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Melih Papila, papila@mae.ufl.edu Assessment of Axisymmetric Piezoelectric Composite Plate Configurations for Optimum Volume Displacement Melih Papila Multidisciplinary & Structural Optimization Group Interdisciplinary Microsystems Group Slide 2 Melih Papila, papila@mae.ufl.edu 2 Acknowledgement Guigin Wang Quentin Gallas Dr. Bhavani Sankar Dr. Mark Sheplak Dr. Lou Cattafesta SPONSOR: NASA Langley Research Center Slide 3 Melih Papila, papila@mae.ufl.edu 3 Design Problem: Piezoelectric composite driver Synthetic Jets Sound generating/receiving devices MEMS PZT Microphone Displacement actuators Maximum volume displacement Maximum natural frequency Orifice Cavity Oscillating Piezo-Composite Diaphragm Net Flow Applications Gallas (2002) Slide 4 Melih Papila, papila@mae.ufl.edu 4 Volume displacement Electric field (Voltage ) PZT layer expands/contracts Plate bends Lateral deflection w(r) piezoceramic shim V Slide 5 Melih Papila, papila@mae.ufl.edu 5 Configurations Outer ring piezoceramic shim V piezoceramic shim V Inner disc Bimorph piezoceramic shim Unimorph piezoceramic shim V Slide 6 Melih Papila, papila@mae.ufl.edu 6 Objective Investigate trade off between volume displacement and natural frequency via Pareto Optimization BEAT THE EXISTING DESIGN Find the optimum dimensions of the shim and piezoelectric layers in order to achieve optimum volume displacement Slide 7 Melih Papila, papila@mae.ufl.edu 7 Outline Design problem & objective Analysis tool and verification Optimization of Circular Piezo-composite plate Design variables Objective function and Constraints Results Trade-off via Pareto Optimization: Volume displacement versus Natural Frequency Concluding Remarks Slide 8 Melih Papila, papila@mae.ufl.edu 8 Analysis: Natural Frequency P C eq M eq analytical Slide 9 Melih Papila, papila@mae.ufl.edu 9 Analysis: Volume displacement V P analytical Slide 10 Melih Papila, papila@mae.ufl.edu 10 Analysis: Lateral deflection Classical lamination theory Each layer is isotropic, linear elastic, constant thickness Bonding line and electrode layer are neglected Equilibrium equations Constitutive equations including piezoelectric effect Boundary and interface matching conditions piezoceramic shim (3) (2) (1) R1R1 R2R2 R3R3 Wang et al. (2002) Prasad et al. (2002) Slide 11 Melih Papila, papila@mae.ufl.edu 11 Analysis: Model verification Using scanning laser vibrometer V 10 mm 11.5 mm 0.20 mm 0.23 mm Gallas (2002) f nat (Hz) 3505 3542 Test Analysis Slide 12 Melih Papila, papila@mae.ufl.edu 12 Analysis: Model verification 17.6 mm 18.5 mm 0.12 mm 0.08 mm 16.9 mm Slide 13 Melih Papila, papila@mae.ufl.edu 13 Outline Design problem & objective Analysis tool and verification Optimization of Circular Piezo-composite plate Design variables Objective function and Constraints Results Trade-off via Pareto Optimization: Volume displacement versus Natural Frequency Concluding Remarks Slide 14 Melih Papila, papila@mae.ufl.edu 14 Design Variables R 1 : radius of the inner PZT layer(s) R 2 : inner radius of the outer ring PZT layer(s) t s : thickness of the shim and PZT layer(s) t p : thickness of the PZT layers (R 3 : radius of the shim fixed) Lateral deflection of the composite plate determines volume displacement and operational frequency limit tsts R1R1 R2R2 R3R3 tptp tptp Slide 15 Melih Papila, papila@mae.ufl.edu 15 Objective Function: Maximum Volume displacement Electric field (Voltage ) PZT layer expands/contracts Plate bends Lateral deflection w(r) Large PZT coverage Small t s Slide 16 Melih Papila, papila@mae.ufl.edu 16 Formulation & Implementation Solved by MATLAB Optimization Toolbox tsts R1R1 R2R2 R3R3 tptp tptp Slide 17 Melih Papila, papila@mae.ufl.edu 17 R 3 =11.5 mm, t min = 0.076 mm Maximum volume displacement t min R1R1 R2R2 tptp tptp 1.05 1.42 Bimorph/unimorph Amount of PZT Volume displacement Slide 18 Melih Papila, papila@mae.ufl.edu 18 R 3 =11.5 mm Maximum volume displacement effect of lower bound, t min 1.38 1.42 0.025/0.076 Amount of PZT Volume displacement Slide 19 Melih Papila, papila@mae.ufl.edu 19 Outline Design problem & objective Analysis tool and verification Optimization of Circular Piezo-composite plate Design variables Objective function and Constraints Results Trade-off via Pareto Optimization: Volume displacement versus Natural Frequency Concluding Remarks Slide 20 Melih Papila, papila@mae.ufl.edu 20 Methodology: Pareto Optimization In multi-objective optimization problem with conflicting objectives Pareto optimal points: one objective cannot be improved without deterioration in one of the other objectives, Construct a Pareto hypersurface minimized maximized Objective 1 maximized Objective 2 maximized Slide 21 Melih Papila, papila@mae.ufl.edu 21 R 3 =11.5 mm : Pareto front natural frequency versus volume displacement baseline Freq., Vol. -45%, 15% Freq., Vol. 23%, -15% Slide 22 Melih Papila, papila@mae.ufl.edu 22 Analytical solutions allowed numerical optimization Baseline designs were beaten and substantial improvement is predicted Bimorph configuration without the outer ring offers the optimum performance Minimum gauge for the layers is a limiting factor Pareto optimization was used to understand tradeoff between Maximum volume displacement Maximum natural frequency Concluding Remarks Slide 23 Melih Papila, papila@mae.ufl.edu 23 Prasad et al. (2002), Two-Port Electroacoustic Model of an Axisymmetric piezoelectric Composite Plate, 43rd AIAA Structures, Structural Dynamics and Materials Conference, Denver, CO. Wang et al. (2002), Analysis of a composite piezoelectric circular plate with initial stresses for MEMS, ASME International Mchanical Engineering Congress, 2002, New Orleans, LA. Gallas et al. (2003), Optimization of Synthetic Jet Actuators, AIAA Aerospace Sciences Meeting, 2003, Reno, NV. Relevant work THANK YOU Slide 24 Melih Papila, papila@mae.ufl.edu 24 R 3 =11.5 mm Maximum volume displacement effect of lower bound, t min 1.21 1.14 0.025/0.076 Amount of PZT Volume displacement Slide 25 Melih Papila, papila@mae.ufl.edu 25 Effect of oppositely polarized outer ring R1R1 R2R2 R3R3 tptp tsts EfEf EfEf Slide 26 Melih Papila, papila@mae.ufl.edu 26 Results: R 3 =18.5 mm Maximum volume displacement lower bound on t= 0.076 mm Slide 27 Melih Papila, papila@mae.ufl.edu 27 Linear Theory The piezoelectric term The piezoelectric effect is added by using the following relation for generalized force resultants: Where Slide 28 Melih Papila, papila@mae.ufl.edu 28 Piezoelectric Composite Plate Optimization Problem Objective function Maximum volume displacement Design variables Shim Structural Variables : Thickness Piezoelectric layer Variables : Radii and thickness Constraints Frequency Limit Strength Limit Variable Bounds Slide 29 Melih Papila, papila@mae.ufl.edu 29 Configurations R1R1 R2R2 R3R3 tptp tsts EfEf EfEf V AC E fT = E f = V AC /t p positive R1R1 R2R2 tptp tptp tsts EfEf -E f EfEf V AC E fB = -E f = -V AC /t p positive E fT = E f = V AC /t p