Vibrations

The study and analysis of vibrations (or signals) has grown considerably in recent years, due to the development of increasingly sophisticated techniques and a wide range of needs in various fields: mechanics (transport, machinery, etc.), acoustics, optics, transmissions, etc. The study and analysis of vibrations (or signals) has grown considerably in recent years, due to the development of increasingly sophisticated techniques and a wide range of needs in various fields (mechanics (transport, machinery, etc.), acoustics, optics, transmissions, etc.).

Current concerns can be broadly divided into three categories.

• The first, which is theoretical, concerns the dynamic calculation of structures as an extension of strength of materials and continuum mechanics. While it is possible in simple cases, i.e. for a limited number of problems, to calculate the behavior of these structures and their insulation to limit nuisance, in the majority of cases, analytical methods become insufficient to obtain, for example, the high-order resonance frequencies of continuous systems. Calculating the first eigenmodes of a straight-axis beam of constant cross-section, embedded at one end and free at the other, poses no difficulty whatsoever; however, if one or more other beams of different directions and cross-sections are associated with it, solutions become almost impossible to find. And yet, in many cases, it is absolutely essential to know these frequencies, since, for reasons of material economy, constructions are becoming lighter and lighter, and are therefore called upon to vibrate at low frequencies, generally located in zones that are dangerous for the structure or its environment.

• Secondly, the relatively recent introduction of computers and microcomputers, combined with high-performance software packages based on the finite element method, is an extremely valuable aid to design offices, and is not prohibitively expensive, making the calculation part easy. While the results are valid in most cases, the utmost caution must be exercised when using them, as some software packages, for example, blur intermediate eigenmodes. This leads us to temper the enthusiasm of novices for these tempting calculation methods, since, although they enable us to predict the behavior of structures that would be impossible to envisage with the calculator alone, the operator must remain extremely vigilant and critical with regard to the values displayed on the screen, all the more so as he or she has not had to intervene once the modeling has been completed, as the program sequence is completely blind. In certain circumstances, this button-pressing strategy can lead to unpleasant surprises.

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