By Tony L. Schmitz
Mechanical Vibrations: Modeling and Measurement describes crucial thoughts in vibration research of mechanical platforms. It contains the necessary arithmetic, experimental innovations, basics of version research, and beam concept right into a unified framework that's written to be obtainable to undergraduate scholars, researchers, and working towards engineers. To unify many of the thoughts, a unmarried experimental platform is used in the course of the textual content. Engineering drawings for the platform are integrated in an appendix. also, MATLAB programming options are built-in into the content material through the text.
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Extra info for Mechanical Vibrations: Modeling and Measurement
If an astronaut were to tap this beam at its end, it would begin to rotate about its center of mass – this is referred to as rigid body motion – and it would also begin vibrating. Since nothing is touching the beam and there is no obvious resistance to motion, why does the vibrating motion eventually stop? This is solid damping and we will describe it using a complex elastic modulus for the beam material, Es in Sect. 3. See Eq. 58, where is the material-dependent solid damping factor. 4 2 Single Degree of Freedom Free Vibration Damped System Behavior Since viscous damping is the most common modeling choice, we will consider it now to represent our single degree of freedom spring–mass–damper system.
As we saw with the 2 2 rolling cylinder problem, J ¼ mr2 ¼ md8 , where r indicates radius, d is diameter, and m is the disk mass. The units are kg Á m2 , but we will again include radians in the 2 denominator for compatibility with the equation of motion: kgÁm . Let’s now verify rad the natural frequency units. 54) Nonlinear Springs In this text, we are only considering vibration of linear systems. However, there are instances where a nonlinear model better describes the system behavior. One way to incorporate nonlinear behavior is through the use of nonlinear springs, or springs where the force is not linear with displacement as we showed in Fig.
IN A NUTSHELL It might seem like a long (mathematical) way to go, but the end result is that free vibration of a single degree of freedom system with no damping is sinusoidal and occurs at the natural frequency of the system. The initial conditions might make the vibration larger or smaller or make it look more like a sine or a cosine. However, the initial conditions do not change the frequency of the motion. The natural frequency is a fundamental property of a single degree of freedom system. 1 Consider the spring–mass system shown in Fig.