Blake Martin and Armaghan Salehian
Vibration Analysis, Natural Frequencies, Homogenization, Cable-Harnessed Structure
A homogenization method for deriving an analytical con- tinuum model is presented for determining the vibration frequencies of cable-harnessed beam structures with peri- odic wrapping patterns. The cable is assumed to exhibit a beam-like behaviour and the potential and kinetic ener- gies of the structure can be formulated. The partial dif- ferential equation for the transverse displacement of the structure is obtained by applying Hamilton’s principle and the method of separation of variables is used to calculate the frequencies of vibration. Numerical results are pre- sented for varying system parameters. The introduction of the cable causes a stiffening effect on the system which in turn causes an upward shift in the natural frequencies when compared to an Euler-Bernoulli beam model that only takes into account the additional mass of the cable.
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