Vibratory characteristics of axially-loaded Timoshenko beams with arbitrary number of cracks


Aydin K.

JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME, cilt.129, ss.341-354, 2007 (SCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 129 Konu: 3
  • Basım Tarihi: 2007
  • Doi Numarası: 10.1115/1.2731411
  • Dergi Adı: JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME
  • Sayfa Sayıları: ss.341-354

Özet

A simple and efficient analytical approach is presented to determine the vibrational frequencies and mode shape functions of axially-loaded Timoshenko beams with an arbitrary number of cracks. The local compliance induced by a crack is described by a massless rotational spring model. A set of boundary conditions are used as initial parameters to define the mode shape of the segment of the beam before the first crack. Using this, the remaining set of boundary conditions and recurrence formula developed in the study, the mode shape function of vibration of the beam containing multiple cracks can be easily determined. Four different classical boundary conditions (pinned-pinned, clamped-pinned, clamped-free, and clamped-clamped) are considered. Elastically-restrained support condition with concentrated masses is also considered. Three crack depths and five axial force levels representing the conditions under service loads are used. A parametric study is carried out for each case of support conditions to investigate the effect of crack and axial load on the vibrational properties of cracked Timoshenko beams. The influence of crack on the buckling load of the beam is also studied statically. Part of the results obtained is checked against the published values. The study concludes that the crack location, crack severity, and axial force level strongly affect the eigenfrequencies.

A simple and efficient analytical approach is presented to determine the vibrational

frequencies and mode shape functions of axially-loaded Timoshenko beams with an arbitrary

number of cracks. The local compliance induced by a crack is described by a

massless rotational spring model. A set of boundary conditions are used as initial parameters

to define the mode shape of the segment of the beam before the first crack.

Using this, the remaining set of boundary conditions and recurrence formula developed

in the study, the mode shape function of vibration of the beam containing multiple cracks

can be easily determined. Four different classical boundary conditions (pinned-pinned,

clamped-pinned, clamped-free, and clamped-clamped) are considered. Elasticallyrestrained

support condition with concentrated masses is also considered. Three crack

depths and five axial force levels representing the conditions under service loads are

used. A parametric study is carried out for each case of support conditions to investigate

the effect of crack and axial load on the vibrational properties of cracked Timoshenko

beams. The influence of crack on the buckling load of the beam is also studied statically.

Part of the results obtained is checked against the published values. The study concludes

that the crack location, crack severity, and axial force level strongly affect the

eigenfrequencies.