弦长对弦振动实验的影响研究

弦振动实验中,在固定端施加张力不变的前提下,改变弦长度。利用振动频率与驻波波长的关系,得到弦的线密度。通过比较不同弦长下得到的弦的线密度与弦质量长度比结果的比较,讨论了弦长对弦线密度测量结果的影响,分析了弦振动实验中合理选择弦长的必要性。     

利用光的反射对弦振动实验的改进

为了解决弦振动实验在操作过程中拉力杆无法水平而导致实验误差偏大的问题,研究改进了弦振动装置,使实验误差得到了很大程度的降低。本文利用光的反射原理,很好地解决了传统弦振动实验用肉眼观察拉力杠杆水平带来的较大误差的问题。研究表明通过改进的实验装置探究共振频率和弦上波腹数的关系其相对误差平均降低了1.94%,很好地验证了改进方案的可行性和有效性。     

共振频率激励下弦振动定解问题的求解

对于一端固定、另一端施加正弦激励的弦线振动定解问题,采用分离变量法在共振与非共振两种激励频率下对其进行了求解;通过对两种不同形式解的研究发现:对非共振频率激励下的解求极限,亦可得到共振频率激励下的解;最后通过分析可知:共振频率激励下的解即为无阻尼条件下的驻波状态解.     

非齐次边界条件时的半无界弦自由振动问题

基于达朗贝尔公式,讨论了半无界弦自由振动时的非齐次边界条件的延拓问题.结果表明:对半无界弦自由振动时的非齐次边界条件的延拓,理论上可有多种方法,尽管延拓表达式不同,但不会影响最终结果.文中最后还给出了两种相对简单的延拓方法.     

弦振动定解问题级数解的截断误差分析

基于弦振动方程在定解条件下的三种不同形式的级数解,讨论了是否忽略自变量两种条件下级数解的截断误差.其中,在考虑自变量的情况下通过对普遍截断误差进行估计,定义出类吉布斯现象,从而得到最大截断误差的估计.     

基于Matlab GUI的弦振动仿真课件制作

利用Matlab GUI制作弦振动仿真课件,集成多种功能,可以模拟弦线上驻波波长随弦线密度、弦线张力、振源频率的变化。可实现数据的定量测量,自动读取、记录数据。集成数据处理功能,采用对数作图法处理数据,并给出拟合曲线和拟合系数。     

再论用Laplace变换法求解端点系有集中质量的弹性杆的振动问题

将作者在《大学物理》2004年第12期上的一篇文章的解法推广到弹性杆的强迫纵振动问题,并求解了两端系有集中质量的弹性杆的自由纵振动问题．     

用Laplace变换法求解端点系有集中质量的弹性杆的振动问题

用Laplace变换法求解了一端为齐次边界条件,另一端系有集中质量的弹性杆的纵振动问题,推广了相关文献的结果。     

Vibrations of a beam fixed at one end and carrying a guided mass at the other

This paper presents an exact solution of the title problem, using classical beam theory. It is also assumed that the tip mass is guided in such a manner that the end of the beam does not rotate.     

Free and forced vibration of layered one-dimensional quasicrystal nanoplates with modified couple-stress effect

正To the editor,A new type of solid, called quasicrystal (QC) was discovered after Shechtman et al.[1] accidently got in 1982 a five-fold symmetry diffraction image of rapidly cooled Al-Mn alloys.In contrast with crystals with periodic atomic arrangement,QCs have perfect long-range order (like mirror symmetry)but no periodic translational symmetry. Due to their intrinsic brittleness at room temperature, QCs cannot be used directly as structural materials. However, QCs as thin films and coatings of metals in industry are applied to surface modified materials and the reinforcing phase in structural materials.     

Vibrations of a timoshenko beam clamped at one end and carrying a finite mass at the other

The present paper deals with an exact solution of the title problem. Modal shapes and natural frequency coefficients are determined for a significant range of the mechanical and geometric parameters that come into play. When the parameter I/AL² (where I is cross-sectional moment of inertia, A is cross-sectional area, and L beam length) approaches zero, the beam dynamic characteristics agree with values already available in the open literature.     

Vibration frequencies for a uniform beam with one end spring-hinged and subjected to a translational restraint at the other end

The purpose of the present study is to deal with the free vibration of a beam hinged at one end by a rotational spring and subjected to the restraining action of a translational spring at the other end. The eigenfrequencies for the fundamental mode are presented for different values of the parameters K_RL/EI and K_TL³/EI, where KR and K_T are the stiffness constants of the springs.     

关于受迫振动、共振的实验研究

简要分析了现行中学物理课本中关于受迫振动和共振的演示实验中存在的缺点,并针对其不足加以改进.改进后的实验装置演示效果更好,便于学生理解和掌握相应的物理规律.