Analytical solutions for 1-Dimensional peridynamic systems by considering the effect of damping

For the solution of peridynamic equations of motion, a meshless approach is typically used instead of utilizing semi-analytical or mesh-based approaches. In contrast, the literature has limited analytical solutions. This study develops a novel analytical solution for one-dimensional peridynamic models, considering the effect of damping. After demonstrating the details of the analytical solution, various demonstration problems are presented. First, the free vibration of a damped system is considered for under-damped and critically damped conditions. Peridynamic solutions and results from the classical theory are compared against each other, and excellent agreement is observed between the two approaches. Next, forced vibration analyses of undamped and damped conditions are performed. In addition, the effect of horizon size is investigated. It is shown that for smaller horizon sizes, peridynamic results agree well with classical results, whereas results from these two approaches deviate from each other as the horizon size increases.