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Gravitational waves emitted from stellar binary black hole (sBBH) mergers canbe gravitationally lensed by intervening galaxies and detected by futureground-based detectors. A large amount of effort has been put into theestimation of the detection rate of lensed sBBH originating from the evolutionof massive binary stars (EMBS channel). However, sBBHs produced by thedynamical interaction in dense clusters (dynamical channel) may also bedominant in our universe and their intrinsic distribution of physicalproperties can be significantly different from those produced by massive stars,especially mass and redshift distribution. In this paper, we investigate theevent rate of lensed sBBHs produced via dynamical channel by Monte Carlosimulations and the number is $16_{-12}^{+4.7} $ $\rm yr^{-1}$ for the Einsteintelescope and $24_{-17}^{+6.8}$ $ \rm yr^{-1}$ for Cosmic Explorer, of whichthe median is about $\sim 2$ times the rate of sBBHs originated from EMBSchannel (calibrated by the local merger rate density estimated for thedynamical and the EMBS channel, i.e., $\sim 14_{-10}^{+4.0}$ and$19_{-3.0}^{+42} \rm Gpc^{-3}yr^{-1}$ respectively). Therefore, one mayconstrain the fraction of both EMBS and dynamical channels through thecomparison of the predicted and observed number of lensed sBBH eventsstatistically.

Event Rate of Strongly Lensed Gravitational Waves of Stellar Binary Black Hole Mergers Produced by Dynamical Interactions