I'm trying to analyse the behaviour of a wind turbine blade rigidly connected to a wall during fatigue testing, being excited in it's first mode in two orthogaonal directions simultaneously (the first 'up and down' and the first 'side to side' mode). I currently do this in two ways, both of which use a beam element model of the blade:
Modal superposition (build the stiffness and mass matrices of the system, perform modal analysis, project applied forcing onto eigenmodes, create time history by superposition of sinusoidal time histories)
Nonlinear transient analysis (update the stiffness and mass matrix at each time step, apply forcing using beam elements which displace like the hydraulic cylinders actually used to apply the force). Very computationally expensive so no use in an optimisation loop!
Both methods produce comparable natural frequencies and mode shapes, but the modal superposition fails to capture behaviour which is seen in real life. The plot below shows this. The red line is generated by modal superposition, the blue line is real test data (but is similar to what is obtained with the nonlinear transient analysis). If I do a linear transient analysis then the behaviour is as the red line - it seems like when the loading in the $M_X$ direction is in phase with the loading in the $M_Y$ direction, the modes create some extra loading (and the opposite thing happens) when the two modes are opposed to each other, which keeps the overall amount of energy in the system constant over time.
Does anybody know of any less computationally expensive methods than nonlinear transient which may be able to capture this behaviour? I don't want to create a fudge ideally - I'd like a physics based result!
Any help will be very much appreciated!