In structural mechanics there are several occasions where a linearized formulation of the original nonlinear
problem reduces considerably the computational effort for the response analysis. In a broader
sense, a linearized formulation can be viewed as a first-order expansion of the dynamic equilibrium of
the system about a `static¿ configuration; yet caution should be exercised when identifying the `correct¿
static configuration. This paper uses as a case study the rocking response of a rigid block stepping on
viscoelastic supports, whose non-linear dynamics is the subject of the companion paper, and elaborates on
the challenge of identifying the most appropriate static configuration around which a first-order expansion
will produce the most dependable results in each regime of motion. For the regime when the heel of
the block separates, a revised set of linearized equations is presented, which is an improvement to the
unconservative equations published previously in the literature. The associated eigenvalues demonstrate
that the characteristics of the foundation do not affect the rocking motion of the block once the heel
separates.
| Identifer | oai:union.ndltd.org:BRADFORD/oai:bradscholars.brad.ac.uk:10454/603 |
| Date | January 2008 |
| Creators | Palmeri, Alessandro, Makris, N. |
| Source Sets | Bradford Scholars |
| Language | English |
| Detected Language | English |
| Type | Article |
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