# Dynamic Response of an Optomechanical System to a Stationary Random Excitation in the Time Domain

## Abstract

Modern electro-optical instruments are typically designed with assemblies of optomechanical members that support optics such that alignment is maintained in service environments that include random vibration loads. This paper presents a nonlinear numerical analysis that calculates statistics for the peak lateral response of optics in an optomechanical sub-assembly subject to random excitation of the housing. The work is unique in that the prior art does not address peak response probability distribution for stationary random vibration in the time domain for a common lens-retainer-housing system with Coulomb damping. Analytical results are validated by using displacement response data from random vibration testing of representative prototype sub-assemblies. A comparison of predictions to experimental results yields reasonable agreement. The Type I Asymptotic form provides the cumulative distribution function for peak response probabilities. Probabilities are calculated for actual lens centration tolerances. The probability that peak response will not exceed the centration tolerance is greater than 80% for prototype configurations where the tolerance is high (on the order of 30 micrometers). Conversely, the probability is low for those where the tolerance is less than 20 micrometers. The analysis suggests a design paradigm based on the influence of lateral stiffness on the magnitude of the response.

- Authors:

- Sandia National Laboratories, P.O. Box 5800, MS 01304, Albuquerque, NM, USA
- Thomas Paez Consulting, 175 Iron King, Durango, CO, USA

- Publication Date:

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1197978

- Grant/Contract Number:
- AC04-94AL8500

- Resource Type:
- Published Article

- Journal Name:
- Shock and Vibration

- Additional Journal Information:
- Journal Name: Shock and Vibration Journal Volume: 18 Journal Issue: 5; Journal ID: ISSN 1070-9622

- Publisher:
- Hindawi Publishing Corporation

- Country of Publication:
- Egypt

- Language:
- English

### Citation Formats

```
Palmer, Jeremy A., and Paez, Thomas L. Dynamic Response of an Optomechanical System to a Stationary Random Excitation in the Time Domain. Egypt: N. p., 2011.
Web. doi:10.1155/2011/607923.
```

```
Palmer, Jeremy A., & Paez, Thomas L. Dynamic Response of an Optomechanical System to a Stationary Random Excitation in the Time Domain. Egypt. doi:10.1155/2011/607923.
```

```
Palmer, Jeremy A., and Paez, Thomas L. Sat .
"Dynamic Response of an Optomechanical System to a Stationary Random Excitation in the Time Domain". Egypt. doi:10.1155/2011/607923.
```

```
@article{osti_1197978,
```

title = {Dynamic Response of an Optomechanical System to a Stationary Random Excitation in the Time Domain},

author = {Palmer, Jeremy A. and Paez, Thomas L.},

abstractNote = {Modern electro-optical instruments are typically designed with assemblies of optomechanical members that support optics such that alignment is maintained in service environments that include random vibration loads. This paper presents a nonlinear numerical analysis that calculates statistics for the peak lateral response of optics in an optomechanical sub-assembly subject to random excitation of the housing. The work is unique in that the prior art does not address peak response probability distribution for stationary random vibration in the time domain for a common lens-retainer-housing system with Coulomb damping. Analytical results are validated by using displacement response data from random vibration testing of representative prototype sub-assemblies. A comparison of predictions to experimental results yields reasonable agreement. The Type I Asymptotic form provides the cumulative distribution function for peak response probabilities. Probabilities are calculated for actual lens centration tolerances. The probability that peak response will not exceed the centration tolerance is greater than 80% for prototype configurations where the tolerance is high (on the order of 30 micrometers). Conversely, the probability is low for those where the tolerance is less than 20 micrometers. The analysis suggests a design paradigm based on the influence of lateral stiffness on the magnitude of the response.},

doi = {10.1155/2011/607923},

journal = {Shock and Vibration},

number = 5,

volume = 18,

place = {Egypt},

year = {2011},

month = {1}

}

DOI: 10.1155/2011/607923