# Instantaneous Frequency and Damping from Transient Ring-Down Data

## Abstract

Broadband impact excitation in structural dynamics is a common technique used to detect and characterize nonlinearities in mechanical systems since it excites many frequencies of a structure at once and can be applied with a variety of boundary conditions. Non-stationary time signals from transient ring-down measurements require time-frequency analysis tools to observe variations in frequency and energy dissipation as the response evolves. This work uses the short-time Fourier transform to estimate the instantaneous frequency and damping ratio from either measured or simulated transient ring-down data. By combining the discrete Fourier transform with an expanding or contracting window function that moves along the time axis, the resulting spectrum is used to estimate the instantaneous frequencies, damping and complex Fourier coefficients. This method is demonstrated on a multi-degree-of-freedom beam with a cubic spring attachment, and investigates the amplitudefrequency dependence in connection to the undamped nonlinear normal modes. A second example shows the results from experiment ring-down response on a beam with a lap joint, and reveals how the system behaves as energy dissipates.

- Authors:

- Publication Date:

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

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

- OSTI Identifier:
- 1337971

- Report Number(s):
- SAND2015-9173C

Journal ID: ISSN 2191-5644; 608035

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Conference

- Resource Relation:
- Conference: Proposed for presentation at the International Modal Analysis Conference (IMAC) held January 25-28, 2016 in Orlando, FL.

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING

### Citation Formats

```
Kuether, Robert J., and Brake, Matthew Robert.
```*Instantaneous Frequency and Damping from Transient Ring-Down Data*. United States: N. p., 2015.
Web. doi:10.1007/978-3-319-29763-7_24.

```
Kuether, Robert J., & Brake, Matthew Robert.
```*Instantaneous Frequency and Damping from Transient Ring-Down Data*. United States. doi:10.1007/978-3-319-29763-7_24.

```
Kuether, Robert J., and Brake, Matthew Robert. Thu .
"Instantaneous Frequency and Damping from Transient Ring-Down Data". United States. doi:10.1007/978-3-319-29763-7_24. https://www.osti.gov/servlets/purl/1337971.
```

```
@article{osti_1337971,
```

title = {Instantaneous Frequency and Damping from Transient Ring-Down Data},

author = {Kuether, Robert J. and Brake, Matthew Robert},

abstractNote = {Broadband impact excitation in structural dynamics is a common technique used to detect and characterize nonlinearities in mechanical systems since it excites many frequencies of a structure at once and can be applied with a variety of boundary conditions. Non-stationary time signals from transient ring-down measurements require time-frequency analysis tools to observe variations in frequency and energy dissipation as the response evolves. This work uses the short-time Fourier transform to estimate the instantaneous frequency and damping ratio from either measured or simulated transient ring-down data. By combining the discrete Fourier transform with an expanding or contracting window function that moves along the time axis, the resulting spectrum is used to estimate the instantaneous frequencies, damping and complex Fourier coefficients. This method is demonstrated on a multi-degree-of-freedom beam with a cubic spring attachment, and investigates the amplitudefrequency dependence in connection to the undamped nonlinear normal modes. A second example shows the results from experiment ring-down response on a beam with a lap joint, and reveals how the system behaves as energy dissipates.},

doi = {10.1007/978-3-319-29763-7_24},

journal = {},

issn = {2191-5644},

number = ,

volume = ,

place = {United States},

year = {2015},

month = {10}

}