Random Vibration

Christi Lalanne

• Publisher: CRC Press
• Year: 2020
• ISBN:
  9781000723793
• Edition: 1
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

The vast majority of vibrations Encountered in the real Environment are random in nature. Such vibrations are intrinsically complicated, and this volume describes the Enabling process for simplification of the analysis required. and the analysis of the signal in the frequency domain. Power spectrum density is also defined, with the requisite precautions to be taken in its calculation described together with the processes (windowing. overlapping) necessary for improved results. A further complementary method, the analysis of statistical properties of the time signal. is described. This enables the distribution law of the maxima of a random Gaussian signal to be determined and simplifies calculation of fatigue damage to be made by the avoidance of the direct counting of peaks.

Chapter 1

Statistical properties of a random process

1.1. Definitions

1.1.1. Random variable

A random variable is a quantity whose instantaneous value cannot be predicted. Knowledge of the values of the variable before time t not does make it possible to deduce the value at the time t from it.

Example: the Brownian movement of a particle.

1.1.2. Random process

Let us consider, as an example, the acceleration recorded at a given point on the dial of a truck travelling on a good road between two cities A and B. For a journey, recorded acceleration obeys the definition of a random variable. The vibration characterized by this acceleration is said to be random or stochastic.

If n journeys are performed, one obtains as many different ${}^{\text{i}}\ell (\text{t})$ curves, each recording having a random character.

We define as a random process or stochastic process the ensemble of the time functions $\left\{{}^{\text{i}}\ell (\text{t})\right\}$ for t included between − ∞ and + ∞, this ensemble being able to be defined by statistical properties [JAM 47].

Random movements are not erratic in the common meaning of the term, but follow a well defined law. They have specific properties and can be described by a law of probability.

The principal characteristic of a random vibration is simultaneously to excite all the frequencies o...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Introduction
• List of symbols
• 1 Statistical properties of a random process
• 2 Properties of random vibration in the frequency domain
• 3 Rms value of random vibration
• 4 Practical calculation of power spectral density
• 5 Properties of random vibration in the time domain
• 6 Probability distribution of maxima of random vibration
• 7 Statistics of extreme values
• Appendices
• Bibliography
• Index
• Synopsis of five volume series