Superharmonic vibrations of sandwich beams with viscoelastic core layer with the multiple scale method

Abdelhak Benaoum, Hadj Youzera, Moussa Abualnour, Mohammed Sid Ahmed Houari, Sid Ahmed Meftah and Abdelouahed Tounsi

Abstract

In this work, mathematical modeling of the passive vibration controls of a three-layered sandwich beam under hard excitation is developed. Kelvin-Voigt Viscoelastic model is considered in the core. The formulation is based on the higher-order zig-zag theories where the normal and shear deformations are taken into account only in the viscoelastic core. The dynamic behaviour of the beam is represented by a complex highly nonlinear ordinary differential equation. The method of multiple scales is adopted to solve the analytical frequency-amplitude relationships in the super-harmonic resonance case. Parametric studies are carried out by using HSDT and first-order deformation theory by considering different geometric and material parameters.

Key Words

forced nonlinear vibration; higher-order zig-zag theories; multiple scale method; perturbation method; sandwich beams; viscoelastic model

Address

Abdelhak Benaoum, Hadj Youzera, Moussa Abualnour, Mohammed Sid Ahmed Houari: Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté des Sciences et de la Technologie, Université Mustapha Stambouli, B.P. 305, R.P. 29000, Mascara, Algérie Sid Ahmed Meftah: Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de DjellaliLiabes, Sidi Bel Abbes, Algérie Abdelouahed Tounsi: YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea; Department of Civil and Environmental Engineering, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Eastern Province, Saudi Arabia

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