Cakmak, A. S.

Köylüoglu, H. U.

Micaletti, R. C.

Nielsen, Søren R. K.

English

Differential equations are derived which exactly govern the evolution of the second-order response moments of a single-degree-of-freedom (SDOF) bilinear hysteretic oscillator subject to stationary Gaussian white noise excitation. Then, considering cases for which response stationarity will be achieved, i.e., excluding the case of an elastic-perfectly-plastic oscillator, algebraic equations for the response moments are found. By the nature of the problem, these moments depend on the probability of the oscillator being in the plastic state. Upon considering oscillators with low yield levels and using analytically-available information, physical reasoning, and approximations supported by empirical observation, an equation for the probability of the oscillator being in the plastic state is derived. Upon numerical solution of this equation, analytical approximations to the response moments can be obtained. All analytical, approximate, and numerical results are verified by extensive Monte Carlo simulations

Approximate Analytical Solution for the 2nd Order Moments of a SDOF Hysteretic Oscillator with Low Yield Levels Excited by Stationary Gaussian White Noise

https://vbn.aau.dk/ws/files/198378314/Approximate_Analytical_Solution_for_the_2nd_Order_Moments_of_a_SDOF_Bilinear_Hysteretic_Oscillator_with_Low_Yield_Levels_Excited_by_Stationary_Gaussian_White_Noise.pdf

Approximate Analytical Solution for the 2nd Order Moments of a SDOF Hysteretic Oscillator with Low Yield Levels Excited by Stationary Gaussian White Noise

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