2012-03-20

SDOF Response to Harmonic Loading

We will see that linear systems are mostly studied by superposition of SDOF responses to arbitrary loadings, that in their turn can be derived by superposition of responses to harmonic loadings. Hence the importance of studying the response of a SDOF system subjected to a harmonic excitation, for both undamped and damped systems.

For the undamped oscillator, we will see the complementary solution for a harmonic loading, define the response ratio and the particular case of resonant response. A particular attention will be given to the study of the response when starting from initial zero conditions.

Analogous treatment is given for the damped oscillator, where we introduce the concept of steady-state response, the necessity of a phase angle to describe the steady-state response of a damped system and the different characteristics of an overdamped system. The presentation is repeated for an exponential harmonic load, that leads to a simpler algebra for the s-s response.

Using properly damped systems, it is possible to measure accelerations or displacements (accelerometres and seismometres).

Using a suspension system it is possible to get some degree of insulation from forced vibrations. We discuss some guidelines and formulas necessary for an efficient design of suspension systems

Finally, we discuss some of the available method for measuring the damping of a given structure/mechanical system.

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Giacomo Boffi