Nonlocal strain gradient beam model for nonlinear secondary resonance analysis of functionally graded porous micro/nano-beams under periodic hard excitations

A. M. Fattahi, S. Sahmani, N. A. Ahmed

Research output: Contribution to journalArticlepeer-review

64 Citations (Scopus)

Abstract

Functionally graded porous materials (FGPMs) have a wide range of applications as hollow members in biomedical and aeronautical engineering. In the FGPMs, the porosity is varied over the material volume because of the density change of pores. In the present work, an analytical treatment on the size-dependent nonlinear secondary resonance of FGPM micro/nano-beams subjected to periodic hard excitations is proposed in the simultaneous presence of the nonlocality and strain gradient size dependencies. Based upon the closed-cell Gaussian-random field scheme, the mechanical properties of the FGPM micro/nano-beams are extracted corresponding to the uniform and three different functionally graded patterns of the porosity dispersion. The nonlocal strain gradient theory of elasticity is applied to the classical beam theory to formulate a newly combined size-dependent beam model. Thereafter, an analytical solving methodology based on the multiple time-scales together with the Galerkin technique is adopted to achieve the nonlocal strain gradient frequency–response and amplitude–response curves associated with the subharmonic and superharmonic external excitations. For the subharmonic excitation, it is observed that the nonlocality causes to shift the junction point of the stable and unstable branches to the higher value of the detuning parameter. However, the strain gradient size dependency plays an opposite role. For the superharmonic one, it is illustrated that the nonlocal size effect makes an increment in the height of jump phenomenon and shifts the peak to higher value of the detuning parameter. However, the strain gradient small scale effect leads to decrease the height of the jump phenomenon and shifts the peak to lower value of the detuning parameter.

Original languageEnglish
Pages (from-to)403-432
Number of pages30
JournalMechanics Based Design of Structures and Machines
Volume48
Issue number4
DOIs
Publication statusPublished - 3 Jul 2020

Keywords

  • Gaussian-random field scheme
  • Porous material
  • multiple time-scales method
  • nonlinear dynamics
  • size dependency

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • General Mathematics
  • Automotive Engineering
  • Aerospace Engineering
  • Condensed Matter Physics
  • Ocean Engineering
  • Mechanics of Materials
  • Mechanical Engineering

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