非光滑特性在实际机械和结构系统中广泛存在，如隔振器和能量收集装置，其强非线性特征可能会导致多稳态共存、混沌鞍和分形边界等复杂的动力学行为，来自初始条件、系统参数以及噪声的微小扰动都对系统的最终响应形式起着决定性的作用。为了从根源避免响应发生不受预期的改变，有必要从全局动力学的角度深入探究非光滑系统的复杂特性及其内在机理。本文针对在此过程中面临的计算和存储瓶颈，提出了基于状态子空间并行化的高效全局动力学分析方法，并将其应用于一类具有时变间隙的非光滑系统中，从确定和随机两个方面揭示了在非光滑和随机因素综合作用下所引发的全局分岔、响应跃迁以及稳定性改变等复杂动力学行为。论文主要工作如下：

首先，为了解决在全局分析时所面临的效率和存储难题，结合广义胞映射方法和基于图形处理器(GPU)的并行算法，提出一种基于状态子空间并行化的高效全局动力学分析方法。通过将原始较大的状态空间划分为具有可承受存储需求的较小子域，采用并行加速技术对各子域的动力学信息进行计算，最终构造虚拟不变集对系统的整体动力学信息进行恢复。同时利用不变集结点的特性对有向图规模进行缩减，解决不变集搜索过程只能串行计算的瓶颈，使对具有高维、高分辨率、复杂系统全局结构的揭示成为可能。

其次，采用基于状态子空间并行化的高效全局动力学分析方法，定性地揭示了一个因基础运动而具有随时间变化接触间隙系统的稳定和不稳定响应、吸引域和边界等全局动力学结构，并对系统随初始间隙变化的全局分岔行为进行研究。发现该系统中共存了多个常规和稀疏吸引子，初始间隙的变化对系统共存吸引子吸引域的面积、边界的复杂度以及吸引子的动力学完整性均会产生影响。

最后，建立了在Gauss白噪声激励下时变间隙非光滑系统的随机动力学模型，研究了噪声干扰可能会诱发的随机分岔现象，以及噪声强度变化对响应瞬态概率密度(PDF)演化行为以及随机吸引域的影响，发现噪声会诱导稳态响应沿不稳定流形快速演化至共存的其他吸引子上，并迫使系统的全局结构发生膨胀从而加速边界激变的产生，系统随机吸引域的动力学完整性被增强或削弱，进而导致系统发生不可逆的失稳现象。

Non-smooth characteristics are widely encountered in practical mechanical and structural systems, such as vibration isolators and energy harvesting devices. The strong nonlinear characteristics make these non-smooth systems with intricate dynamical structures, including coexisting multi-stable responses, chaotic saddles, and fractal boundaries. Any small disturbance from initial conditions, system parameters, and noise plays a decisive influence on the ultimate response. Therefore, to avoid unexpected changes in response, it is necessary to explore the complex characteristics and internal structure of non-smooth systems from the perspective of global dynamics. Aiming at the computational and storage bottlenecks in revealing the global structure of complex or high-dimensional systems, this thesis proposes an efficient global dynamics analysis method based on state subspace parallelization and applies it to a class of non-smooth systems with time-varying clearances. The complex dynamic behaviors such as global bifurcation, response transition, and stability change caused by the combination of non-smooth and random factors are revealed from both deterministic and stochastic aspects. The main works of this thesis are listed as follows:

Firstly, to solve the huge storage consumption in the numerical calculation, an efficient global dynamics analysis method based on state subspace parallelization is proposed by combining the Generalized Cell Mapping (GCM) and the parallel algorithm based on a graphics processing unit (GPU). This method partitions the predefined chosen large state space into smaller subdomains with affordable memory requirements under the expected cell resolution and uses parallel acceleration technology to calculate the dynamic information of each sub-domain. Subsequently, construct virtual invariant sets to recover the overall dynamical information. At the same time, the scale of the directed graph is reduced by using the characteristics of the invariant nodes, which address the shortcoming of serial computation in invariant set search processes, and makes it possible to reveal the global structure of high-dimensional, high-resolution, and complex systems.

Secondly, the global dynamics analysis method based on state subspace parallelization is used to qualitatively reveal the global dynamic structures such as stable and unstable response, the basin of attractions and boundary of a non-smooth system with time-varying contact clearances due to basic motion, and the global bifurcation behavior of the system with initial clearance is investigated. It is found that multiple regular and rare attractors coexist in the system. The change of the initial clearance will affect the area of the basin of attractions, the complexity of the boundary, and the dynamical integrity of the attractors.

Finally, a stochastic dynamical model for the time-varying clearance non-smooth system under Gaussian white noise excitation is established. The stochastic bifurcation phenomenon that may be induced by noise interference and the influence of noise intensity change on the evolution behavior of response transient probability density (PDF) and the stochastic basin of attractions are studied. Results indicate that noise drives steady-state responses to rapidly evolve along unstable manifolds towards other coexisting attractors, compelling the global structure to expand, accelerating boundary sudden changes, and strengthening or weakening the dynamical integrity of stochastic basin of attractions, ultimately causing the instability of the system through an irreversible process.