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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
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Outline
• Objectives and background
• Approach
• Modeling methods
• Aluminum beam testbed description/results
• Composite beam testbed description/results
• Concluding remarks
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Objective
Investigate and validate techniques for modeling structures with surface bonded piezoelectric actuators using commercially available FEM codes.
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Approach
Develop and validate FEM models of the following structures: Aluminum beam testbed Composite beam testbed
Study the following piezoelectric modeling approaches: Piezoelectric effect via thermal analogy and Ritz vectors Piezoelectric element using NASTRAN dummy element
capability ANSYS piezoelectric element
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Modeling Approaches
Thermal Strain Analogy Induced strain using thermal load 4-node composite quadrilateral element Ritz vectors computed to capture local effect
MRJ piezoelectric elements implemented in User-Modifiable MSC/NASTRAN Piezoelectric induced strains Coupled field 4-node composite quadrilateral element
ANSYS 3-D Coupled Field Solid element Full harmonic analysis
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Aluminum Beam Testbed
Aluminum Beam
LaRC Piezoelectric Actuator
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Aluminum Beam Testbed
16”
3.625”
2.78”
Actuator
Back to Back Strain gages
Strain gage
Actuator (3”x1.75”)
0.04”
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Instrumented Aluminum Beam
Strain gages and Actuator Proximity Probe
Two strains gagesmounted back to back
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Aluminum Beam Analysis Results
Mode 1@ 5.06 Hz
Mode 2@ 31.8 Hz
Mode 3@ 57.6 Hz
Mode 4@ 89.4 Hz
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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
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AL Beam Correlation from Various Analysis Codes
10-1
100
101
102
103
10-10
10-5
Frequency (Hz)
MRJ Ritz Test v-bondANSYS
10-1
100
101
102
103
-200
-100
0
100
200
Strainin/in/volt
Phase (Degree)
Strain measurements versus Analysis Correlation
Frequency (Hz)
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AL Beam Correlation from Various Analysis Codes
Out of Plane Displacement Measurement versus Analysis Correlation
10-1
100
101
102
103
10-10
10-5
100
MRJ-e116 Ritz-e116 Test v-bondANSYS
Frequency (Hz)
TipDisplacement in/volt
Phase (Degree)
10-1
100
101
102
103
-200
0
200
400
600
Frequency (Hz)
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Results from Thermal Mapping Test on AL Beam
Thermal mapping image of actuator bonded to the aluminum beam
Possibledisbonds
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Comparison of Actuator Effectiveness on AL Beam
10-1
100
101
102
103
10-10
10-5
Test p-bondTest v-bond
10-1
100
101
102
103
10-10
10-5
100
Test p-bondTest v-bond
Frequency (Hz)
Tip Displacement in/volt
Frequency (Hz)
Strainin/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
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Instrumented Composite Box Beam Testbed
Beam
Proximity Probe
Actuators
Strain Gage
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Composite Box Beam Analysis Results
11.1 Hz 68.9 Hz
186.7 Hz 279.6 Hz
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Box Beam Test versus Analysis Correlation
10-1
100
101
102
103
10-8
10-7
10-6
10-5
Analysis Test
10-1
100
101
102
103
-200
-100
0
100
200
Frequency (Hz)
Strainin/in/volt
Phase (Degree)
Strain measurements versus Analysis Correlation
Frequency (Hz)
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Box Beam Test versus Analysis Correlation
10-1
100
101
102
103
10-8
10-6
10-4
10-2
AnalysisTest
Out of Plane Displacement Measurement versus Analysis Correlation
Frequency (Hz)
TipDisplacement in/volt
Phase (Degree)
Frequency (Hz)10
-110
010
110
210
3-200
0
200
400
600
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Concluding Remarks
Two testbeds developed and tested for validation of commercial analysis toolsFrequency response functions results using three different analysis approaches provided comparable test/analysis correlation Low frequency resonance predicted within 5 and 13% but antiresonance showed errors of 16%Improper bonding of actuators showed reductions in electrical to mechanical effectiveness of 64 %