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This paper investigates antiresonance in continuous dynamic systems consisting of beam networks with inherent inertial coupling. An analytical non-dimensional transfer function model is developed to predict the isolation behavior of a cantilever beam with a tip mass. It is shown that beam network isolators exhibit a good degree of versatility at the design level. The static stiffness and the isolation forces are scalable at the design level, the dynamic stiffness can also be tuned to achieve any force reduction ratio in the absence of damping. Furthermore mutlifrequency isolation is possible due to the nature of continuous systems, thus, multi-mode isolation frequencies can be tuned closer to each other. Isolation frequency clustering is also possible by tuning the beam-mass components. As a proof of concept, the analytical results are validated with an experimental study whereby the shear force is recorded at the root of a cantilever beam with a tip mass that is subject to harmonic point force excitation. The experimental results show that the root shear response at the first isolation frequency is reduced by 78% after the addition of a tip mass equivalent to 230% of the beam mass.

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Based on an assumed form that the entropy should take for black holes, the statistics for mass fluctuations are derived from Gauss's law of error. The normal density which results is not a limiting form of any type of physical statistics. The analysis shows that the temperature and mass may become negative while the heat capacities are positive.