Modeling of the quasi-periodic galloping response type under combined harmonic and random excitation

Abstract The paper presents a mathematical Single-Degree-of-Freedom model of a cable with ice accretion vibrating in an air flow. It follows an experimental investigation of several aeroelastic models in a wind tunnel. The analysis of the experimental data is very complicated because a number of structural and stream characteristics mutually interact. Distinction between deterministic and random response components is only possible using a theoretical solution. The vibrational movement of the models used can be expressed by van der Pol-Duffing type equations. The aeroelastic excitation that is due to the air flow is modeled as an additive process consisting of a deterministic periodic part and random components. The paper investigates several particular configuration parameter settings for a non-white Gaussian random part of an excitation process and characterizes corresponding response properties. The Fokker-Planck equation is constructed for the random part of the response, and its semi-analytical solution in exponential form is expressed using a probability potential. Partial amplitudes of a harmonic approximation of the response are determined using the stochastic averaging strategy. The existence of a stationary probability distribution of the response is investigated, and its stochastic stability is assessed. Open problems and further research steps are outlined.