Nonlinear Reduced-Order Analysis with Time-Varying Spatial Loading Distributions

Adam Przekop, Stephen A. Rizzi
2009 Journal of Aircraft  
Oscillating shocks acting in combination with high-intensity acoustic loadings present a challenge to the design of resilient hypersonic flight vehicle structures. This paper addresses some features of this loading condition and certain aspects of a nonlinear reduced-order analysis with emphasis on system identification leading to formation of a robust modal basis. The nonlinear dynamic response of a composite structure subject to the simultaneous action of locally strong oscillating pressure
more » ... adients and high-intensity acoustic loadings is considered. The reduced-order analysis used in this work has been previously demonstrated to be both computationally efficient and accurate for time-invariant spatial loading distributions, provided that an appropriate modal basis is used. The challenge of the present study is to identify a suitable basis for loadings with time-varying spatial distributions. Using a proper orthogonal decomposition and modal expansion, it is shown that such a basis can be developed. The basis is made more robust by incrementally expanding it to account for changes in the location, frequency and span of the oscillating pressure gradient. Nomenclature a = quadratic modal stiffness coefficient b = cubic modal stiffness coefficient [ ],[ ] C C = physical degree-of-freedom damping matrix, modal damping matrix d = linear modal stiffness coefficient { },{ } f f = physical degree-of-freedom force vector, modal force vector { },{ NL NL } f f = physical degree-of-freedom restoring force vector, modal restoring force vector [ ],{ } φ Φ = matrix of normal modes, normal mode vector [ ] I = identity matrix L = number of modal basis functions [ ] λ = proper orthogonal value matrix m = number of nodes in finite element model M = number of most contributing proper orthogonal modes [ ],[ ] M M = physical degree-of-freedom mass matrix, modal mass matrix n = number of displacement fields used in snapshot matrix N = number of physical degrees-of-freedom [ ],{ } P p = matrix of proper orthogonal modes, proper orthogonal mode vector q = modal (generalized) coordinate [ ] R = correlation matrix
doi:10.2514/1.39790 fatcat:sowbiz4z2bf77dfb7dlw5kh5ty