About the Mechanical Shock Course
Mechanical shock is one of the most common causes of nonstructural failure in mechanical and electrical systems. Shocks occur in routine shipping and handling, accidental abuse, normal operational environments of ground vehicles and aircraft, and as a result of explosive events in warfare. Shocks also occur in special environments such as during the actuation of explosive bolts and other pyrotechnics.
The shock response spectrum (SRS) was devised as a way to describe the severity of a shock. It is employed as a design aide and as a basis for shock testing specifications The SRS has proven to be an extremely useful engineering tool and is widely employed. Nevertheless the deterministic foundation of the SRS does not account for the inherently stochastic nature of shocks in modern applications. Use of the SRS may result in extreme over-design and testing in some cases and, simultaneously, marginal design and testing in other cases.
There are other approaches besides the SRS that account for the stochastic nature and offer improved balance. These range from simple probabilistic treatments of the SRS to full treatments of shocks as non-stationary random processes. However, for most practicing engineers, these methods are inaccessible because a gap exists between their formal training and these methods. This course is designed to bridge that gap.
This course reviews the fundamentals of shock engineering including the SRS and applications, measurement of shock, shock testing methods, and development of shock testing specifications. Also presented are advanced methods. The SRS is treated as a statistic of the random process that may be used for reliability based design and testing. This leads to fully probabilistic treatments in the time and frequency domains, including Priestly's non-stationary spectral approach.
A bachelor's degree in engineering, or equivalent, is presumed.
Course Format
Each approximately one-hour long lecture is followed by a short problem designed to reinforce the concepts presented. There is ample class time for discussion of the fundamental concepts. Questions are encouraged.
The instructors are also available for discussion about specific situations or problems students may have at work.
Class hours are 8:00 am to 5:00 pm, with a one hour lunch break.
Course Materials
Each participant will receive:
Course Notes: A copy of all viewgraphs, problems and solutions.
Educational Software: Sample routines in MATLAB for calculating SRS and other approaches presented in class
Preparation
Although it is not a prerequisite, it is recommended that you review the fundamentals of probability and statistics from an undergraduate text. You may wish to review the documentation you have for testing equipment, analysis software, etc. Bring a calculator to work in-class problems. If you wish to discuss a particular problem, bring the necessary materials to explain the problem
Course Outline
Introduction to Shock Engineering:
Motivation; typical environments
Review of Structural Dynamics:
Single-degree-of-freedom and multi-degree-of-freedom systems
The Shock Response Spectrum (SRS):
Definition; fundamentals; examples
Fourier Transforms:
Fourier series and transforms; convolution; Uncertainty Theorem
Design to Avoid Damage Under Shock:
Failure modes; linear and nonlinear systems
Review of Shock Environments:
Shock environment characteristics; examples
Measurement and Validation of Shock:
Data acquisition systems; accelerometers, signal conditioning, digitizers; data validation
Efficient Computation of SRS:
Shock response as filter output
Review of Probability and Statistics:
Random variables; distribution; moments
Shock Test Specification:
Deterministic; statistical
Shock Synthesis:
Compensation; sum of decaying sinusoids; chirps; wavelets
Shock Test Methods:
Shaker shock; shock machines; actuators
Review of Random Processes:
Ensemble; mean; variance; autocorrelation; spectral density
Random Vibration: Input-output relation; shock as stationary random process
Time Varying Spectral Density:
Priestly's spectrum; estimation; synthesis of non-stationary random process realizations
Alternatives to SRS:
Least favorable response; temporal moments; examples
New Alternatives to the SRS:
Wavelets; examples
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About The Mechanical Shock Characterization and Synthesis Course
Instructor: David O. Smallwood
This is a two-day short course for the practicing professional who wants control over the shock synthesis process. The first day will present the theory behind the characterization and synthesis software. The second day will cover the application software provided as part of the course.
For the persons performing shock testing on shakers who would like control of the synthesis of the shock waveforms.
For the analyst performing transient analysis who would like to synthesize transient time histories as input to your models.
The software toolbox provided is all MATLABÔ based scripts and functions that gives the user complete control over the synthesis processes. Because the software is MATLAB script and functions the user can see exactly how the code operates. Modifications or extensions are easily accomplished. The time histories are then exported to your favorite analysis code or vibration control system. The toolbox requires the basic MATLAB software and the signal analysis toolbox.
Shock Response Spectrum (SRS) analysis
Software is provided to compute and plot the SRS.
SRS Methods
Because of the popularity of the method of the shock response spectrum, several methods are provided to generate transients that match a specified shock response spectrum. These include:
Exponentially decaying sinusoids
Two methods of compensating for velocity and displacement
One method of self compensating decaying sinusoids
Wavesy Wavesyn
ompo Components composed of an odd number of half sinusoids multiplied by half sine window
Both left edge and centered waveforms
Windo Windowed Random
This method uses the product model to generate random transients that will match a specified SRS or the Fourier energy spectrum in the mean.
Temporal Mo MIL_STD 810F Effective Shock Duration
Learn how to synthesize shocks that will match the SRS and meet the effective shock duration as specified in MIL_STD810F section (516.5) and ANNEX B.
Tem Temporal Moment Methods
I n a d d i t In addition to matching the SRS or the Fourier energy, methods will be presented for matching the band limited temporal moments
Wavelets
Wavelets Methods will be presented to generate transient (non-stationary) random waveforms characterized with wavelets (requires the wavelet toolbox from MATLAB)
Karhunen-Lo Karhunen-Loeve (K-L) Expansion
The Karhunen-L The Karhunen-Loeve (K-L) expansion can be used to characterize and simulate non-stationary random events.
Choi-Williams (CW) Expansion
The Choi-Williams (CW) expansion can be used to characterize and simulate non-stationary random events.
Prerequisites: A basic familiarity is MATLAB is highly desired. The Mechanical Shock 3-day short course is highly desired, but not required. If the Mechanical Shock short course is not taken a general familiarity with the method of the Shock Response Spectrum and a basic knowledge of statistics and matrix algebra is highly recommended. Students who have a laptop with MATLAB installed ( with the signal processing toolbox) are encouraged to bring it to the course in order to work sample problems.
Mechanical Shock Condensed Version: The course will be presented over 2 days instead of 3-1/2.
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