多场作用下轴向运动浸液板非线性振动的理论、数值与实验研究

An axially moving plate immersed in fluid is modeled. Nonlinear vibration of the plate is studied in electromagnetic field, temperature field, and force field, etc. Theoretical analysis, numerical simulation, and vibration test are focused on. Based on the nonlinear plate theory, the mathematical model for the in-plane and out-of-plane coupling vibration and the multi-field coupling vibration of the axially moving viscoelastic plate is established. The approximate analytical and numerical simulation methods are applied to solve the inherent characteristics of the linear derivative system. The correlation between axial force and axial acceleration is solved from the mechanism. The sensitive instability boundary of the weakly dissipative system with internal resonance is given. The approximate analytical methods are employed to analyze the steady-state responses and their stabilities of nonlinear vibration caused by the magnetic force, damping nonlinearity, and structural nonlinearity. The numerical methods are developed to identify the various dynamic behaviors. Vibration tests are designed to measure the nonlinear vibration. The experimental and numerical results confirm the approximate analytical results. The optimum parameters are found to maintain the stability of the system. The project can give theoretical basis, technical reserves, and guidance to reveal the coupling of the axially moving plate and multi-physics and mechanical design and development of steel, paper, textile, and new energy and other industries from the physical essence.

以轴向运动浸液板为模型，探索其在电磁场、温度场和力场等多场作用下的非线性振动，聚焦其理论分析、数值模拟和振动测试。基于非线性薄板理论，建立轴向运动黏弹性板在多场作用下面内和面外耦合振动以及多场耦合振动的数学模型；应用近似解析方法和数值方法分别分析线性派生系统的固有特性；从机理上解决轴向加速度与轴力之间的内在关联性；给出内共振时弱耗散系统的更加敏感的失稳边界；利用近似解析方法研究由磁场力、结构非线性和阻尼非线性等因素引起的系统非线性振动的稳态响应及其稳定性；发展数值方法识别系统的各类动力学行为。设计振动实验，测量多场作用下板的非线性振动情况。实验与数值结果和理论分析结果相互印证，寻求多场中系统保持稳定的最佳参数。该项研究的开展，将为进一步从物理本质上揭示轴向运动板和多场耦合作用的振动规律，为钢铁、造纸、纺织以及新能源等行业的机械设计和研制提供多场耦合动力学的理论依据和技术储备并具有指导意义。

以轴向运动浸液板为模型，探索了其在电磁场、温度场和力场等多场作用下的非线性振动，聚焦其理论分析、数值模拟和振动测试。基于非线性薄板理论，建立了轴向运动黏弹性板在多场作用下面内和面外耦合振动以及多场耦合振动的数学模型；应用近似解析方法和数值方法分别分析线性派生系统的固有特性；从机理上解决了轴向加速度与轴力之间的内在关联性；给出了内共振时弱耗散系统的更加敏感的失稳边界；利用近似解析方法研究了由磁场力、结构非线性和阻尼非线性等因素引起的系统非线性振动的稳态响应及其稳定性；发展数值方法识别了系统的各类动力学行为。设计振动实验，测量了多场作用下板的非线性振动情况。实验与数值结果和理论分析结果相互印证，寻求了多场中系统保持稳定的最佳参数。该项研究的开展，将为进一步从物理本质上揭示轴向运动板和多场耦合作用的振动规律，为钢铁、造纸、纺织以及新能源等行业的机械设计和研制提供多场耦合动力学的理论依据和技术储备并具有指导意义。

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