Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4631795 | Applied Mathematics and Computation | 2010 | 11 Pages |
Abstract
This paper is concerned with a class of conservative oscillators the restitution force of which is of a power form which includes positive non-integer exponents. It is shown how an approximate Lagrangian and Hamilton's variational principle can be used to obtain a second-order approximate solution for their free vibrations. Due to the fact that, in a general case, when the restoring force is multi-term, the period cannot be obtained from the energy conservation law in a closed form, the problem is formulated as a one-point boundary-value problem, and a non-simultaneous variation is introduced. The explicit expressions for the amplitudes and frequency of oscillations are derived, in which there are no restrictions on the values of the non-integer powers. The analytically obtained results are compared with numerical results as well as with some approximate analytical results from the literature.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Ivana Kovacic, Zvonko Rakaric, Livija Cveticanin,