Nonlinear Reduced Order Random Response Analysis of Structures with Shallow Curvature

Abstract

The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures with shallow curvature under random loadings. For reduced order analysis, the modal basis selection must be capable of reflecting the coupling in both the linear and nonlinear stiffness.

Dynamic Snap-Through of Thin-Walled Structures by a Reduced-Order Method

“…However, it has been subsequently shown that a significant improvement can be obtained using a basis consisting of both low-frequency transverse-dominated modes and high-frequency in-plane-dominated modes. 11,12 The present work concentrates on selecting such a basis so that both the transverse and in-plane dynamic behaviors of the system can be accurately modeled.…”

Dynamic Snap Through of Thin-Walled Structures by a Reduced Order Method

“…11 In this case, a combination of low-frequency ST modes and high-frequency AI modes was found to compare very well with a numerical simulation in physical DoF. From the study of shallowly curved structures, 12 the additional inclusion of AT and SI modes was required to capture the in-plane behavior associated with autoparametric resonance. The geometry of the curved structure is similar to that of the thermally post-buckled beam, and hence the inclusion of AT and SI modes for the present problem is likely beneficial.…”

“…For example, for a symmetric planar structure under symmetric transverse loading, a modal basis consisting of only ST modes may suffice. While such intuition may be useful for a linear analysis, it has been demonstrated for both flat 11 and curved 12 structures that such a rationale will lead to an inadequate basis selection for the nonlinear problem. This is due to coupling in the quadratic and cubic stiffness terms.…”

Dynamic buckling analysis of composite cylindrical shells using a finite element based perturbation method

“…However, finite element based transient analysis is computationally expensive and not suitable for the repeated runs necessary for a design and optimization process, and often it is difficult to interpret the result and to judge its correctness. Reduction methods for general transient analysis of structures have therefore received considerable attention in recent years [16][17][18][19].…”