The paper is based on the analytical and experimental results from ,  and reveals, by mathematical methods, the degradation of ma- terial stifiness due to the decrease of the first natural frequency, when the driving frequency is slightly lower than the first natural frequency of the undegradated structure. By considering the vibration of the uni- form slender cantilever beam as an oscillating system with degrading hysteretic behavior the following equation is considered subjected to the boundary conditions To approximate the solution of the this problem, we use the method of Newton interpolating series (see ) and the Taylor series method (see ).
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