Transverse vibrations analysis of a beam with degrading hysteretic behavior by using Euler-Bernoulli beam model

The paper is based on the analytical and experimental results from [14], [15] and reveals, by mathematical methods, the degradation of material stiffness 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 uniform slender cantilever beam as an oscillating system with degrading hysteretic behavior the following equation is considered partial derivative(2)y(x,t)/partial derivative t(2) + 2 zeta(t)omega(t) partial derivative y(x,t)/partial derivative t + l(4)omega(2)(t) partial derivative(4)y(x,t)/partial derivative x(4) = 0 subjected to the boundary conditions y(0,t) = y(0) sin omega(input)t, partial derivative y(0,t)/partial derivative x = 0, partial derivative(2)y(l,t)/partial derivative x(2) = 0, partial derivative(3)y(l,t)/partial derivative x(3) = 0. To approximate the solution of the this problem, we use the method of Newton interpolating series (see [6]) and the Taylor series method (see [8]).