Porosity effects on the dynamic response of arbitrary restrained FG nanobeam based on the MCST

Uzun B., Yaylı M. Ö.

Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences, cilt.79, sa.2, ss.183-197, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 79 Sayı: 2
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1515/zna-2023-0261
  • Dergi Adı: Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Chemical Abstracts Core, zbMATH
  • Sayfa Sayıları: ss.183-197
  • Anahtar Kelimeler: arbitrary boundary condition, modified couple stress, porosity, Rayleigh beam theory, Stokes’ transformation
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

In this study, two different general eigenvalue problems for nanobeams made of functionally graded material with pores in their sections according to Rayleigh beam theory using modified couple stress theory are established. Fourier sine series and Stokes transformation are used for the solution. First, the partial differential equation of motion of the problem is discretized into an ordinary differential equation. Then, the Fourier sine series of infinite series is substituted into this ordinary differential equation to determine the Fourier coefficient. Using the force boundary conditions of the system, Stokes' transformation is performed at both ends to include elastic spring parameters. The unknown displacement terms are discretized to form two eigenvalue problems. By solving these eigenvalue problems, vibration frequencies for different boundary conditions can be found analytically. The variations of some parameters are discussed in a series of graphs.