Nonlinear forced vibration analysis of clamped functionally graded beams

• Published in: Acta mechanica Vol. 221; no. 1-2; pp. 23 - 38
• Main Authors: Shooshtari, A., Rafiee, M.
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 01-09-2011; Springer; Springer Nature B.V
• Subjects: Analysis; Beams (structural); Classical and Continuum Physics; Control; Dynamical Systems; Engineering; Engineering Thermodynamics; Exact sciences and technology; Forced vibration; Functionally gradient materials; Fundamental areas of phenomenology (including applications); Galerkin methods; Heat and Mass Transfer; Laws, regulations and rules; Materials science; Mathematical analysis; Mechanical engineering; Nonlinear dynamics; Nonlinearity; Physics; Solid Mechanics; Structural and continuum mechanics; Theoretical and Applied Mechanics; Vibration; Vibration analysis; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Sandwich Beam; Primary Resonance; Forced Vibration; Functionally Grade; Free Vibration Analysis; Exponential distribution; Forced vibration; Bernoulli Euler model; Modeling; Beam(mechanics); Natural frequency; Primary resonance; Multiple solution; Multiscale method; Functionnally graded material; Galerkin method; Frequency response; Von Kárman equation; Non linear effect; Power law; Structural analysis
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-011-0491-1

Multiple time scale solutions are presented to study the nonlinear forced vibration of a beam made of symmetric functionally graded (FG) materials based on Euler–Bernoulli beam theory and von Kármán geometric nonlinearity. It is assumed that material properties follow either exponential or power law distributions through the thickness direction. A Galerkin procedure is used to obtain a second-order nonlinear ordinary equation with cubic nonlinear term. The natural frequencies are obtained for the nonlinear problem. The effects of material property distribution and end supports on the nonlinear dynamic behavior of FG beams are discussed. Also, forced vibrations of the system in primary and secondary resonances have been studied, and the effects of different parameters on the frequency-response have been investigated.