Open Access

ARTICLE

Analytical Solutions for 1-Dimensional Peridynamic Systems by Considering the Effect of Damping

Zhenghao Yang¹, Erkan Oterkus^2,*, Selda Oterkus², Konstantin Naumenko¹

1 Engineering Mechanics, Institute of Mechanics, Otto von Guericke University, Magdeburg, 39106, Germany
2 PeriDynamics Research Centre, Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, Glasgow, G4 0LZ, UK

* Corresponding Author: Erkan Oterkus. Email:

(This article belongs to the Special Issue: Peridynamic Theory and Multi-physical/Multiscale Methods for Complex Material Behavior)

Computer Modeling in Engineering & Sciences 2025, 143(2), 2491-2508. https://doi.org/10.32604/cmes.2025.062998

Received 01 January 2025; Accepted 07 May 2025; Issue published 30 May 2025

Abstract

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.

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Keywords

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