Nonlinear Stochastic Interaction in Aeroelastic Structures.
Abstract
The linear and nonlinear modal interactions in aeroelastic structures under wide band random excitation are examined analytically and experimentally. The analytical investigation deals with the random response characteristics of two- and three-degree-of-freedom nonlinear models in the neighborhood of internal resonance conditions. These conditions take the form of linear relationships between the normal mode frequencies and are established from the linear modal analysis of each model. The Fokker-Planck equation approach is used to derive a general differential equation for the response joint moments. In view of the models nonlinearity the differential equation is found to constitute a set of infinite coupled first order differential equations. These equations are closed by using two different truncation schemes which are based on the properties of response joint cumulants. These two schemes are known as Gaussian and non-Gaussian closures. The analytical manipulations are performed by using the computer algebraic software MACSYMA, while the response statistical moments are determined by numerical integration by using the IMSL software DVERK. The Gaussian closure solution gives a quasi-stationary response in the form of fluctuations between two limits. However, the non-Gaussian closure results in a strict stationary response. The general trend of the nonlinear interaction takes the form of energy exchange between the interacted modes when the system is internally tuned.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 29, 1988
- Accession Number
- ADA193427
Entities
People
- Raouf A. Ibrahim
Organizations
- Texas Tech University