Research directions in Engineering Dynamics COPPE/UFRJ and Swansea Workshop November 2014 Sondipon Adhikari http://engweb.swan.ac.uk/~adhikaris/ Twitter: @ProfAdhikari
Engineering Dynamics • Principal investigators: Prof Friswell, Prof Adhikari, Dr Haddad • Main research areas • Summary of current research works – Morphing Aircraft and Nonlinear dynamics – Vibration energy harvesting – Uncertainty quantification – Model updating • Future works
Michael I. Friswell: Morphing Aircraft and Dynamics Modelling, analysis, simulation, identification & optimisation of engineering structures Nonlinear Structural and Rotor Morphing Aircraft Dynamics 10 0 Model Updating and Inverse Problems 10 –2 10 –4 MORPHLET – Morphing Winglet 10 –6 0 2 4 6 Automatic Rotor Balancing FishBAC Active Camber FE Model Identification Bistable Plates Energy Rotating Machine Harvesting Diagnostics Corrugated Skins
Hamed Haddad Khodaparast : Uncertainty analysis in aircraft structures Using non-probabilistic models for uncertainty analysis and robust design in aircraft structures Uncertainty Quantification Development of non-probabilistic of Aeroelastic Stability Stochastic Model Updating techniques Variations in the fuel load and its Simplified AIRcraft MODel- AIRMOD Surrogate modelling effect on the aeroelastic behavior of (DLR-Germany) (Kriging and Polynomial the Semi-Span Super-Sonic Transport Chaos Expansion) wind-tunnel model (S4T) Probabilistic Comparison of non-probabilistic and probabilistic stochastic model updating using the DLR AIRMOD test structure Rapid perdition of worst case Non-probabilistic-Fuzzy gust loads
Sondipon Adhikari: Structural dynamics across different length scales Uncertainty quantification and model validation Vibration Energy Harvesting Dynamics of Nanoscale Structures L Stochastic Structural Dynamics ρ A y x Non linear vibration energy harvesting Nonlocal continuum method of Novel computational methods for under random ambient excitations transient dynamic response of vibration based nanosensors System Identification dynamical systems with uncertainty 9 8 Fitted coefficient matrix C kj 7 6 5 4 3 2 1 0 30 25 20 30 15 25 10 20 15 5 10 5 0 0 Atomistic finite element method for Experimental methods for Damping identification from dynamics of general nano scale structures uncertainty quantification in like DNA, Graphene sheets, Boron Nitride experimental measurements structural dynamics
Morphing Aircraft and Nonlinear dynamics Title of Title of presentation presentation Click to edit subtitle style Click to edit subtitle style
Morphing Aircraft Camber morphing - FishBAC Span Extension Morphing Winglet - MORPHLET Corrugated Skins
Nonlinear Structural and Rotor Dynamics Bistable plates – applications, design, analysis, control Rotating machine analysis & diagnostics – breathing cracks, unbalance, rotor-stator Automatic ball balancers, contact, etc bifurcation analysis
Vibration energy harvesting Title of Title of presentation presentation Click to edit subtitle style Click to edit subtitle style
Vibration energy harvesting • Wireless sensor network for structural health monitoring • Self-powered sustainable sensors – vibration energy harvesting
Energy harvesting with broadband noice Proof Mass x Piezo- v R l ceramic + Base The average harvested power due to white-noise base acceleration with a circuit without an inductor x b can be obtained as 5 Normalized mean power 4 3 The optimal condition is 2 1 0 0 4 3 0.1 2 1 0.2 0 ζ α
Vibration energy harvesting
Uncertainty quantification Title of Title of presentation presentation Click to edit subtitle style Click to edit subtitle style
Uncertainty in Structural Dynamics Stochastic dynamical systems across the length-scale
Uncertainty modeling in structural dynamics Uncertainty modeling Nonparametric uncertainty: Parametric uncertainty: mean matrices + a single mean matrices + random dispersion parameter for each field/variable information matrices Random matrix model Random field discretization
Dynamic Response • For parametric uncertainty propagation: • For nonparametric uncertainty propagation • Unified mathematical representation • Can be useful for hybrid experimental-simulation approach for uncertainty quantification
Plate with Stochastic Properties • Thin plate with stochastic bending modulus (nominal properties 1m x 0.6m, t=03mm, E=2 x 10 11 Pa) • 16 random variables approximating the random field • We study the deflection of the plate under the action of a point The bending modulus is taken to be a homogeneous stationary Gaussian random field with exponential autocorrelation function (correlation lengths L/5) • Constant modal damping is taken with 1% damping factor for all modes.
Response Statistics − 3 10 − 3 10 direct MCS deterministic 2nd order spectral direct MCS Standard deviation of deflection (m) 3rd order spectral − 4 10 2nd order spectral − 4 4th order spectral 10 3rd order spectral Mean of deflection (m) 4th order spectral − 5 10 − 5 10 − 6 10 − 6 10 − 7 − 7 10 10 − 8 − 8 10 10 0 100 200 300 400 500 0 100 200 300 400 500 Frequency (Hz) Frequency (Hz) Standard deviation with σ a = 0.1 Mean with σ a = 0.1 Proposed approach: 150 x 150 equations 4 th order Polynomial Chaos: 9113445 x 9113445 equations
Plate with randomly placed oscillators 10 oscillators with random stiffness values are attached at random locations in the plate by magnet
Mean of a cross-FRF 60 50 40 30 Mean of amplitude (dB) 20 10 0 − 10 − 20 Reduced diagonal Wishart − 30 Experiment − 40 0 500 1000 1500 2000 2500 3000 3500 4000 Frequency (Hz)
Standard deviation of a cross-FRF 1 10 Reduced diagonal Wishart Experiment Relative standard deviation 0 10 − 1 10 − 2 10 0 500 1000 1500 2000 2500 3000 3500 4000 Frequency (Hz)
Model updating and inverse problems Title of Title of presentation presentation Click to edit subtitle style Click to edit subtitle style
Model Updating Vibration measurement, modal analysis Improve FE models using measured data,regularisation Choose parameters: car body, Lynx tail
Stochastic model updating: DLR AIRMOD Structure Identifying joint stiffness variability due to assembling and reassembling process. Physical structure FE NASTRAN MODEL
Experimental mode shapes 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
AIRMOD – Observed Variability Natural Frequency Damping Modal Mass 26
Stochastic model updating procedure Finite Element representation p ⎧ ⎫ … Young’s modulus 1 ⎪ ⎪ Randomise p … joint stiffness ⎪ ⎪ Parameters 2 (Latin ⎨ ⎬ M Hypercube ⎪ ⎪ Sampling) 1 p ⎪ ⎪ … density 2 ⎩ n ⎭ in-plane bend. Monte Carlo Simulation (MCS) Correlation of visible in Mode 12 scatter diagram Mode 13 frequency 4n wing bend. Scatter Diagram 3 4
Interval updating vs. perturbation method
Other research interests Title of Title of presentation presentation Click to edit subtitle style Click to edit subtitle style
Stochastic multiscale mechanics • New generation of structural materials • Nano-composites, bio-composites • Self-sensing, multifunctional, self-healing and sustainable materials – high strength to weight ratio • We need to embrace new materials and develop next generation of analysis and design tools • Requires multiscale and multiphysics approach
Nano-scale stochastic mechanics • Uncertainty in modeling (geometry, boundary condition, system parameters) • There are defects which may not be known a-priori • Analysis using the principles of structural mechanics, dynamics, stochastic finite element method • Propagation of uncertainty across the length and time-scale
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