Ladder frame structures are used as models for multistorey buildings. These periodic structures exhibit alternating propagating and attenuating frequency bands. Of the six different wave modes of propagation, two modes strongly attenuate at all frequencies. The other four modes have nonoverlapping stop band characteristics. Thus, it is challenging to isolate such structures when subjected to broadband, multimodal base excitation. In this study, we seek to synthesize a periodic ladder frame structure that has attenuation characteristics over the maximal range of frequencies for all the modes of wave propagation. We synthesize a unit cell of the periodic structure, which comprises two distinct regions having different inertial, stiffness, and geometric properties. The eigenvalues of the transfer matrix of the unit cell determines the attenuating or the nonattenuating characteristics of the structure. A novel pictorial presentation in the form of eigenvalue map is developed. This is used to synthesize the optimal unit cell. Also, design guidelines for suitable selection of the design parameters are presented. It is shown that a large finite periodic structure comprising a unit cell synthesized using the present approach has significantly better isolation characteristics in comparison to the homogeneous or any other arbitrarily chosen periodic structure.