitted

OCTOBER 2018

This thesis is dedicated to my respected parents Smt. Surendra Sood and Sh. Om Prakash Sood, my supervisors Prof. S. P. Singh, Dr. A. K. Darpe

&

wife Nidhi Sood, son Dhruv Sood and

daughter Snigdha Sood

CERTIFICATE

_______________ _______________

_______________

_______________

ACKNOWLEDGEMENTS

ABSTRACT

सार

Table of Contents

List of Figures

List of Tables

Nomenclature and Abbreviations

_ _