A method for the vibration analysis of built-up structures, Part II: Analysis of the plate-stiffened beam using a combination of finite element analysis and analytical impedances

This is the second of two companion papers which collectively present a method for the analysis of complex structures built-up from stiff beams and flexible plates. The method separates the stiff parts of the structure (which support the vibration sources) and the flexible parts of the structure, models the two parts separately in order to accommodate the significantly different wavelengths of the waves in them, then recombines the two parts to obtain the response of the complete structure. The companion paper analyzed the plate-stiffened beam consisting of a directly driven uniform beam attached to a rectangular plate in order to demonstrate the theoretical foundation of the method. However, the theoretical work is limited to very simple geometries. Hence, this paper implements the method using a combination of numerical analysis to model the stiff beam and analytical impedances to model the flexible plate. In particular, the response of the beam separate from the plate is modelled using finite element analysis. The response of the plate separate from the beam is modelled using analytical impedances in a manner identical to that used in the companion paper. The two separate responses are finally coupled together using a standard sub-structuring procedure. Predictions of input and transfer response for two geometrically different plate-stiffened beams, one with a rectangular plate and one with a trapezoidal plate, compare well with measurements. Additionally, the method allows estimation of the mean-square acceleration of the plates which also compare favourably with measurements