  Nonlinear random vibration under excitations of both Gaussian and Poisson
white noises is considered. The model is based on stochastic differential
equations, and the corresponding stochastic integrals are defined in such a way
that the energy conservation law is satisfied. It is shown that Stratonovich
integral and Di Paola-Falsone integral should be used for excitations of
Gaussian and Poisson white noises, respectively, in order for the model to
satisfy the underlining physical laws (e.g., energy conservation). Numerical
examples are presented to illustrate the theoretical results.
