Exact Radial Free Vibration Frequencies of Power-Law Graded Spheres

YILDIRIM V.

JOURNAL OF APPLIED AND COMPUTATIONAL MECHANICS, cilt.4, sa.3, ss.175-186, 2018 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 4 Sayı: 3
  • Basım Tarihi: 2018
  • Doi Numarası: 10.22055/jacm.2017.22987.1145
  • Dergi Adı: JOURNAL OF APPLIED AND COMPUTATIONAL MECHANICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.175-186
  • Anahtar Kelimeler: Free vibration, Functionally graded, Exact solution, Hollow sphere, Thick-walled, LAMINATED HOLLOW SPHERES, NATURAL FREQUENCIES, BEAMS
  • Çukurova Üniversitesi Adresli: Evet

Özet

This study concentrates on the free pure radial vibrations of hollow spheres made of hypothetically functionally simple power rule graded materials having identical inhomogeneity indexes for both Young's modulus and the density in an analytical manner. After offering the exact elements of the free vibration coefficient matrices for free-free, free-fixed, and fixed-fixed restraints, a parametric study is fulfilled to study the effects of both the aspect ratio and the inhomogeneity parameters on the natural frequencies. The outcomes are presented in both graphical and tabular forms. It was seen that the fundamental frequency is mostly affected by the inhomogeneity parameters rather than the higher ones. However, the natural frequencies except the fundamental ones are dramatically affected by the thickness of the sphere. It is also revealed that there is a linear relationship between the fundamental frequency and others in higher modes of the same sphere under all boundary conditions.