The Effect of Basis Selection on Thermal-Acoustic Random Response Prediction Using Nonlinear Modal Simulation

Abstract

The goal of this investigation is to further develop nonlinear modal numerical simulation methods for prediction of geometrically nonlinear response due to combined thermalacoustic loadings. As with any such method, the accuracy of the solution is dictated by the selection of the modal basis, through which the nonlinear modal stiffness is determined. In this study, a suite of available bases are considered including (i) bending modes only; (ii) coupled bending and companion modes; (iii) uncoupled bending and companion modes; and (iv) bending and membrane modes. Comparison of these solutions with numerical simulation in physical degrees-of-freedom indicates that inclusion of any membrane mode variants (ii -iv) in the basis affects the bending displacement and stress response predictions. The most significant effect is on the membrane displacement, where it is shown that only the type (iv) basis accurately predicts its behavior. Results are presented for beam and plate structures in the thermally pre-buckled regime. Nomenclature

Nonlinear Reduced Order Random Response Analysis of Structures with Shallow Curvature

“…The modal solution is transformed back to physical coordinates and can be post-processed as desired. It should be pointed out that for the purpose of analyzing non-planar structures, the formulation previously presented 7,8,11 has not been redeveloped. However, the guidelines for the selection of basis functions must be substantially revised.…”

“…8 The linear eigenvectors, commonly employed as basis functions, are first obtained from a commercial finite-element program (in this study ABAQUS v.6.5-1). Following a transformation of the nonlinear system of equations to modal coordinates, the modal stiffness coefficients are evaluated and the resulting coupled system of equations is numerically integrated to obtain the modal displacement time history.…”

“…The majority of research performed in the field of reduced order numerical simulation of thin-walled aerospace structures has been primarily focused on isotropic planar configurations. 1,[6][7][8][9][10][11][12] Through comparison with numerical simulation in physical DoFs, the authors recently demonstrated the ability of a reduced order method to accurately predict geometrically nonlinear random displacement and stress response for a planar isotropic structures, provided that a suitable modal basis is utilized. 8 However, most practical aerospace applications involve more complex geometries.…”

“…1,[6][7][8][9][10][11][12] Through comparison with numerical simulation in physical DoFs, the authors recently demonstrated the ability of a reduced order method to accurately predict geometrically nonlinear random displacement and stress response for a planar isotropic structures, provided that a suitable modal basis is utilized. 8 However, most practical aerospace applications involve more complex geometries. Thus, the focus of this study is to extend the authors' previous work using an indirect stiffness evaluation approach to determine the effect of modal basis selection on the response of structures with shallow curvature.…”

Nonlinear Reduced Order Random Response Analysis of Structures with Shallow Curvature

“…Previous work indicated this to be the case for a planar isotropic and uniformly loaded beam, regardless the excitation level applied. 8 For the loading level of 0.6517 lb/in., the mid-span u displacement of the arch exhibits intermittent damped transients. At the excitation level of 1.3033 lb/in., the motion is of a permanent nature.…”