多柔体系统动力学拟变分原理及其应用
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摘要
多柔体系统动力学的发展,与航天技术的发展是密切相关的。从多体角度看,多柔体系统动力学是多刚体系统动力学的延伸,从动力学角度讲,刚体是柔性体的特殊情况。多柔体系统动力学考虑多体运动与柔性效应之间的交耦作用。最常见的多柔体系统为多柔体簇系统和多柔体链系统。本文研究多柔体簇系统。
多柔体系统动力学的拟变分原理的研究涵盖了许多学科,需要一般力学、固体力学等多个学科。
首先,研究了分析动力学含阻尼非保守系统的拟变分原理。从基本方程出发,应用变积方法推导了分析动力学含阻尼非保守系统的拟Hamilton原理,并给出了其它表达形式；建立了两类变量的广义拟势能原理和广义拟余能原理；建立了三类变量的广义拟势能原理和广义拟余能原理。建立了反映本构关系、几何条件和动态平衡方程的广义拟变分原理。应用分析动力学含阻尼非保守系统的拟Hamilton原理,研究二自由度系统的振动方程,并且得到随阻尼衰减解以及稳态解。
其二,研究了弹性动力学拟变分原理和广义拟变分原理。建立非保守系统弹性动力学拟Hamilton原理、拟余Hamilton原理、第一、第二类两类变量广义拟变分原理和三类变量广义拟变分原理。
其三,研究了单柔体动力学的拟变分原理。将变分方法推广应用到单柔体动力学问题中,推导了单柔体动力学的拟Hamilton原理,建立了两类变量的拟Hamilton原理。提出了单柔体动力学问题的拟驻值条件的概念,通过推导拟变分原理的拟驻值条件对拟变分原理进行了检验。以拦截器为例,说明了单柔体动力学两类变量的拟Hamilton原理的拟驻值条件和先决条件的物理意义；应用拟Hamilton原理的拟驻值条件建立了火箭垂直发射时的纵向振动方程,并且说明在单柔体动力学中“一力二用”的特性。
其四,研究了多柔体系统动力学的拟变分原理。将变分方法推广应用到多柔体系统动力学问题中。考虑附件三种运动情况：可伸展平动、转动、既可伸展平动又转动。推导了附件三种运动情况时的多柔体系统动力学的拟Hamilton原理,建立了两类变量的拟Hamilton原理。提出了多柔体系统动力学问题的拟驻值条件的概念,通过推导拟变分原理的拟驻值条件对拟变分原理进行了检验。应用可伸展平动附件多柔体系统动力学拟Hamilton原理的拟驻值条件,建立空间飞行器可伸展平动柔性梁横向振动微分方程,得到横向振动圆频率；应用转动附件多柔体系统动力学拟Hamilton原理的拟驻值条件,建立空间飞行器转动柔性梁横向振动微分方程,得到横向振动圆频率。
The development of flexible multi-body system dynamics is closely related to the development of space technology. From the multi-body point of view, flexible multi-body system dynamics is an extension of multiple rigid body system dynamics and from the perspective of dynamics, rigid body is flexible in the special circumstances. Flexible multi-body system dynamics considers more cross-link roles between the multi-body movement and flexible effects. The most common flexible multi-body system is flexible multi-body cluster system and flexible multi-body linked system. In this paper, the flexible multi-body cluster system is researched.
Quasi-variational principles of flexible multi-body system dynamics covers a lot of subjects, general mechanics, solid mechanics, and other disciplines are needed.
Firstly, analysis dynamics which contains the quasi-variational principle of damping non-conservative system is studied. From the basic equation, variational integral method is applied to deduce the analysis dynamics which contains the quasi-Hamilton of damping non-conservative system and the other forms of expression are given. Generalized quasi-potential energy principle and generalized quasi-complementary energy principle which include two kinds of variables are established. Generalized quasi-potential energy principle and generalized quasi-complementary energy principle which include three kinds of variables are established. Generalized quasi-variational principle which reflects constitutive relations, geometric conditions and dynamic balance equation are also built up. Analysis dynamics which contains the quasi-Hamilton principle of damping non-conservative system is applied to research the two degree of freedom on the vibration equation. Meanwhile, the author also gets the decayed solution with the damper and the steady-state solution.
Secondly, quasi-variational principle and generalized quasi-variational principle in elasto-dynamics is studied. Quasi-Hamilton, quasi-complementary Hamilton principle, the first and second types generalized quasi-variational principles with two kinds of variables, and generalized quasi-variational principle with three kinds of variables in non-conservative elasto-dynamics system are established.
Thirdly, quasi-variational principle of single flexible body dynamics is studied. Variational methods are applied to deduce the problems of single flexible body dynamics. At the same time, quasi-Hamilton principle of single flexible body dynamics, the quasi-Hamilton principle which include two kinds of variables are established. The concept of quasi-stationary value condition of single flexible body dynamics is proposed. Through the deduction of the quasi-stationary value condition of quasi-variational principles, quasi-variational principles have been tested. Taking the interceptor as an example, the author has explained the physical meaning of the quasi-stationary value condition and prerequisite in the quasi-Hamilton principles of single flexible body dynamics with two kinds of variables. The quasi-stationary value condition of quasi-Hamilton principles are applied to establish the vertical vibration equation when the rockets launch vertically and the author also has illustrated the features of "one force for two effects" in a single flexible body dynamics.
Forthly, quasi-variational principle of flexible multi-body system dynamics is also studied. Variational methods are applied to deduce the problems of flexible multi-body system dynamics. Three kinks of movement in annex are considered: extendable translation, rotation, extendable translation and rotation. Quasi-Hamilton principles of flexible multi-body system dynamics in the three kinds of movement in annex are deduced, the quasi-Hamilton principle which include two kinds of variables are established. The concept of quasi-stationary value condition of flexible multi-body system dynamics is proposed. Through the deduction of quasi-stationary value condition of quasi-variational principles, the author has tested the quasi-variational principles. Due to the application of quasi-stationary value condition of quasi-Hamilton principle in the extendable translation annex of flexible multi-body system dynamics, the author has established vibration differential equations of extendable translation flexible beam in space vehicles, and also has got round lateral vibration frequencies. The purpose is that the quasi-stationary value condition of quasi-Hamilton principle in rotation annex of flexible multi-body system dynamics is applied to establish the spacecraft rotation flexible beam vibration differential equations and to get round lateral vibration frequencies.
多柔体系统动力学的拟变分原理的研究涵盖了许多学科,需要一般力学、固体力学等多个学科。
首先,研究了分析动力学含阻尼非保守系统的拟变分原理。从基本方程出发,应用变积方法推导了分析动力学含阻尼非保守系统的拟Hamilton原理,并给出了其它表达形式；建立了两类变量的广义拟势能原理和广义拟余能原理；建立了三类变量的广义拟势能原理和广义拟余能原理。建立了反映本构关系、几何条件和动态平衡方程的广义拟变分原理。应用分析动力学含阻尼非保守系统的拟Hamilton原理,研究二自由度系统的振动方程,并且得到随阻尼衰减解以及稳态解。
其二,研究了弹性动力学拟变分原理和广义拟变分原理。建立非保守系统弹性动力学拟Hamilton原理、拟余Hamilton原理、第一、第二类两类变量广义拟变分原理和三类变量广义拟变分原理。
其三,研究了单柔体动力学的拟变分原理。将变分方法推广应用到单柔体动力学问题中,推导了单柔体动力学的拟Hamilton原理,建立了两类变量的拟Hamilton原理。提出了单柔体动力学问题的拟驻值条件的概念,通过推导拟变分原理的拟驻值条件对拟变分原理进行了检验。以拦截器为例,说明了单柔体动力学两类变量的拟Hamilton原理的拟驻值条件和先决条件的物理意义；应用拟Hamilton原理的拟驻值条件建立了火箭垂直发射时的纵向振动方程,并且说明在单柔体动力学中“一力二用”的特性。
其四,研究了多柔体系统动力学的拟变分原理。将变分方法推广应用到多柔体系统动力学问题中。考虑附件三种运动情况：可伸展平动、转动、既可伸展平动又转动。推导了附件三种运动情况时的多柔体系统动力学的拟Hamilton原理,建立了两类变量的拟Hamilton原理。提出了多柔体系统动力学问题的拟驻值条件的概念,通过推导拟变分原理的拟驻值条件对拟变分原理进行了检验。应用可伸展平动附件多柔体系统动力学拟Hamilton原理的拟驻值条件,建立空间飞行器可伸展平动柔性梁横向振动微分方程,得到横向振动圆频率；应用转动附件多柔体系统动力学拟Hamilton原理的拟驻值条件,建立空间飞行器转动柔性梁横向振动微分方程,得到横向振动圆频率。
The development of flexible multi-body system dynamics is closely related to the development of space technology. From the multi-body point of view, flexible multi-body system dynamics is an extension of multiple rigid body system dynamics and from the perspective of dynamics, rigid body is flexible in the special circumstances. Flexible multi-body system dynamics considers more cross-link roles between the multi-body movement and flexible effects. The most common flexible multi-body system is flexible multi-body cluster system and flexible multi-body linked system. In this paper, the flexible multi-body cluster system is researched.
Quasi-variational principles of flexible multi-body system dynamics covers a lot of subjects, general mechanics, solid mechanics, and other disciplines are needed.
Firstly, analysis dynamics which contains the quasi-variational principle of damping non-conservative system is studied. From the basic equation, variational integral method is applied to deduce the analysis dynamics which contains the quasi-Hamilton of damping non-conservative system and the other forms of expression are given. Generalized quasi-potential energy principle and generalized quasi-complementary energy principle which include two kinds of variables are established. Generalized quasi-potential energy principle and generalized quasi-complementary energy principle which include three kinds of variables are established. Generalized quasi-variational principle which reflects constitutive relations, geometric conditions and dynamic balance equation are also built up. Analysis dynamics which contains the quasi-Hamilton principle of damping non-conservative system is applied to research the two degree of freedom on the vibration equation. Meanwhile, the author also gets the decayed solution with the damper and the steady-state solution.
Secondly, quasi-variational principle and generalized quasi-variational principle in elasto-dynamics is studied. Quasi-Hamilton, quasi-complementary Hamilton principle, the first and second types generalized quasi-variational principles with two kinds of variables, and generalized quasi-variational principle with three kinds of variables in non-conservative elasto-dynamics system are established.
Thirdly, quasi-variational principle of single flexible body dynamics is studied. Variational methods are applied to deduce the problems of single flexible body dynamics. At the same time, quasi-Hamilton principle of single flexible body dynamics, the quasi-Hamilton principle which include two kinds of variables are established. The concept of quasi-stationary value condition of single flexible body dynamics is proposed. Through the deduction of the quasi-stationary value condition of quasi-variational principles, quasi-variational principles have been tested. Taking the interceptor as an example, the author has explained the physical meaning of the quasi-stationary value condition and prerequisite in the quasi-Hamilton principles of single flexible body dynamics with two kinds of variables. The quasi-stationary value condition of quasi-Hamilton principles are applied to establish the vertical vibration equation when the rockets launch vertically and the author also has illustrated the features of "one force for two effects" in a single flexible body dynamics.
Forthly, quasi-variational principle of flexible multi-body system dynamics is also studied. Variational methods are applied to deduce the problems of flexible multi-body system dynamics. Three kinks of movement in annex are considered: extendable translation, rotation, extendable translation and rotation. Quasi-Hamilton principles of flexible multi-body system dynamics in the three kinds of movement in annex are deduced, the quasi-Hamilton principle which include two kinds of variables are established. The concept of quasi-stationary value condition of flexible multi-body system dynamics is proposed. Through the deduction of quasi-stationary value condition of quasi-variational principles, the author has tested the quasi-variational principles. Due to the application of quasi-stationary value condition of quasi-Hamilton principle in the extendable translation annex of flexible multi-body system dynamics, the author has established vibration differential equations of extendable translation flexible beam in space vehicles, and also has got round lateral vibration frequencies. The purpose is that the quasi-stationary value condition of quasi-Hamilton principle in rotation annex of flexible multi-body system dynamics is applied to establish the spacecraft rotation flexible beam vibration differential equations and to get round lateral vibration frequencies.
引文
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