1. LaRC Test Cases for Modeling and Validation of Structures with Piezoelectric Actuators Mercedes C. Reaves and Lucas G. Horta Structural Dynamics Branch NASA Langley Research Center Hampton, Virginia Presented at the NASA Innovative Finite Element Solutions to Challenging Problems Workshop May 18, 2000 at NASA GSFC

2. LaRC Outline Objectives and background Approach Modeling methods Aluminum beam testbed description/results Composite beam testbed description/results Concluding remarks

3. LaRC Objective Investigate and validate techniques for modeling structures with surface bonded piezoelectric actuators using commercially available FEM codes.

4. LaRC Approach l Develop and validate FEM models of the following structures: l Aluminum beam testbed l Composite beam testbed l Study the following piezoelectric modeling approaches: l Piezoelectric effect via thermal analogy and Ritz vectors l Piezoelectric element using NASTRAN dummy element capability l ANSYS piezoelectric element

5. LaRC Modeling Approaches l Thermal Strain Analogy l Induced strain using thermal load l 4-node composite quadrilateral element l Ritz vectors computed to capture local effect l MRJ piezoelectric elements implemented in User-Modifiable MSC/NASTRAN l Piezoelectric induced strains l Coupled field 4-node composite quadrilateral element l ANSYS l 3-D Coupled Field Solid element l Full harmonic analysis

6. LaRC Aluminum Beam Testbed Aluminum Beam LaRC Piezoelectric Actuator

7. LaRC Aluminum Beam Testbed 16” 3.625” 2.78” Actuator Back to Back Strain gages Strain gage Actuator (3”x1.75”) 0.04”

8. LaRC Instrumented Aluminum Beam Strain gages and ActuatorProximity Probe Two strains gages mounted back to back

9. LaRC Aluminum Beam Analysis Results Mode 1 @ 5.06 Hz Mode 2 @ 31.8 Hz Mode 3 @ 57.6 Hz Mode 4 @ 89.4 Hz

10. LaRC Composite Box Beam Testbed 66 “ 0.75 ” 3.0 ” laminate thickness = 0.03” laminate layout [45,-45,0] s Beam cross section (Outside dimensions) Material T300/976 0.5” PZT actuator PZT actuators 3.0” Strain gage

11. LaRC AL Beam Correlation from Various Analysis Codes 10 10 0 1 2 3 -10 10 -5 Frequency (Hz) MRJ Ritz Test v-bond ANSYS 10 10 0 1 2 3 -200 -100 0 100 200 Strain in/in/volt Phase (Degree) Strain measurements versus Analysis Correlation Frequency (Hz)

12. LaRC AL Beam Correlation from Various Analysis Codes Out of Plane Displacement Measurement versus Analysis Correlation 10 10 0 1 2 3 -10 10 -5 10 0 MRJ-e116 Ritz-e116 Test v-bond ANSYS Frequency (Hz) Tip Displacement in/volt Phase (Degree) 10 10 0 1 2 3 -200 0 200 400 600 Frequency (Hz)

13. LaRC Results from Thermal Mapping Test on AL Beam Thermal mapping image of actuator bonded to the aluminum beam Possible disbonds

14. LaRC Comparison of Actuator Effectiveness on AL Beam 10 10 0 1 2 3 -10 10 -5 Test p-bond Test v-bond 10 10 0 1 2 3 -10 10 -5 10 0 Test p-bond Test v-bond Frequency (Hz) Tip Displacement in/volt Frequency (Hz) Strain in/in/volt Strain Measurements Displacement Measurements v-bond- 14.5 psi, 24 hrs cure, vacuum bag p-bond- 1 psi, 24 hrs cure, ambient Bonding Technique

15. LaRC Instrumented Composite Box Beam Testbed Beam Proximity Probe Actuators Strain Gage

16. LaRC Composite Box Beam Analysis Results 11.1 Hz 68.9 Hz 186.7 Hz 279.6 Hz

17. LaRC Box Beam Test versus Analysis Correlation 10 10 0 1 2 3 -8 10 -7 10 -6 10 -5 Analysis Test 10 10 0 1 2 3 -200 -100 0 100 200 Frequency (Hz) Strain in/in/volt Phase (Degree) Strain measurements versus Analysis Correlation Frequency (Hz)

18. LaRC Box Beam Test versus Analysis Correlation 10 10 0 1 2 3 -8 10 -6 10 -4 10 -2 Analysis Test Out of Plane Displacement Measurement versus Analysis Correlation Frequency (Hz) Tip Displacement in/volt Phase (Degree) Frequency (Hz) 10 10 0 1 2 3 -200 0 200 400 600

19. LaRC Concluding Remarks l Two testbeds developed and tested for validation of commercial analysis tools l Frequency response functions results using three different analysis approaches provided comparable test/analysis correlation l Low frequency resonance predicted within 5 and 13% but antiresonance showed errors of 16% l Improper bonding of actuators showed reductions in electrical to mechanical effectiveness of 64 %