This volume considers the shock response spectrum, its various definitions, properties and the assumptions involved in its calculation. In developing the practical application of these concepts, the forms of shock most often used with test facilities are presented together with their characteristics and indications of how to establish test configurations comparable with those in the real, measured environment. This is followed by a demonstration of how to meet these specifications using standard laboratory equipment – shock machines, electrodynamic exciters driven by a time signal or a response spectrum – with a discussion on the limitations, advantages and disadvantages of each method.
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Shock is defined as a vibratory excitation with a duration between one and two times the natural period of the excited mechanical system.
Example 1.1.
Figures 1.1 and 1.2 show accelerometric signals recorded during an earthquake and during the functioning of a pyrotechnic device.
Figure 1.1.Example of shock
Figure 1.2.Acceleration recorded during an earthquake
Shock occurs when a force, position, velocity or acceleration is abruptly modified and creates a transient state in the system being considered.
The modification is usually regarded as abrupt if it occurs in a time period which is short compared to the natural period concerned (AFNOR definition) [NOR 93].
1.1.2. Transient signal
This concerns a vibratory signal of short duration (a fraction of a second up to several dozen seconds) – mechanical shock – but also a phase between two different states or a state of short duration, as with the functioning of airbrakes on an aircraft.
Figure 1.3.Example of transient signal
1.1.3. Jerk
A jerk is defined as the derivative of acceleration with respect to time. This parameter thus characterizes the rate of variation of acceleration with time.
1.1.4. Simple (or perfect) shock
This is a shock whose signal can be represented exactly in simple mathematical terms, e.g. half-sine, triangular or rectangular shock.
1.1.5. Half-sine shock
This is a simple shock for which the acceleration-time curve has the form of a half-period (part positive or negative) of a sinusoid.
The excitation, zero for t < 0 and t > τ , can be written in the interval (0, τ), in the form
[1.1]
where
m is the amplitude of the shock and τ its duration. The pulsation is equal to
Figure 1.4.Half-sine shock
Expression [1.1] becomes, in generalized form,
(t) =
m sin Ω t.
For an excitation of the type force
and for an acceleration,
,etc.
In reduced (dimensionless) form, and with the notations used in Volume 1, Chapter 3, the definition of shock can be:
[1.2]
Note that
[1.3]
1.1.6. Versed sine (or haversine) shock
Figure 1.5.Period of a sine curve between two minima
This is a simple shock for which the acceleration curve according to time has the shape of a period of a sine curve between two minima.
Figure 1.6.Haversine shock pulse
The versed sine1 (or haversine2) shape can be represented by
This is a simple shock for which the acceleration-time curve has the shape of a triangle, where acceleration increases linearly up to a maximum value and then instantly decreases to zero.
Figure 1.7.Terminal peak sawtooth pulse
Terminal peak sawtooth shock pulse can be described by
[1.5]
It can be written in a generalized form:
and a reduced form:
1.1.8. Initial peak sawtooth (IPS) shock
This is a simple shock for which the acceleration-time curve has the shape of a triangle, where acceleration instantaneously increases up to a maximum, and then decreases to zero.
Figure 1.8.IPS shock pulse
Analytical expression of the initial peak sawtooth is of the form:
[1.6]
It can be written in a generalized form:
and a reduced form:
1.1.9. Square shock
This is a simple shock for which the acceleration-time curve increases instantaneously up to a given value, remains constant throughout the signal and decreases instantaneously to zero.
Figure 1.9.Square shock pulse
This shock pulse is represented by
[1.7]
It can be written in a generalized form:
and a reduced form:
1.1.10. Trapezoidal shock
This is a simple shock for which the acceleration-time curve grows linearly up to a given value remains constant for a certain time af...
Table of contents
Cover
Table of Contents
Title Page
Copyright
Foreword to Series
Introduction
List of Symbols
Chapter 1: Shock Analysis
Chapter 2: Shock Response Spectrum
Chapter 3: Properties of Shock Response Spectra
Chapter 4: Development of Shock Test Specifications
Chapter 5: Kinematics of Simple Shocks
Chapter 6: Standard Shock Machines
Chapter 7: Generation of Shocks Using Shakers
Chapter 8: Control of a Shaker Using a Shock Response Spectrum
Chapter 9: Simulation of Pyroshocks
Appendix: Similitude in Mechanics
Mechanical Shock Tests: A Brief Historical Background
