Abstract
In order to characterize the acceleration response of a structure due to shock environments, the Shock Response Spectrum method is widely used in the qualification process for the spacecraft industry. Generally, this test is performed with a shock testing machine but alternate test fixture designs, including a shock plate, have recently been considered. In order to develop an appropriate design methodology to design such a fixture, a simple beam type structure is utilized to deploy the approach; the beam is chosen so as to introduce the SRS method into an educationally motivated treatment of the material for use in a graduate level course.
In this paper, the development of a Shock Response Spectrum for a beam-type structure from both analytical and experimental approaches is presented. From these models, frequencies, damping and mode shapes can be extracted to identify the response at various locations on the structure that are needed to develop the Shock Response Spectrum. In order to customize the shock spectrum, various mass perturbations applied to the structure can be considered by using Mass Sensitivity Analysis. The effects of the changes to the mass of the basic shock test fixture can be easily developed by using the Structural Dynamic Modification technique.
A comparison of the Shock Response Spectrum computed from the Analytical Model and from the Experimental Model is provided for various scenarios of different configurations studied.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
For the SDM, subscript 1 means parameter for the original model and subscript 2 means parameters for the modified model. In general, original structural and modal matrices will be presented without any subscripts.
- 2.
A term written in capital alphabet means matrix. A term with small alphabet means a component of matrix. For example, \( \overline{M} \) means a modal mass matrix and \( {\overline{m}}_i \) means a modal mass value for “i”th mode.
Abbreviations
- [M]:
-
Mass matrix in physical space
- [K]:
-
Stiffness matrix in physical space
- [C]:
-
Damping matrix in physical space
- \( \hbox{[}\overline{\mathrm{M}}\hbox{]} \) :
-
Mass matrix in modal space
- \( \hbox{[}\overline{\mathrm{K}}\hbox{]} \) :
-
Stiffness matrix in modal space
- \( \overline{\hbox{[}\mathrm{C}}\hbox{]} \) :
-
Damping matrix in modal space
- [U]:
-
Mode shapes
- [λ]:
-
Eigenvalues
- X:
-
Physical displacement in time domain
- \( \ddot{\mathrm{X}} \) :
-
Physical Acceleration in time domain
- F:
-
Time vector of applied force
- P:
-
Modal displacement in time domain
- \( \ddot{\mathrm{p}} \) :
-
Modal acceleration in time domain
- X(s)| s = jω :
-
Physical displacement in frequency domain
- \( \ddot{\mathrm{X}}\left(\mathrm{s}\right)\Big|{}_{s= j\omega} \) :
-
Physical acceleration in frequency domain
- H(s)| s = jω :
-
Frequency response Function (FRF)
- [ΔM]:
-
Mass modification matrix in physical space
- [ΔK]:
-
Stiffness modification matrix in physical space
References
NASA-STD-7003A (2011) NASA technical standard-pyroshock test criteria, National Aeronautics and Space Administration, Dec 2011
ISO 18431-4 Mechanical vibration and shock-signal processing—part 4: shock response spectrum analysis
Tuma J, Koci P (2009) Calculation of shock response spectrum. Colloquium dynamics of machines 2009, Feb 2009
Edward Alexander J (2009) Shock response spectrum—a primer. Sound Vib
Richard Hsieh et al (2013) Analysis and dynamic characterization of a resonant plate for shock testing. Proceedings of the 31st international modal analysis conference
Irvine T An introduction to the shock response spectrum
Rao S (2010) Mechanical vibrations, 5th edn. Prentice Hall, New Jersey, pp 968–971
Okubo N, Toi T (2000) Sensitivity analysis and its application for dynamic improvement. Sadhana 25(3):291–303
Kohei Furuya et al (2005) FRF-sensitivity analysis using eigenvalue analysis of stiffness matrix for a car body structure. Proc. Jpn Soc Automot Eng. No 37-05-188
Avitabile P (2001) Twenty years of structural dynamics modification—a review. Proceedings of the 20th international modal analysis conference, Feb 2001
ISO 1683-2008 Acoustics—preferred reference values for acoustical and vibratory levels
Acknowledgements
This research was done in the Structural Dynamics and Acoustic Systems Laboratory (SDASL) of the University of Massachusetts Lowell. The first author of this paper is a graduate student of the Acoustic Systems Laboratory (CAMAL) of the Chuo University and visited at the SDASL as a research scholar for a year of 2013 and, at that time, this research was performed. The author would like to thank to Dr. Peter Avitabile for the invitation and invaluable advice and to Dr. Nobuyuki Okubo and Dr. Takeshi Toi for the recommendation for the position.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 The Society for Experimental Mechanics, Inc.
About this paper
Cite this paper
Aizawa, K., Avitabile, P. (2014). Shock Response Fixture Developed from Analytical and Experimental Data and Customized Using Structural Dynamics Modification Techniques. In: Foss, G., Niezrecki, C. (eds) Special Topics in Structural Dynamics, Volume 6. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-04729-4_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-04729-4_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04728-7
Online ISBN: 978-3-319-04729-4
eBook Packages: EngineeringEngineering (R0)