Dominant Modal Model of a Clamped-Free Beam System with a Cart and a Sliding Eccentric Mass: An Euler–Bernoulli-Based Analytical-Numerical Study

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Zafer N.

10. BILSEL International World Science and Research Congress, 9 - 10 Mayıs 2026, ss.466-476, (Tam Metin Bildiri)

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Sayfa Sayıları: ss.466-476
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

In this study, a dominant modal model is derived analytically for a system consisting of an elastic beam clamped to a cart moving in the horizontal direction and an eccentric mass traveling along the beam. Numerical time responses are computed for two different operating conditions. The investigated cases are: (i) the motion of the sliding eccentric mass along the beam while the cart is stationary, and (ii) the effect of the same sliding mass motion on the beam dynamics when the cart moves with a trapezoidal velocity profile. The continuous system is formulated using the Euler–Bernoulli beam equation, reduced to the first mode via the assumed-modes approach, and the time-varying inertia, damping-like, and stiffness-like contributions of the moving mass and its eccentric offset are incorporated into the dominant modal equation. 

Since the resulting dominant modal equation has time-varying coefficients and is not amenable to a closed-form solution with constant parameters, it is solved numerically in MATLAB using ode45. The numerical investigation shows that even the sliding mass alone significantly alters the equivalent modal frequency of the beam; when base acceleration due to cart motion is included, peak displacement and residual vibration levels increase markedly. Therefore, the results demonstrate that the dominant mode approach provides strong physical insight for cart–beam systems with a sliding mass, and that it is essential to consider the combined effects of base motion and moving mass dynamics. 

Keywords: euler–bernoulli beam, assumed modes, moving mass, moving base (base excitation), dominant mode, analytical–numerical solution, matlab simulation