Arch Appl Mech https://doi.org/10.1007/s00419-020-01656-9 ORIGINAL Amir Jahangiri · Nader K. A. Attari · Ali Nikkhoo · Zakariya Waezi Nonlinear dynamic response of an Euler–Bernoulli beam under a moving mass–spring with large oscillations Received: 21 July 2019 / Accepted: 4 January 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract This article presents a new approach for the nonlinear dynamic behavior of an Euler–Bernoulli beam under a moving mass. The governing equations for the behavior of the beam under a moving mass in large oscillations including the effect of horizontal and vertical beam displacements are considered via energy method. The systems of governing equations are solved in the condition of external and autoparametric resonance using Galerkin and perturbation methods. In order to validate the solution, the results are compared with a numerical solution and those available in the literature. The governing equations are used for the stability analysis of the beam in different points that will result in spectral responses in stable circumstances. Keywords Geometrically nonlinear beam · Moving mass · Perturbation method · Nonlinear resonance 1 Introduction Evaluation of the dynamic response of structures excited by moving loads has large applications in engineering problems and attracted the attention of many researchers [1]. Studying the behavior of a continuum under moving loads for the purpose of designing a safe structural system is very important for engineers. Railways and bridges are good examples in transportation industry where the effects of moving bodies with a large mass or velocity have to be examined with high accuracy. The dynamic behavior of such structures under the influence of the moving mass has to be analyzed to ensure a safe and economical structure [2]. Slab-type bridges [3] and ship decks used for the takeoff and landing of planes [4] can be modeled as beam elements under a moving mass. In mechanical engineering, high-speed precision machinery systems also require an assessment of the structure under a moving mass [4, 5]. Furthermore, some part of structural systems can be idealized as beams carrying a concentrated mass at their free end such as flexible robot arms, water towers, wind A. Jahangiri · N. K. A. Attari (B) Structural Engineering Department, Road, Housing and Urban Development Research Center (BHRC), Hekmat Ave, Noori Highway, Tehran, Iran E-mail: n.attari@bhrc.ac.ir A. Jahangiri E-mail: mr.jahangiri.amir@gmail.com A. Nikkhoo Department of Civil Engineering, University of Science and Culture, Tehran, Iran E-mail: nikkhoo@usc.ac.ir Z. Waezi Department of Civil Engineering, Shahed University, Tehran, Iran E-mail: waezi@shahed.ac.ir