A NEW DERIVATION OF THE FREQUENCY RESPONSE FUNCTION MATRIX FOR VIBRATING NON-LINEAR SYSTEMS

✍ Scribed by D.E. ADAMS; R.J. ALLEMANG

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 272 KB
• Volume: 227
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1999.2396

✦ Synopsis

Frequency response function matrices relate the inputs and the outputs of structural dynamic systems. If a system is linear the frequency response function matrix is the same for any combination or types of inputs over the entire operating range. Furthermore, the frequency response matrix of a linear vibrating system is a simple combination of temporal and spatial characteristics, the modal frequencies, modal vectors and modal scale factors. When a system is non-linear, the inputs interact through an exchange of energy between the linear and non-linear elements in the system. No general combination of the temporal and spatial non-linear characteristics has to date been proposed to describe these linear}non-linear interactions. This article introduces a unifying perspective of non-linearities as internal feedback forces that act together with the external forces to generate the response of the non-linear system. This perspective of the non-linearities is spatial in nature and leads to two simple but conceptually powerful relationships between the frequency response function matrix of a non-linear multiple-degree-of-freedom system and its linear counterpart. Several single-and multiple-degree-of-freedom systems are used to demonstrate the use and interpretation of these relationships. The broad implication of the new input}output frequency response representation for both linear and non-linear systems are also addressed. In particular, the merits of the spatial perspective of non-linear systems and the new frequency response relationships are stated in the context of linear and non-linear system characterization and identi"cation. One implication is that these relationships suggest there is an input}output-dependent temporal-spatial (modal) decomposition of the frequency response function matrix for non-linear systems.