We have used the vibrational density of state (DoS) derived from classical molecular dynamic (MD) simulations to investigate the origin of the generation-dependent stability of the hydrogen-bond-mediated self-assembly of supramolecular dendritic structures synthesized and characterized by Zimmerman and co-workers. In this method, the DoS distribution is calculated from the Fourier transform of the velocity autocorrelation function, and the thermodynamic properties are determined by weighting each vibrational mode with the harmonic oscillator statistics. Our simulation results confirm the experimental findings that circular and linear configurations may coexist at lower generations but that only circular forms are stable at higher generations. From analyzing the free energy extracted from the MD on both linear and hexagonal forms of the first through fourth generation dendrimers, we find that entropic contributions dominate the stability of these self-assembled systems. This method provides additional detailed information on the thermodynamic properties of suprastructures, which should be useful in the study of other complex systems such as proteins and DNA.