无限弹簧振子链的脉冲波  

PULSE WAVE OF INFINITE SPRING OSCILLATOR CHAIN

作　　者：邱为钢[1] 

机构地区：[1]湖州师范学院理学院,浙江湖州313000

出　　处：《物理与工程》2016年第4期62-64,68,共4页Physics and Engineering

基　　金：湖州师范学院中青年教师卓越教学能力培养计划专题项目(2014ZYJH017);国家自然科学基金(11475062;11275067)资助

摘　　要：给出了一维和两维无限长弹簧振子链的波动方程,这些方程可以看作数列的递推关系式,从而用产生函数法求解.一维解是偶数和奇数阶贝塞尔函数,对应于第一类和第二类脉冲波,分别取起始位移或速度离散奇异分布,两维解也是两种类型的脉冲波.文章还讨论了它们的级数展开式,渐近展开式,波形图及对称性.The wave equations of infinite spring oscillator chain are derived in one and two dimensions.These equations can be viewed as the recursive relation sequence,and can be solved by the generating function method.The one dimensional solutions are even order and odd order Bessel functions,corresponding to the first and the second pulse wave,respectively.The initial conditions are the discrete delta distributions of displacements or velocities,respectively.The two dimensional solutions are also two type of pulse wave.The series expansions,asymptotic expansions,configurations and symmetries of these pulse waves are discussed.

关 键 词：弹簧振子 产生函数法 脉冲波 

分 类 号：O32-4[理学—一般力学与力学基础] G652[理学—力学]