# Presentation: 791108

## 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

## Outline

- Objectives and background
- Approach
- Modeling methods
- Aluminum beam testbed description/results
- Composite beam testbed description/results
- Concluding remarks

## Objective

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

## 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

## 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

## Aluminum Beam Testbed

- Aluminum
-     Beam

-      LaRC
- Piezoelectric
-     Actuator

## Aluminum Beam Testbed

- 16”

- 3.625”

- 2.78”

- Actuator

- Back to Back Strain gages

- Strain gage

-  Actuator (3”x1.75”)

- 0.04”

## Instrumented Aluminum Beam

- Strain gages and Actuator

- Proximity Probe

-   **Two strains gages**
**mounted back to back**

## Aluminum Beam Analysis Results

-   Mode 1
- @ 5.06 Hz

-   Mode 2
- @ 31.8 Hz

-   Mode 3
- @ 57.6 Hz

-   Mode 4
- @ 89.4 Hz

## 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

## AL Beam Correlation from Various Analysis Codes

- 10

- -1

- 10

- 0

- 10

- 1

- 10

- 2

- 10

- 3

- 10

- -10

- 10

- -5

**Frequency (Hz)**

- MRJ

- Ritz

- Test v-bond

- ANSYS

- 10

- -1

- 10

- 0

- 10

- 1

- 10

- 2

- 10

- 3

- -200

- -100

- 0

- 100

- 200

** ****Strain**
**in/in/volt**

**   ****Phase**
** ****(Degree)**

**Strain measurements versus Analysis Correlation**

**Frequency (Hz)**

## AL Beam Correlation from Various Analysis Codes

**Out of Plane Displacement  Measurement versus Analysis Correlation**

- 10

- -1

- 10

- 0

- 10

- 1

- 10

- 2

- 10

- 3

- 10

- -10

- 10

- -5

- 10

- 0

- MRJ-e116

- Ritz-e116

- Test v-bond

- ANSYS

**Frequency (Hz)**

**      ****Tip**
**Displacement**
**    ****in/volt**

**   ****Phase**
** ****(Degree)**

- 10

- -1

- 10

- 0

- 10

- 1

- 10

- 2

- 10

- 3

- -200

- 0

- 200

- 400

- 600

**Frequency (Hz)**

## Results from Thermal Mapping Test on AL Beam

- Thermal mapping image of actuator
-    bonded to the aluminum beam

- Possible
- disbonds

## Comparison of Actuator Effectiveness on AL Beam

- 10

- -1

- 10

- 0

- 10

- 1

- 10

- 2

- 10

- 3

- 10

- -10

- 10

- -5

- Test p-bond

- Test v-bond

- 10

- -1

- 10

- 0

- 10

- 1

- 10

- 2

- 10

- 3

- 10

- -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**

## Instrumented Composite Box Beam Testbed

- Beam

- Proximity
-   Probe

- Actuators

- Strain
-  Gage

## Composite Box Beam Analysis Results

- 11.1 Hz

- 68.9 Hz

- 186.7 Hz

- 279.6 Hz

## Box Beam Test versus Analysis Correlation

- 10

- -1

- 10

- 0

- 10

- 1

- 10

- 2

- 10

- 3

- 10

- -8

- 10

- -7

- 10

- -6

- 10

- -5

- Analysis

- Test

- 10

- -1

- 10

- 0

- 10

- 1

- 10

- 2

- 10

- 3

- -200

- -100

- 0

- 100

- 200

**Frequency (Hz)**

** ****Strain**
**in/in/volt**

**   ****Phase**
** ****(Degree)**

**Strain measurements versus Analysis Correlation**

**Frequency (Hz)**

## Box Beam Test versus Analysis Correlation

- 10

- -1

- 10

- 0

- 10

- 1

- 10

- 2

- 10

- 3

- 10

- -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

- -1

- 10

- 0

- 10

- 1

- 10

- 2

- 10

- 3

- -200

- 0

- 200

- 400

- 600

## Concluding Remarks

- Two testbeds developed and tested for validation of commercial analysis tools
- Frequency 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 %