Abstract
Once the fundamental concepts of dynamics are defined, it is important to describe mechanical vibrations. Mechanical vibrations cover a broad field of knowledge; thus, in this chapter we start defining the basic aspects of linear vibrations. The concepts are derived from the equation of motion, which is formulated from the energy methods introduced in the previous chapter. The equation of motion is a second order differential equation, and the linear term comes from the assumption that the coefficients of this equation are constant. The equation of motion depends on the generalized coordinates, and for each generalized coordinate we set a degree of freedom. The basic concepts are introduced with the analysis of a single degree of freedom system. For this system, three cases are presented: free undamped vibration, forced vibration and damped vibration. From the forced vibration concept, a definition of transmissibility is introduced and finally a system with multiple degrees of freedom is presented. The example included in this chapter is a gear box with four degrees of freedom; this example will be used thoughout the book.
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