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Whether it be in everyday appliances such as mobile telephones, wristwatches, electronic components in cars ... or more specific material such as components on board satellites or flight equipment in aircraft, they are all at some point during their lifetime subjected to various environmental stresses of temperature, humidity .... and more especially to mechanical shocks and vibrations. They must therefore be designed to withstand such conditions without damage, and the design must be verified by calculations and/or significant laboratory tests.

To avoid oversizing materials and to reduce development costs, the current trend is to use environmental test specifications that are close to the real environment.

The main methods for analysis and laboratory simulation of these mechanical environments are described in a five-volume work entitled "Mechanical Shocks and Vibrations", which also proposes an original method for drafting sizing and testing specifications on the basis of the life cycle profile of the material and measurements of the real environment:

	Volume 1 is devoted to sinusoidal vibration (North America) and to swept sine vibration, widely used in tests to characterize the dynamic behavior of structures (natural frequencies, damping).
	Volume 2 addresses the topic of mechanical shock (North America), presenting the shock response spectrum (S.R.S.) with its different definitions, its properties and the precautions to be observed in its calculation. The shocks most widely used in the usual facilities are identified, with their characteristics, indicating how test specifications with the same degree of severity as that of the real measured environment can be drafted.
		This volume then describes how these specifications can be reached using classic laboratory facilities : shock machines, electrodynamic exciters controlled from a time signal or from a response spectrum, specifying the limitations, advantages and disadvantages of each solution.
	Volume 3 examines the analysis of random vibrations (North America), which account for the vast majority of the vibrations encountered in the real environment. This volume describes the overall properties of the process enabling a simplification of analysis, before presenting the analysis of the signal in the frequency domain. The definition of the power spectral density is recalled, specifying the precautions to be taken in its calculation, together with the processes employed to improve results (windowing, overlapping). A additional third avenue consists of analyzing the statistical properties of the time history.
	This study makes it possible to determine, in particular, the law of distribution of the maxima of a random Gaussian signal and to simplify the calculation of fatigue damage by avoiding direct peak counting. Volume 4, after establishing relationships providing the response of a linear system with one degree of freedom to a random vibration, is devoted to the calculation of fatigue damage (North America). It presents the hypotheses adopted to describe the behavior of a material subjected to fatigue, the laws governing the accumulation of damage, together with methods for counting the peaks of the response, used to draw a histogram when it is impossible to use the probability density of the peaks obtained with a Gaussian signal. The expressions of mean damage and its standard deviation are established, followed by the examination of a few cases using other hypotheses (static mean stress, taking account of the limit of endurance, non linear accumulation law, etc.).
	Volume 5 is more particularly designed to present the method for drafting test specifications (North America) according to the principle of tailoring. The extreme response and fatigue damage spectra are defined for each type of stress (sinusoidal vibrations, swept sine, shocks, random vibrations, etc.). The process for establishing a specification as from the life cycle profile of the material is then detailed, taking account of an uncertainty coefficient (or safety factor) intended to cover the uncertainties related to the dispersion of the real environment and of mechanical resistance, together with another coefficient, the test factor, which takes account of the number of tests performed to demonstrate the resistance of the material.

This method, which requires the processing of a large number of measurements of vibrations and shocks (time histories, power spectral densities) can be effectively employed only with computer facilities. Software programs have been developed for use on PC's and UNIX stations to construct the profile of the lifetime of the material studied, with the association of measurements of the real environment, and, after calculation of the various spectra and coefficients, to determine a specification for a customized severity test in compliance with the two criteria of equivalence chosen (extreme response and fatigue damage).

Maximax Response Spectrum Mean maximum relative displacement (multiplied by (2 p f0)2) response of a linear on degree of freedom mechanical system (natural frequency f0, damping x) subjected to a vibration over a duration T, for a given x, in function of f0.
Fatigue Damage Spectrum A representative curve of the variations of fatigue damage D incurred by a linear one degree of freedom mechanical system (natural frequency f0, damping x) subjected to a vibration over a duration T, for a given x, in function of f0. Frequently Asked Questions ... and Answers.

Mechanical Vibrations and Shocks   Christian Lalanne Updated : 09 août 2011 08:40