Random response of structures by a force derivative approach

• Published in: Journal of sound and vibration 1992-05, Vol.155 (1), p.13-29
• Main Authors: Maldonado, G.O., Singh, M.P., Suarez, L.E.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/0022-460X(92)90642-B

The practice of truncating modes is common in the mode superposition analysis of linear structures. To reduce the error due to the truncation of modes in the random vibration analysis of structures, a generalized force derivative approach is presented. In this approach, the response is expressed as a sum of two parts: (1) the dynamic part, representing the contribution of the retained modes; and (2) the pseudo-static part, representing the contribution of the truncated modes. The accuracy of the latter contribution can be improved by including higher order force derivative terms. This contribution can be calculated by a static analysis involving the stiffness and damping matrices of the system. Recursive formulas are presented to facilitate the calculations for increasing orders of force derivative. Numerical results demonstrating the applicability of the proposed response calculating scheme and the effectiveness of the approach in improving the accuracy of mode truncation analysis are presented.