Among the techniques used to control or mitigate the structural vibrations induced by dynamic input, such as wind and earthquake, the dissipative coupling is one of the most applied, especially for its ease of implementation. Indeed, for example in large urban areas, it is common to find adjacent structures where the space between the buildings becomes smaller. To optimally select the visco-elastic features of the dissipative device to be used, the paper retraces the path followed by the previous scientific works proposing new design criteria. Such criteria are based on the nonlinear stochastic response of two simple oscillators linked by a damper whose hysteretic behavior is represented by a Bouc-Wen model. A state-space formulation of the equations of motion has been adopted to facilitate the analysis of the dynamic response. At the same time, the loading is hypothesized as a zero-mean Gaussian excitation. Consequently, the nonlinear response has been approximately evaluated by the equivalent linearized standard deviations for both displacements and accelerations. Subsequently, formulations of objective functions, based on the Minimax and Total Energy of the equivalent linearized stochastic response, have been applied to determine the optimal configurations of the coupled system. The influence of both noise power amplitude and soil typology on the designed systems has been also investigated. Suggestions related to the path to achieve pre-fixed targets (as balancing of displacements and accelerations) are provided.

The probabilistic methods are receiving increasing recognition in assessing the hazards due to landslides, owing to the ability of these methods to consider the estimation uncertainties and geographical heterogeneity of geomorphological, geotechnical, geological, and seismological components. Therefore, the present study developed a probabilistic method to model the parametric uncertainties of modified Newmark's method using the Monte Carlo simulation technique. The proposed methodology was applied to evaluate the hazard potential for co-seismic landslides in the Uttarakhand state, located in the Indian Himalayan region. The modified Newmark model considered in the study incorporates the rock joint shear strength properties instead of soil shear strength parameters in the permanent displacement computation of slopes. The simulations were done pixel-by-pixel by seamlessly integrating into the current GIS computational settings. When analyzing these data, statistical distributions were used to account for uncertainties and variations in the input parameters. Monte Carlo simulations were employed to generate various probability density functions for each individual pixel within the study area. These simulated distributions were then maintained consistently across the entire computational workflow, ensuring that the generated samples were preserved throughout the analysis. With no limitations on the symmetry or complexity of the underlying distributions, the resultant numbers were then turned into probabilistic hazard maps. In the final step, a hazard map was produced, where each pixel indicates the probability that slope displacement will surpass the 5 cm threshold. Values of probability are distributed between 0.1 and 1, with elevated values primarily observed in the upper Himalayan region, emphasizing the greater likelihood of co-seismic landslides in this zone. This seismic landslide hazard map serves as a valuable tool for local planners and authorities, enabling them to assess regions vulnerable to seismic landslide hazards and implement measures to mitigate potential losses.