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Numerical algorithm for the dynamic analysis of base-isolated structures with dry friction |
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| Authors: | S. Dimova V. Georgiev |
| Affiliation: | (1) Central Laboratory for Seismic Mechanics and Earthquake Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. bl. 3, 1113 Sofia, Bulgaria;(2) Institute of Mathematics, Section Mathematical Physics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. bl. 8, 1113 Sofia, Bulgaria |
| Abstract: | This paper deals with the techniques for solving ordinary differential equations with essential nonlinearity arising from the representation of frictional force by the sign function of the relative velocity. This problem is connected with dynamic behavior studies of base-isolated structures with dry friction devices.Mathematical evidence is presented concerning the inaccuracies of the solution which are connected with the representation of the frictional force by the sign function. An approximation of this sign model is made on the basis of the appropriate linearization of a small part of the frictional force function. A numerical algorithm for the dynamic analysis of base-isolated structures with dry friction is proposed. Numerical tests are carried out for establishing the exactness of the proposed techniques. The obtained results prove the accuracy of the techniques. |
| Keywords: | Frictional force modeling numerical algorithm ordinary differential equation with essential nonlinearity sign function numerical solution base-isolated structures dynamic behavior studies |
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