I am trying to analyze a structure comprising two vertical beams connected by a horizontal beams. The vertical beams are bent inwards to apply a axial pre-load tension to the horizontal beam (see attached sketch). I am trying to figure out the equation of motions of the system where a bending displacement of horizontal beams would result in some bending displacement of the vertical beams.
I am currently employing a Transfer Matrix Method [1] technique to get the mode shape of the entire structure, using the mode shape I am evaluating the [M], [K] matrices using Rayleigh-Ritz formulation. While this works fine when the applied axial preload tension is 0 (vertical beams are straight), I am not sure how to incorporate the effect of pre-load tension. Any help is appreciated.
[1] Wickenheiser, a. M., “Eigensolution of piezoelectric energy harvesters with geometric discontinuities: Analytical modeling and validation,” J. Intell. Mater. Syst. Struct. 24(6), 729–744 (2012)
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