Mechanical Vibration and Shock Analysis, Specification Development

Christian Lalanne

• Publisher: Wiley-ISTE
• Year: 2014
• ISBN:
  9781118931233
• Edition: 3
• Topic: Physical Sciences
• Subtopic: Mechanics

Everything engineers need to know about mechanical vibration and shock...in one authoritative reference work!

This fully updated and revised 3rd edition addresses the entire field of mechanical vibration and shock as one of the most important types of load and stress applied to structures, machines and components in the real world. Examples include everything from the regular and predictable loads applied to turbines, motors or helicopters by the spinning of their constituent parts to the ability of buildings to withstand damage from wind loads or explosions, and the need for cars to maintain structural integrity in the event of a crash. There are detailed examinations of underlying theory, models developed for specific applications, performance of materials under test conditions and in real-world settings, and case studies and discussions of how the relationships between these affect design for actual products.

Invaluable to engineers specializing in mechanical, aeronautical, civil, electrical and transportation engineering, this reference work, in five volumes is a crucial resource for the solution of shock and vibration problems.

This volume focuses on specification development in accordance with the principle of tailoring. Extreme response and the fatigue damage spectra are defined for each type of stress (sinusoidal vibration, swept sine, shock, random vibration, etc.). The process for establishing a specification from the life cycle profile of equipment which will be subject to these types of stresses is then detailed. The analysis takes into account the uncertainty factor, designed to cover uncertainties related to the real-world environment and mechanical strength, and the test factor, which takes account of the number of tests performed to demonstrate the resistance of the equipment.

Chapter 1

Extreme Response Spectrum of a Sinusoidal Vibration

1.1. The effects of vibration

Vibrations can damage a mechanical system as a result of several processes, among which are:

– the exceeding of characteristic instantaneous stress limits (yield stress, ultimate stress etc.);

– the damage by fatigue following the application of a large number of cycles.

In what follows we will consider the case of a single degree-of-freedom linear system only. This model will be used to characterize the relative severity of numerous vibrations. It will be assumed that, if the greatest stresses and damage due to fatigue generated in the system are equal, then these excitations are of the same severity in the model and, by extension, in a real structure undergoing such excitations.

Since it is only the largest stresses in a single degree-of-freedom standard model with mass-spring-damping that are of interest here, this is equivalent to consideration of extreme stress or extreme relative displacement, these two parameters being linked, for a linear system, by a constant:

[1.1]

1.2. Extreme response spectrum of a sinusoidal vibration

1.2.1. Definition

The extreme response spectrum (ERS) [LAL 84] (or maximum response spectrum (MRS)) is defined as a curve giving the value of the highest peak z_sup of the response of a linear one-degree-of-freedom system to vibration, according to its natural frequency f₀, for a given damping ratio ξ. The response is described here by the relative movement z(t) of the mass in relation to its support, and the coordinate axis refers to the quantity (2 πf₀)² z_sup, by analogy with the shock response spectrum (Figure 1.1).

Figure 1.1. ERS calculation model

1.2.2. Case of a single sinusoid

A sinusoidal vibration can be defined in terms of a force, a displacement, a velocity or an acceleration.

1.2.2.1. Excitation defined by acceleration

Given an excitation defined by a sinusoidal acceleration of frequency f and amplitude

where Ω = 2 π f. The response of a single degree-of-freedom linear system, characterized by the relative displacement z(t) of the mass m with respect to the support, is expressed by:

[1.2]

(ω₀ = 2 π f₀) and the highest response displacement (extremum) by

[1.3]

The extreme response spectrum (ERS) is defined as the curve that represents variations of the quantity

as a function of the natural frequency f₀ of the system subjected to the sinusoid, for a given damping ratio ξ (or Q = 1/2 ξ).

[1.4]

NOTE.– The relative displacement is multiplied by

in order to obtain a homogeneous parameter compatible with an acceleration (as with the shock response sp...

Table of contents

• Cover
• Table of Contents
• Title Page
• Copyright
• Foreword to Series
• Introduction
• List of Symbols
• Chapter 1: Extreme Response Spectrum of a Sinusoidal Vibration
• Chapter 2: Extreme Response Spectrum of a Random Vibration
• Chapter 3: Fatigue Damage Spectrum of a Sinusoidal Vibration
• Chapter 4: Fatigue Damage Spectrum of a Random Vibration
• Chapter 5: Fatigue Damage Spectrum of a Shock
• Chapter 6: Influence of Calculation Conditions of ERSs and FDSs
• Chapter 7: Tests and Standards
• Chapter 8: Uncertainty Factor
• Chapter 9: Aging Factor
• Chapter 10: Test Factor
• Chapter 11: Specification Development
• Chapter 12: Influence of Calculation Conditions of Specification
• Chapter 13: Other Uses of Extreme Response, Up-Crossing Risk and Fatigue Damage Spectra
• Appendix
• Formulae
• Bibliography
• Index