The vector field of a continuously piecewise-linear oscillator under periodic excitation is by nature nonsmooth. However, the nonsmoothness in studying the oscillator dynamics has drawn little attention. The paper presents the nonsmoothness effect on the differentiability of the Poincar

The paper presents a systematic method of stability analysis for high-dimensional dynamic systems involving a time delay and some unknown parameters. Here, the term "unknown" means that the parameters are constants but yet to be determined. The analysis focuses on the stability switches of those systems with increase of the time delay from zero to infinity. On the basis of the generalized Sturm criterion, the parameter space of concern is divided into several regions determined by a discrimination sequence and the Routh-Hurwitz conditions. It is found, as the time delay increases, that the system may undergo no stability switch, exactly one stability switch, or more than one stability switches when the parameters are chosen from different regions. To demonstrate the approach, a detailed analysis of the stability switches is made in the paper for an active vehicle suspension equipped with a delayed "sky-hook" damper and a four-wheel steering vehicle with time delay in driver's response, respectively.

On the basis of generalized Sturm theory, this paper presents a simple, but systematic approach to the delay-independent stability analysis of the linear dynamic systems involving multiple degrees of freedom and possibly two time delays. The approach enables one to complete the stability analysis in a much simpler way than before through the use of a MAPLE routine given in the paper. To demonstrate the approach, the paper gives a detailed analysis, the corresponding sufficient and necessary conditions as well as stable regions in parameter space of concern for the delay-independent stability of a vibrating system with time delays in state feedback, an active-tendon for a tall structure and an active suspension of a quarter car model.

The non-linear behavior of ice-induced vibration of an offshore platform with four legs is investigated in this paper. The equations of motion of the system are derived by using the Hamiltonian Principle The force of moving ice based on the self-excitation and locking is used to model the phenomenon of contact between the ice and the platform. By using the approach of multiple scales, the primary resonance of the ice-induced vibration of the platform is analyzed. The numerical results show that there exist several kinds of combination resonances, including self-excited vibration and locking vibration. These results coincide with those observed from an offshore platform in the North China Sea, and hence enable one to gain insight into the ice-induced vibration of offshore platforms.

The paper presents a method of assessing the stability of high dimensional vibrating systems under state feedback control with a short time delay. It is first proved that if the time delay is sufficiently short, an n-degree-of-freedom system with feedback delay maintains 2n eigenvalues near those of the corresponding system without feedback delay. A perturbation approach is then proposed to determine the first order variation of an arbitrary eigenvalue and corresponding eigenvector of the system with feedback delay by solving a set of linear algebraic equations only. The computation in this approach can be simplified to a matrix multiplication provided that the product of the time delay and the modulus of the eigenvalue is much less than 1. Furthermore, the approach is directly related to the Newton-Raphson iteration in the continuation of eigenvalues for long time delay. The efficacy of the approach is demonstrated via a number of case studies on two feedback delay systems of two degrees of freedom and ten degrees of freedom respectively.