板壳的磁弹性与流体弹性问题的混沌运动分析
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摘要
耦合力学问题是研究两个或多个物理场相互作用的力学问题,其中包括磁弹性力学、流固耦合力学、热弹性力学问题等。磁弹性指电磁场同变形场的耦合,即研究弹性固体中,电磁场和变形场相互作用的理论。流固耦合力学是固体力学和流体力学交叉形成的一个力学分支,主要研究变形固体和流体两种介质之间的交互作用,即在流体载荷作用下固体产生的变形和动力学响应,而变形和动力学响应反过来影响流场从而改变流体载荷的分布和大小。
混沌是非线性系统特有的一种运动形式,是产生于确定性系统的敏感依赖于初始条件的往复性稳态非周期运动,具有长期不可预测性,也是近年新兴的一门学科。
板壳是工程结构中常见的元件,通常它们都是在机械场、电磁场、流场等多场作用环境下工作的,其动力特性对系统的结构安全有重要影响。因此,对板壳多场耦合作用动力学问题开展研究具有重要的理论意义与实用价值。
本文在板壳力学与磁弹性力学理论及流体弹性力学的基础上,建立了板壳耦合非线性系统动力学模型,采用数值方法对运动方程求解,研究了磁弹性、流固耦合等多场共同作用下的板壳分岔与混沌问题。主要包括以下内容:
研究了不同边界条件下,圆薄板在横向稳恒磁场、环向电流和机械载荷共同作用下的混沌问题以及在混沌运动中其弹性变形及应力状态。通过变化机械参数及电磁参数,讨论了磁场与电流对系统运动状态及应力状态的的影响,结果表明,机电参数的改变,可以对圆板的运动状态实施控制。
研究了机械场与电磁场耦合作用下两端简支弹性圆柱壳的混沌运动问题。通过变化电磁参量使系统运动状态改变,分析了电磁参量对系统运动的影响。
研究了机械场与电磁场耦合作用下旋转圆盘的混沌问题。通过非线性电磁弹性耦合运动基本方程及电磁力方程,得到了旋转圆盘的在径向稳恒磁场、环向电流和载荷共同作用下的振动方程,由分岔图与Lyapunov指数图来判定系统是否进入混沌状态,讨论了转速与电磁参数对系统运动状态的影响。
研究了充满可压缩气体的气压缸的弹性缸底的混沌问题。在建立流体弹性力学运动方程和弹性力学运动方程的基础上,应用解决流固耦合问题中的单一拉格朗日法,对在活塞按简谐规律运动的情况下,进行了混沌分析。讨论了相关参数的变化对弹性缸底的变形及应力状态的影响,结果表明,在特定的参数变化过程中,系统的通向混沌的道路是有由准周期环面破坏引起的。
以动脉血管为模型,根据流体弹性力学中的连续性方程及运动方程和板壳的弹性理论建立流固耦合方程,利用数值方法求解,通过变化血液的动力粘度、动脉血管壁的泊松比及血液内压力,分析了血管壁的混沌运动。
以内部充气的双层圆筒为模型,根据流体弹性力学中的基本方程和板壳的弹性理论建立流固耦合方程,利用数值方法求解。分析了内层圆筒为振源做简谐振动时,外层圆筒的混沌运动。
课题研究属于耦合非线性动力学的前沿,对国防、医疗、材料等领域有着理论研究价值和学术意义,工程应用前景广阔。
Coupled mechanical problems is to study the interaction of two or more physical fields of mechanical problems. The problems contain the magneto-elastic problem, fluid-solid interaction problem, thermal-elastic problem and so on. The magneto-elastic coupling means the electromagnetic field with the deformation field problem. Fluid-solid coupling of solid mechanics and fluid mechanics is the formation of a mechanical branch of cross.
Chaos is a nonlinear system-specific form of a movement is generated in the deterministic system, sensitive dependence on initial conditions of the steady-state non-periodic movement back and forth, with long-term unpredictability is a new discipline in recent years.
Thin plate and shell is one kind of common project components, and they are usually installated in coupled fields, such as the mechanical field, electromagnetic field and temperature field and so on, the dynamic properties of the system have a significant impact on the structural safety. Therefore, study of many fields coupled dynamics of magneto-elastic thin plate is of great theoretical and practical significance.
In this paper, the nonlinear elastic bifurcation and chaos of the thin plates and shell which in the electromagnetic fields, mechanical force and fluid field are studied. Based on the theory of shell and plate mechanics, magnetoelastic mechanics and fluid elastic mechanics , the nonlinear system dynamics coupled model is founded. The main work can be outlined as follow:
The problem of bifurcation and chaos under the different boundary condition thin circular plate under the electromagnetic fields and mechanic fields is studied. Base on nonlinear electro-magneto-elastic equations of the thin circular plate and the expression of electromagnetic forces, the vibration equations of thin circular plate under uniform transverse magnetic field, round current and mechanical loadings are obtained and then solved numerically using the forth order Runge-Kutta method. By some examples, the wave diagram of displacement, phase diagram and Poincare map are derived. The influences of magnetic field and electrical on vibration properties of the system state are analyzed.
The chaotic motion problem of a thin cylindrical shell with two sides simply supported under the coupled action of mechanical field and electromagnetic field is studied. The results showed that changes of the magnetic intensity as well as the magnitude and direction of the circumferential current will realize the conversion between chaotic motion and periodic motion of the thin cylindrical shell with two sides simply supported under the action of mechanical loads.
The problem of chaos in rotating disk in electromagnetic and mechanical fields is studied. Based on the expression of electromagnetic forces and nonlinear electro-magneto-elastic equations for a rotating disk, vibration equations under the mechanical loading in a steady radial magnetic field together with a circulating electric current are derived. Under certain conditions, the influences of the electromagnetic field and the speed on system vibration properties are analyzed.
On the basic motion equations of fluid mechanics and elastic mechanics, the single Lagrangian method is used to form the fluid-solid interaction problem. In the model of cylinder filled with compressible gas and the piston vibration is the harmonic vibration, the problem of chaos in elastic cylinder is studied.
On the basic motion equations of fluid mechanics and elastic mechanics, the chaotic motion of the artery are analyzed by changing the momentum of blood viscosity, arterial blood pressure and Poisson ratio.
On the basic motion equations of fluid mechanics and elastic mechanics, the chaotic motion of the double-shell cylinder are analyzed.
Research projects are coupled nonlinear dynamics in the forefront. This research has a theoretical value and the scholarly significance of the national defense, medical and material.
混沌是非线性系统特有的一种运动形式,是产生于确定性系统的敏感依赖于初始条件的往复性稳态非周期运动,具有长期不可预测性,也是近年新兴的一门学科。
板壳是工程结构中常见的元件,通常它们都是在机械场、电磁场、流场等多场作用环境下工作的,其动力特性对系统的结构安全有重要影响。因此,对板壳多场耦合作用动力学问题开展研究具有重要的理论意义与实用价值。
本文在板壳力学与磁弹性力学理论及流体弹性力学的基础上,建立了板壳耦合非线性系统动力学模型,采用数值方法对运动方程求解,研究了磁弹性、流固耦合等多场共同作用下的板壳分岔与混沌问题。主要包括以下内容:
研究了不同边界条件下,圆薄板在横向稳恒磁场、环向电流和机械载荷共同作用下的混沌问题以及在混沌运动中其弹性变形及应力状态。通过变化机械参数及电磁参数,讨论了磁场与电流对系统运动状态及应力状态的的影响,结果表明,机电参数的改变,可以对圆板的运动状态实施控制。
研究了机械场与电磁场耦合作用下两端简支弹性圆柱壳的混沌运动问题。通过变化电磁参量使系统运动状态改变,分析了电磁参量对系统运动的影响。
研究了机械场与电磁场耦合作用下旋转圆盘的混沌问题。通过非线性电磁弹性耦合运动基本方程及电磁力方程,得到了旋转圆盘的在径向稳恒磁场、环向电流和载荷共同作用下的振动方程,由分岔图与Lyapunov指数图来判定系统是否进入混沌状态,讨论了转速与电磁参数对系统运动状态的影响。
研究了充满可压缩气体的气压缸的弹性缸底的混沌问题。在建立流体弹性力学运动方程和弹性力学运动方程的基础上,应用解决流固耦合问题中的单一拉格朗日法,对在活塞按简谐规律运动的情况下,进行了混沌分析。讨论了相关参数的变化对弹性缸底的变形及应力状态的影响,结果表明,在特定的参数变化过程中,系统的通向混沌的道路是有由准周期环面破坏引起的。
以动脉血管为模型,根据流体弹性力学中的连续性方程及运动方程和板壳的弹性理论建立流固耦合方程,利用数值方法求解,通过变化血液的动力粘度、动脉血管壁的泊松比及血液内压力,分析了血管壁的混沌运动。
以内部充气的双层圆筒为模型,根据流体弹性力学中的基本方程和板壳的弹性理论建立流固耦合方程,利用数值方法求解。分析了内层圆筒为振源做简谐振动时,外层圆筒的混沌运动。
课题研究属于耦合非线性动力学的前沿,对国防、医疗、材料等领域有着理论研究价值和学术意义,工程应用前景广阔。
Coupled mechanical problems is to study the interaction of two or more physical fields of mechanical problems. The problems contain the magneto-elastic problem, fluid-solid interaction problem, thermal-elastic problem and so on. The magneto-elastic coupling means the electromagnetic field with the deformation field problem. Fluid-solid coupling of solid mechanics and fluid mechanics is the formation of a mechanical branch of cross.
Chaos is a nonlinear system-specific form of a movement is generated in the deterministic system, sensitive dependence on initial conditions of the steady-state non-periodic movement back and forth, with long-term unpredictability is a new discipline in recent years.
Thin plate and shell is one kind of common project components, and they are usually installated in coupled fields, such as the mechanical field, electromagnetic field and temperature field and so on, the dynamic properties of the system have a significant impact on the structural safety. Therefore, study of many fields coupled dynamics of magneto-elastic thin plate is of great theoretical and practical significance.
In this paper, the nonlinear elastic bifurcation and chaos of the thin plates and shell which in the electromagnetic fields, mechanical force and fluid field are studied. Based on the theory of shell and plate mechanics, magnetoelastic mechanics and fluid elastic mechanics , the nonlinear system dynamics coupled model is founded. The main work can be outlined as follow:
The problem of bifurcation and chaos under the different boundary condition thin circular plate under the electromagnetic fields and mechanic fields is studied. Base on nonlinear electro-magneto-elastic equations of the thin circular plate and the expression of electromagnetic forces, the vibration equations of thin circular plate under uniform transverse magnetic field, round current and mechanical loadings are obtained and then solved numerically using the forth order Runge-Kutta method. By some examples, the wave diagram of displacement, phase diagram and Poincare map are derived. The influences of magnetic field and electrical on vibration properties of the system state are analyzed.
The chaotic motion problem of a thin cylindrical shell with two sides simply supported under the coupled action of mechanical field and electromagnetic field is studied. The results showed that changes of the magnetic intensity as well as the magnitude and direction of the circumferential current will realize the conversion between chaotic motion and periodic motion of the thin cylindrical shell with two sides simply supported under the action of mechanical loads.
The problem of chaos in rotating disk in electromagnetic and mechanical fields is studied. Based on the expression of electromagnetic forces and nonlinear electro-magneto-elastic equations for a rotating disk, vibration equations under the mechanical loading in a steady radial magnetic field together with a circulating electric current are derived. Under certain conditions, the influences of the electromagnetic field and the speed on system vibration properties are analyzed.
On the basic motion equations of fluid mechanics and elastic mechanics, the single Lagrangian method is used to form the fluid-solid interaction problem. In the model of cylinder filled with compressible gas and the piston vibration is the harmonic vibration, the problem of chaos in elastic cylinder is studied.
On the basic motion equations of fluid mechanics and elastic mechanics, the chaotic motion of the artery are analyzed by changing the momentum of blood viscosity, arterial blood pressure and Poisson ratio.
On the basic motion equations of fluid mechanics and elastic mechanics, the chaotic motion of the double-shell cylinder are analyzed.
Research projects are coupled nonlinear dynamics in the forefront. This research has a theoretical value and the scholarly significance of the national defense, medical and material.
引文
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