The (nonlinear) response behavior of a piecewise-linear system is investigated under both deterministic and stochastic excitations in this study. A semi-analytical procedure is developed to predict the system behavior by evaluating the joint probability density functions of the Fokker-Planck equations of the stochastic piecewise-linear system under random excitations via a path-integral solution procedure. From an analysis of the deterministic system, nonlinear system behavior is derived for further analysis of the corresponding stochastic system. The influence of variations in other parameters on the response behavior are also examined. In the stochastic system analysis, which represents a more realistic approach to understanding the system behavior, a Markov process approach is used. By introducing random perturbations in the harmonic excitation, the stochastic responses are examined and compared to those of the corresponding deterministic system. Stability of the various responses including regular and chaotic motions, is investigated by varying the noise intensity. Routes to chaos in period-doubling processes with and without external random perturbations are studied and compared. Stationarity and ergodicity of the chaotic responses of the system are examined via time domain and probability domain simulations. Potential coexisting responses of the piecewise-linear system are examined via the path-integral solutions. It is found that the path-integral solutions can provide global information of the system behavior in the probability domain, and can also verify the potential coexisting responses and discern the relative strength of the coexisting response attractors. / Graduation date: 1996