Search results for "Evolutionary excitation"
showing 2 items of 2 documents
Path Integral approach via Laplace’s method of integration for nonstationary response of nonlinear systems
2019
In this paper the nonstationary response of a class of nonlinear systems subject to broad-band stochastic excitations is examined. A version of the Path Integral (PI) approach is developed for determining the evolution of the response probability density function (PDF). Specifically, the PI approach, utilized for evaluating the response PDF in short time steps based on the Chapman–Kolmogorov equation, is here employed in conjunction with the Laplace’s method of integration. In this manner, an approximate analytical solution of the integral involved in this equation is obtained, thus circumventing the repetitive integrations generally required in the conventional numerical implementation of …
Response of nonlinear oscillators with fractional derivative elements under evolutionary stochastic excitations: A Path Integral approach based on La…
2023
In this paper, an approximate analytical technique is developed for determining the non-stationary response amplitude probability density function (PDF) of nonlinear/hysteretic oscillators endowed with fractional element and subjected to evolutionary excitations. This is achieved by a novel formulation of the Path Integral (PI) approach. Specifically, a stochastic averaging/linearization treatment of the original fractional order governing equation of motion yields a first-order stochastic differential equation (SDE) for the oscillator response amplitude. Associated with this first-order SDE is the Chapman–Kolmogorov (CK) equation governing the evolution in time of the non-stationary respon…