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# Multi-degree of Freedom Energy Analysis for Identification of Failure Risk in Structural Components Subjected to Random Vibration and Shock Loading

## Abstract

When designing or analyzing a mechanical system, energy quantities provide insight into the severity of shock and vibration environments; however, the energy methods in the literature do not address localized behavior because energy quantities are usually computed for an entire structure. The main objective of this paper is to show how to compute the energy in the components of a mechanical system. The motivation for this work is that most systems fail functionally due to component failure, not because the primary structure was overloaded, and the ability to easily compute the spatial distribution of energy helps identify failure sensitive components. The quantity of interest is input energy. That input energy can be decoupled modally is well known. What is less appreciated is that input energy can be computed at the component level exactly, using the component effective modal mass. We show the steady state input energy can be decomposed both spatially and modally and computed using input power spectra. A numerical example illustrates the spatial and modal decomposition of input energy and its utility in identifying components at risk of damage in random vibration and shock environments. Our work shows that the modal properties of the structure and the spectralmore »

- Authors:

- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1581980

- Report Number(s):
- SAND-2019-13574J

Journal ID: ISSN 1048-9002; 681201

- Grant/Contract Number:
- AC04-94AL85000; NA0003525

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Vibration and Acoustics

- Additional Journal Information:
- Journal Name: Journal of Vibration and Acoustics; Journal ID: ISSN 1048-9002

- Country of Publication:
- United States

- Language:
- English

- Subject:
- machinery and structural damage identification; mechanical signatures; random vibration

### Citation Formats

```
Babuska, Vit, Sisemore, Carl L., and Skousen, Troy J. Multi-degree of Freedom Energy Analysis for Identification of Failure Risk in Structural Components Subjected to Random Vibration and Shock Loading. United States: N. p., 2019.
Web. doi:10.1115/1.4045581.
```

```
Babuska, Vit, Sisemore, Carl L., & Skousen, Troy J. Multi-degree of Freedom Energy Analysis for Identification of Failure Risk in Structural Components Subjected to Random Vibration and Shock Loading. United States. doi:10.1115/1.4045581.
```

```
Babuska, Vit, Sisemore, Carl L., and Skousen, Troy J. Mon .
"Multi-degree of Freedom Energy Analysis for Identification of Failure Risk in Structural Components Subjected to Random Vibration and Shock Loading". United States. doi:10.1115/1.4045581.
```

```
@article{osti_1581980,
```

title = {Multi-degree of Freedom Energy Analysis for Identification of Failure Risk in Structural Components Subjected to Random Vibration and Shock Loading},

author = {Babuska, Vit and Sisemore, Carl L. and Skousen, Troy J.},

abstractNote = {When designing or analyzing a mechanical system, energy quantities provide insight into the severity of shock and vibration environments; however, the energy methods in the literature do not address localized behavior because energy quantities are usually computed for an entire structure. The main objective of this paper is to show how to compute the energy in the components of a mechanical system. The motivation for this work is that most systems fail functionally due to component failure, not because the primary structure was overloaded, and the ability to easily compute the spatial distribution of energy helps identify failure sensitive components. The quantity of interest is input energy. That input energy can be decoupled modally is well known. What is less appreciated is that input energy can be computed at the component level exactly, using the component effective modal mass. We show the steady state input energy can be decomposed both spatially and modally and computed using input power spectra. A numerical example illustrates the spatial and modal decomposition of input energy and its utility in identifying components at risk of damage in random vibration and shock environments. Our work shows that the modal properties of the structure and the spectral content of the input must be considered together to assess damage risk. Because input energy includes absorbed energy as well as relative kinetic energy and dissipated energy, it is the recommended energy quantity for assessing the severity for both random vibration and shock environments on a structure.},

doi = {10.1115/1.4045581},

journal = {Journal of Vibration and Acoustics},

number = ,

volume = ,

place = {United States},

year = {2019},

month = {12}

}