Free Vibration of Damaged Frame Structures Considering the Effects of Axial Extension, Shear Deformation and Rotatory Inertia: Exact Solution

Eroglu U., Tüfekci E.

INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS, cilt.17, sa.10, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 10
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1142/s0219455417501115
  • Dergi Adı: INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Beam theory, frame structures, free vibrations, crack modeling, fracture mechanics, EULER-BERNOULLI BEAM, FINITE-ELEMENT FORMULATION, DYNAMIC STIFFNESS MATRIX, CRACK DETECTION PROBLEM, NATURAL FREQUENCIES, BOUNDARY-CONDITIONS, BENDING VIBRATIONS, GENETIC ALGORITHMS, MULTIPLE CRACKS, STEPPED BEAMS
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

In this paper, a procedure based on the transfer matrix method for obtaining the exact solution to the equations of free vibration of damaged frame structures, considering the effects of axial extension, shear deformation, rotatory inertia, and all compliance components arising due to the presence of a crack, is presented. The crack is modeled by a rotational and/or translational spring based on the concept of linear elastic fracture mechanics. Only the in-plane motion of planar structures is considered. The formulation is validated through some examples existing in the literature. Additionally, the mode shapes and natural frequencies of a frame with pitched roof are provided. The variation of natural frequencies with respect to the crack location is presented. It is concluded that considering the axial compliance, and axial-bending coupling due to the presence of a crack results in different dynamic characteristics, which should be considered for problems where high precision is required, such as for the crack identification problems.