单自由度振系固有频率不含弹簧静变形的充要条件
发布时间：2018-11-23 06:39
【摘要】：教材示例几乎都使用固有频率表达式不显含弹簧静变形的例子,但确实存在相反的情形.本文针对单自由度振动系统,研究了弹簧静变形从固有频率表达式中消失的充要条件.由于采用了能使广义质量为常数的广义坐标,从而只用研究系统的势能.研究发现静变形消失的充要条件是:在静平衡位置弹簧轴线与其运动端点的轨迹相切,且以弹簧运动端点位移为广义坐标所得到广义质量对广义坐标的导数应为0.
[Abstract]:Examples of textbooks use natural frequency expressions that do not contain spring static deformation, but the opposite is true. In this paper, a necessary and sufficient condition for the spring static deformation to disappear from the natural frequency expression is studied for a single degree of freedom vibration system. Due to the use of generalized coordinates which can make the generalized mass constant, only the potential energy of the system is studied. It is found that the necessary and sufficient condition for the disappearance of static deformation is that the axis of the spring is tangent to the trajectory of the end of its motion at the static equilibrium position, and the derivative of the generalized mass to the generalized coordinate obtained by using the displacement of the end of the spring motion as the generalized coordinate should be 0.
【作者单位】： 中国农业大学理学院;
【分类号】：G642;O32-4
本文编号：2350643
[Abstract]:Examples of textbooks use natural frequency expressions that do not contain spring static deformation, but the opposite is true. In this paper, a necessary and sufficient condition for the spring static deformation to disappear from the natural frequency expression is studied for a single degree of freedom vibration system. Due to the use of generalized coordinates which can make the generalized mass constant, only the potential energy of the system is studied. It is found that the necessary and sufficient condition for the disappearance of static deformation is that the axis of the spring is tangent to the trajectory of the end of its motion at the static equilibrium position, and the derivative of the generalized mass to the generalized coordinate obtained by using the displacement of the end of the spring motion as the generalized coordinate should be 0.
【作者单位】： 中国农业大学理学院;
【分类号】：G642;O32-4
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