PSI - Issue 28

Nikita Kazarinov et al. / Procedia Structural Integrity 28 (2020) 2168–2173

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N. Kazarinov et al/ Structural Integrity Procedia 00 (2020) 000–000

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( ) = ; (1 − cos( )), ≤ CcosC ( − )D − cos( )D, > (2)(2), where = F ⁄ is the oscillator eigen frequency. If the system failure is considered and fracture time is denoted by ∗ , equation ( ∗ ) = ! can be used to build dependency of the pulse duration on the fracture time ∗ for a fixed pulse amplitude. For a threshold case, when fracture takes place right when the loading ends ( = ∗ ) a point #$%&'$()* = #$%&'$()* ∗ = (1 − ! ⁄ )⁄ is present on the ( ∗ ) graph (Fig. 1). All pulses with durations longer than the threshold result in the exact same fracture time #$%&'$()* ∗ yielding a vertical line on ( ∗ ) graph. The fracture with a delay can be studied if > case from (2) is considered. For this case solution of the equation ( ∗ ) = ! (3). Analyzing (3) one can evaluate minimal pulse duration for a given amplitude +,- , which corresponds to a maximal fracture time +∗ ./ indicating maximal fracture delay time: (4b). Formulas (4a,b) impose natural limitation on the pulse amplitude due to restrictions on the argument which should belong the [−1,1] range. Thus, in order to cause the system failure, the pulse amplitude should be more or equal to a half of static critical force (a static force which would break the spring if static problem is considered): ≥ ! ⁄2 . The constructed ( ∗ ) dependence is shown in figure 1. yields the following ( ∗ ) dependence: = − 1 J ! + ( ∗ )K+ ∗ +∗ ./ = 1 J − M ! 2 OK +,- = 1 J − 2 M ! 2 OK (4a),

Fig. 1. Dependence of the breaking pulse amplitude on fracture time