干摩擦结构声辐射系统动力学响应的半解析解研究

项目拟研究干摩擦结构声辐射系统非线性动力学响应的求解方法。针对制动质量与结构组成的典型非光滑系统，考虑结构相对运动产生的非线性力，将声压视为作用于结构表面的未知外力，采用变分法建立由常微分与偏微分描述的含振速和声压的动力学方程。根据边界条件和Rayleigh法，将结构表面振速和声压展开为振型的函数，然后由声场积分公式和相容性条件，获得声压与振速的变分关系。针对非光滑干摩擦激励下的动力学问题，取结构的n阶截断模态，将质点振动、模态坐标和摩擦力展开为谐波函数的叠加，并将其代入耦合方程，利用曲线拟合法和增量谐波平衡法，导出系统动力学响应的半解析解。以制动系统为案例，分别考虑Stribeck模型和滞后模型的非光滑摩擦力，研究制动盘形状、边界条件等对动力学响应的影响；并由实验结果验证半解析解的有效性，获得非光滑系统声辐射特性的求解方法。项目在结构非线性振动与噪声控制方面具有重要的理论与应用价值。

The project will investigate the approach to solve the nonlinear dynamic response of the dry friction structure-acoustic radiation system. For the classical non-smooth system consisted by the braking mass and the structure, takes the nonlinear force due to the structures’ relative motion into account. Considering the surface pressure as an unknown external force on the structure, the dynamic equations including vibration velocity and acoustic pressure described by the ordinary differential and the partial differential equation are established based on variational formulation. According to the boundary condition and the Rayleigh method, the surface vibration velocity and the acoustic pressure are expressed by the mode shape function. Then the integral expression for sound field and the boundary conditions are employed to derive the variational relationship of the acoustic pressure and the vibration velocity. For the dynamic problem under the non-smooth dry friction excitation, selecting the structure’s n order truncation modal, expressing the particle vibration, the modal coordinates and friction force as harmonic components form, then the semi-analytical solution of the dry friction structure is derived by the incremental harmonic balance method and the curve fitting iteration method. Taking the braking system as example, considering the Stribeck friction model and the hysteresis friction model, the effects of the shape and boundary conditions of the brake disc to the vibration and the acoustic radiation characteristics of the system are investigated. The experiment about the vibration and noise of the braking system validates the semi-analytical method. The project will develop the solution to the acoustic radiation characteristics of the nonlinear system, and give the measures to control the vibration and noise which is significant in both theory and practice.