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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 %