Crashworthiness optimization of ultralight metal structures

Abstract

This dissertation extends the use of the dynamic stiffness and transfer matrix methods in marine riser vibration. Marine risers possess a predominant chain topology. The transfer matrix method is appropriate for the analysis of such structures. Wave transmission and reflection matrices are formulated in terms of transfer-matrix elements. The delta-matrix method is introduced to deal with numerical problems associated with very long beams and high frequencies. The general internal relationships between the transfer matrix and dynamic stiffness methods are derived and applied to the problem of a non-uniform beam with discontinuities. An implicit transfer matrix of a general non-uniform beam is derived. The vibration analysis of non-uniform marine risers is addressed by combining the procedure of the dynamic stiffness method with the WKB theory. The WKB-based dynamic stiffness matrix is derived and the frequency-dependent shape function is expressed implicitly. The Wittrick-Williams algorithm is extended to the analysis of a general non-uniform marine riser, allowing automatic computation of natural frequencies. Marine riser models with complex boundary conditions are analyzed. The WKB-based dynamic stiffness method is improved and applied to a non-uniform beam system with discontinuities. A dynamic stiffness library is created. Dynamic vibration absorbers and wave-absorbing terminations are investigated as a means of suppressing vibration. The optimal tuning of multiple absorbers to a non-uniform beam system under varying tension is investigated. The properties of wave-absorbing terminations of a beam system are derived. The vibration of two concentric cylinders coupled by the annulus fluid and by periodic centralizers is modeled. The effects of coupling factors on vibration are numerically evaluated. It is shown that a properly designed inner tubular member may be used to damp the flow-induced vibration of the outer cylinder.