连续弹性介质质元振动分析

Vibration Analysis of Material Element in Continuous Elastic Medium

根据简谐波运动学的定义,弹性介质质元的振动应为简谐振动,但媒介质元的动力学和能量特征与简谐振动并不一致。为了帮助学生深入理解简谐振动概念,明确连续弹性介质质元的振动规律,首先从简谐振动的定义出发,结合简谐振动的本质,将简谐振动分为广义和狭义的简谐振动2种。通过对介质质元的运动学和动力学特征分析,发现连续介质中质元的振动应为广义的简谐振动,而振源质元的振动应为稳定的受迫振动。

According to the definition of simple harmonic wave,the vibration of the elastic medium should be simple harmonic vibration,but the dynamics and energy characteristics of the media element are not consistent with the simple harmonic vibration.In order to help students understand the concept of simple harmonic vibration,combined with its essence,the simple harmonic vibration is divided into two kinds of simple harmonic vibration,that is,general and narrowly simple harmonic oscillations.The kinematics and dynamic characteristics of the material element in the continuous medium are analyzed.It is found that the motion of the material element in the continuous elastic medium should be the general simple harmonic vibrations,and the motion of the source element should be steady forced vibration.