Dynamic instability of channel-section beams under periodic loading

Abstract

This paper presents an analytical investigation on the free vibration, static buckling and dynamic instability of channel-section beams when subjected to periodic loading. The analysis is carried out by using Bolotin's method. By assuming the instability modes, the kinetic energy and strain energy of the beam and the loss of the potential of the applied load are evaluated, from which the mass, stiffness and geometric stiffness matrices of the system are derived. These matrices are then used to carry out the analyses of free vibration, static buckling and dynamic instability of the beams. Theoretical formulae are derived for the free vibration frequency, critical buckling moment, and excitation frequency of the beam. The effects of the lateral restraint applied to the flange, the section size of the beam and the static part of the applied load on the variation of dynamic instability zones are also discussed.

Dynamic stability of CNTs-reinforced non-uniform composite beams under axial excitation loading

“…where a1k, a2k, b1k, and b2k (k=1,2,3,…) are the coefficients of the solution. It is known that [39][40][41][42][43], for a given amplitude of the load the dynamic instability regions of the dynamic system described by Eqs. ( 24) and ( 25) can be determined by examining the periodic solutions with the periods of T=2 and 2T=4.…”

“…By assuming the instability modes, the kinetic energy and strain energy of the composite beams and the loss of the potential of the axially compressive load are evaluated, from which the generalized equation of motion of the CNTs-reinforced FG composite beams is derived. The analysis of the dynamic instability of the composite beams is performed by using Bolotin method [39,40,41,42,43]. Numerical examples are provided for illustrating the dynamic instability behavior of the CNTs-reinforced FG composite beams when subjected to axial excitation loading.…”

Dynamic instability of castellated beams subjected to transverse periodic loading

“…The influence of different supporting boundary conditions on the dynamic instability behaviour of beams has been also studied by Uang and Fan (2001); Yoon and Kim (2002). More recently, Zhu et al (2018) presented a study on the dynamic buckling of cold-formed steel channel section beams under the action of uniformly distributed loading. Gao et al (2019) provided a nondeterministic dynamic stability assessment of Euler-Bernoulli beams using Chebyshev surrogate model.…”