Most stars are born in clusters and the resulting gravitational interactions between cluster members may significantly affect the evolution of circumstellar disks and therefore the formation of planets and brown dwarfs (BDs). Recent findings suggest that tidal perturbations of typical circumstellar disks due to close encounters may inhibit rather than trigger disk fragmentation and so would seem to rule out planet formation by external tidal stimuli. However, the disk models in these calculations were restricted to disk radii of 40 AU and disk masses below 0.1 M . Here, we show that even modest encounters can trigger fragmentation around 100 AU in the sorts of massive (∼0.5 M ), extended ( 100 AU) disks that are observed around young stars. Tidal perturbation alone can do this; no disk-disk collision is required. We also show that very low mass binary systems can form through the interaction of objects in the disk. In our computations, otherwise non-fragmenting massive disks, once perturbed, fragment into several objects between about 0.01 and 0.1 M , i.e., over the whole BD mass range. Typically, these orbit on highly eccentric orbits or are even ejected. While probably not suitable for the formation of Jupiter-or Neptune-type planets, our scenario provides a possible formation mechanism for BDs and very massive planets which, interestingly, leads to a mass distribution consistent with the canonical substellar initial mass function. As a minor outcome, a possible explanation for the origin of misaligned extrasolar planetary systems is discussed.