无约束修正Timoshenko梁的冲击问题

介绍了修正后的Timoshenko梁运动方程，并比较了修正Timoshenko梁与经 典Timoshenko梁的运动方程. 推导了考虑剪切变形引起的转动惯量的修正Timoshenko 梁的正交条件，推导了集中质量对无约束修正Timoshenko梁的正碰撞对梁所引起的瞬态冲 击响应公式，并用算例进行了分析，且与集中质量对经典的无约束Timoshenko梁的正碰撞 对梁所引起的冲击响应进行了比较，另外还用算例分析了梁的刚度的变化和冲击质量比对其 冲击响应产生的影响.     

Why static bound-state calculations of tetraquarks should be met with scepticism

Recent experimental signals have led to a revival of tetraquarks,the hypothetical q~2q~2 hadronic states proposed by Jaffe in 1976 to explain the light scalar mesons.Mesonic structures with exotic quantum numbers have indeed been observed recently,though a controversy persists as to whether these are true resonances and not merely kinematical threshold enhancements,or otherwise states not of a true q~2q~2 nature.Moreover,puzzling non-exotic mesons are also often claimed to have a tetraquark configuration.However,the corresponding model calculations are practically always carried out in pure and static bound-state approaches,ignoring completely the coupling to asymptotic two-meson states and unitarity,especially the dynamical effects thereof.In this short paper we argue that these static predictions of real tetraquark masses are highly unreliable and provide little evidence of the very existence of such states.     

无约束自由杆纵向冲击响应分析

用Fourier级数方法推导了无约束自由杆承受运动刚体纵向冲击作用下的响应,将刚性位移直接由总位移中分离出来,并分析了无约束自由杆的刚性位移与弹性位移的关系及其影响因素。数值算例表明只要选取足够多级数项进行叠加,可以得到精确的结果。     

ANALYSIS ON IMPACT RESPONSES OF UNRESTRAINED PLANAR FRAME STRUCTURE(Ⅱ)-NUMERICAL EXAMPLE ANALYSIS

By using the formula derived in Part (Ⅰ), the instant response of an unrestrained planar frame structure subjected to the impact of a moving rigid-body are evaluated and analysed.The impact force-time history between the structure and the moving rigid-body, shear force and bending moment distribution along the beams, axial force distribution along the bars were calculated. The wave propagation phenomena of the longitudinal wave in the bars, the flexural and shear waves in the beams were also analysed. The numerical results show that the time duration of impact force is controlled by the flexural wave and the longitudinal wave; the shear effect in beams should not be neglected in the impact response analysis of structures.     

无约束平面框架结构冲击响应分析(Ⅱ)——数值算例分析

利用第(Ⅰ)部分推得的公式,对一无约束平面框架结构受运动刚体冲击时的瞬态响应进行了数值计算分析．计算了结构与运动刚体之间的冲击力时程曲线、梁中的剪力及弯矩分布、轴力杆件中的轴力分布．分析了杆中的纵波、Timoshenko梁中弯曲波及剪切波的传播现象．数值分析表明:冲击力的延续时间主要是由挠曲波及纵波控制的;在结构的冲击响应分析中,梁的剪切效应不容忽略．     

ANALYSIS ON IMPACT RESPONSES OF UNRESTRAINED PLANAR FRAME STRUCTURE(Ⅱ)—NUMERICAL EXAMPLE ANALYSIS

By using the formula derived in Part （ Ⅰ ）, the instant response of an unrestrained planar frame structure subjected to the impact of a moving rigid-body are evaluated and analysed. The impact force-time history between the structure and the moving rigid-body, shear force and bending moment distribution along the beams, axial force distribution along the bars were calculated. The wave propagation phenomena of the longitudinal wave in the bars, the flexural and shear waves in the beams were also analysed. The numerical results show that the time duration of impact force is controlled by the flexural wave and the longitudinal wave ; the shear effect in beams should not be neglected in the impact response analysis of structures.     

无约束Timoshenko梁横向冲击响应分析

将运动刚体与受其横向冲击的无约束Timoshenko梁看成一个接触．冲击系统，用广义Fourier，级数方法推导了系统的特征方程和特征函数，得到了冲击响应的解忻解．冲击响应可以分解成弹性响应与刚性响应两部分，验证了接触．冲击系统中弹性响应的动量之和为零，从而得到刚性响应的简便求法．     

ANALYSIS ON IMPACT RESPONSES OF UNRESTRAINED PLANAR FRAME STRUCTURE(Ⅰ)-FORMULA DERIVATION

The generalized Fourier-series method was used to derive the impact responses formula of an unrestrained planar frame structure when subjected to an impact of a moving rigid-body. By using these formula, the analytic solutions of dynamic responses of the contact-impact system can be obtained. During the derivation, the momentum sum of elastic responses of the contact-impact system is demonstrated to be zero. From the derivation, it is seen that the modal method can also be used to solve this kind of impact problem.     

ANALYSIS ON IMPACT RESPONSES OF UNRESTRAINED PLANAR FRAME STRUCTURE(Ⅰ)—FORMULA DERIVATION

Introduction Recently,therehavebeenconsiderablestudiesontransientresponsesandwave propagationofrestrainedstructureswhicharebeingimpacted[1,2].But,fortheunrestrained structures,therearefewrelativeliteratureshavingbeenpublished.Unrestrainedstructures aremai…     

ANALYSIS ON TRANSVERSE IMPACT RESPONSE OF AN UNRESTRAINED TIMOSHENKO BEAM

A moving rigid-body and an unrestrained Timoshenko beam, which is subjected to the transverse impact of the rigid-body, are treated as a contact-impact system. The generalized Fourier-series method was used to derive the characteristic equation and the characteristic function of the system. The analytical solutions of the impact responses for the system were presented. The responses can be divided into two parts : elastic responses and rigid responses. The momentum sum of elastic responses of the contact-impact system is demonstrated to be zero, which makes the rigid responses of the system easy to evaluate according to the principle of momentum conservation.