A time‐integration algorithm for non‐linear dynamic systems of first and second order
Non‐linear dynamic systems are defined by mechanical models involving differential equations of second order where also first order differential equations are present frequently. If some degrees of freedom have no corresponding mass, if the stiffness parameters vanish in a part of the equations or i...
Uloženo v:
| Vydáno v: | Proceedings in applied mathematics and mechanics Ročník 19; číslo 1 |
|---|---|
| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Berlin
WILEY‐VCH Verlag
01.11.2019
|
| ISSN: | 1617-7061, 1617-7061 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Shrnutí: | Non‐linear dynamic systems are defined by mechanical models involving differential equations of second order where also first order differential equations are present frequently. If some degrees of freedom have no corresponding mass, if the stiffness parameters vanish in a part of the equations or if a controller is implemented in the system, then differential equations of first order result. For linear systems of first and second order a variety of solutions is presented in [1] and various numerical procedures for solving the differential equations in [2]. A semi‐analytical method is presented which is exact for the linear dynamic and decoupled systems of first and second order. A modal transformation of the equations is necessary after a suitable partitioning of the system equations. After a discretisation in the time‐domain the relevant equations for a suitable and effective time‐integration algorithm are defined taking the non‐linearity into account. The resulting procedure is derived and the formulation is analogous to the BEM‐formulation in time, described in [3] for a system of second order. The method is extended to the coupled non‐linear differential equations of first order and is applied to a system with two degrees of freedom. |
|---|---|
| ISSN: | 1617-7061 1617-7061 |
| DOI: | 10.1002/pamm.201900397 |