The non-linear dynamic response of the Euler–Bernoulli beam with an arbitrary number of switching cracks

Non-linear dynamic response to simple harmonic excitation of a thin-walled beam with a breathing crack

“…Although this way of considering damping is very simple and usually employed [9,10], it is in fact a rough approximation. First of all, an important matter is missed: the presence of fatigue cracks cause an increase of damping.…”

“…3 frequencies are considered to contribute significantly to the dynamic response and ζ is assumed to be 0.02, as in reference [9]. The free end of the beam is loaded with a shear sinusoidal force given by Q y (L) = 5000 N sin(ϖ t) and f = ϖ/(2π) is defined in order to express the driving frequency in Hz.…”

“…And at the same time it is simple enough for extensive computational treatment, an essentially useful feature when damage diagnosis must be performed in real time. Most studies have focused on Bernoulli-Euler beams [5][6][7][8][9] and, to a lesser extent, on Timoshenko beams [10][11][12][13].…”

Physically-based Dirac’s delta functions in the static analysis of multi-cracked Euler–Bernoulli and Timoshenko beams

“…It basically consists of singularities in the flexural stiffness represented by Dirac's delta functions, which in turn are equivalent to internal hinges with rotational linear-elastic springs. For uniform slender beams under static transverse load, this approach enables one to compute the exact deflection in closed form, and has been also used for a range of further structural problems, including theoretical buckling and modal analyses of multi-cracked Euler-Bernoulli members Calió, 2008, 2009), and experimental static (Buda and Caddemi, 2007) and dynamic (Caddemi et al, 2010) investigations.…”

Identification of two cracks in a rod by minimal resonant and antiresonant frequency data

“…Indeed, in addition to the high number of applications, cracked beams have the advantage of being described by consolidated mechanical models and being relatively manageable from the mathematical point of view, at least in the case of cracks that remain open during the vibration of the system. Of course, there are contexts in which it is necessary to take into account the phenomena of opening/closing of cracks, and more sophisticated nonlinear models of crack must be implemented, see, among other contributions, [6] and [7] for an analysis of the direct problem in beams and rotors, respectively, and [8] for the identification of breathing cracks in a vibrating beam. Without claiming of completeness, the reader may refer to [9][10][11][12][13] for an overview of some recent contributions on damage detection based on frequency data.…”