现行高中物理课本中提到,当军队或火车过桥的时候,整齐的步伐或车轮对铁轨接头处的撞击,都是周期性的策动力。当它的频率按近桥梁的固有频率时,就会发生共振而使桥梁受到破坏这是个相当复杂而能引起学生兴趣的问题,本文想在这方面作一介绍。现代混凝土桥、钢箱梁桥和桁梁桥,我们常将其简化为一变截面直梁,如图1所示。取位置坐标x和时间t为独立变量,现设图1中直梁的抗弯刚度为EJ,单位长度的质量为m。它们沿跨度τ随位置x而任意变化。横向负荷P和横向位移y随x和t变化。图2表示梁上某一微段dx Current high school physics textbooks mention that when the army or train crosses a bridge, the regular pace or the impact of wheels on the rail joints is a cyclical driving force. When its frequency is near the natural frequency of the bridge, resonance will occur and the bridge will be damaged. This is a very complicated problem that can arouse students’ interest. This article would like to give an introduction in this regard. Modern concrete bridges, steel box girder bridges and truss girder bridges are often reduced to a straight beam with variable cross sections, as shown in Figure 1. Take the position coordinate x and the time t as independent variables. Now the bending stiffness of the straight beam in Figure 1 is EJ, and the mass per unit length is m. They vary arbitrarily along the span τ with position x. The lateral load P and the lateral displacement y change with x and t. Figure 2 shows a segment dx on a beam