PSI - Issue 75

Robert Goraj et al. / Procedia Structural Integrity 75 (2025) 691–708 Goraj/ Structural Integrity Procedia (2025)

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Fig. 1. Bearing cap with positioning of dumpers and indication of vibration masses

This force consists of a sudden (infinitely short) switch on/off the propeller thrust F th and the propeller unbalance F ub oscillating with the angular frequency ω =2 πf : ( ) = ( ℎ + ( )) ∑[ ( − 2 ) − ( − (2 + 1) )] ∞ =0 (1) The function θ in (1)is the Heaviside function, t is time and 2 T a period between propeller switches according to: = 2 , ∈ + (2) The time dependent function u x (t) is plotted in figure Fig. 2.

Fig. 2 Propeller excitation u x (t) Transforming u x (t) ⊶ U x (s) using the Laplace transformation results in: ( ) = ( ℎ + 2 + 2 ) 1 + ex1p(− ) The derivation of (3) is described in the appendix A. The analyzed alignment is considered as a coupled damped oscillator. A graphical representation of this oscillator is shown in Fig. 3. (3)