Mechanical Vibration and Shock Analysis, Mechanical Shock

Christian Lalanne

• Publisher: Wiley-ISTE
• Year: 2014
• Print ISBN: 9781848216457
• eBook ISBN: 9781118931141
• Edition: 3
• Topic: Physical Sciences
• Subtopic: Mechanics

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.

Chapter 1

Shock Analysis

1.1. Definitions

1.1.1. Shock

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

[1.4]

1.1.7. Terminal peak sawtooth (TPS) shock (or final peak sawtooth (FPS))

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
• Bibliography
• Index
• Summary of other Volumes in the series