作业帮土木专业英语在线翻译The converse of this true;but we cannot conclude t
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土木专业英语在线翻译
The converse of this true;but we cannot conclude that a system is in equilibrium just because the viatual work is zero due to a specific virtual displacement.this fact is amply demonstrated bu the particle showm in fig.1.5,which , even though a displacement parallel to the x axis results in zero work,is obviously not in equilibrium. It may appear that all possible virtual displace must be investigated in order to estabilsh the equilibrium of a particle. If this is were true,to use the principle to study equilibrium would be an extremely laborious an impractical task, since, even for a single particle, the number of possible virtual displacements is infinite. Fortunately , this is not the case. A quick calculation will show that every possible displacement of the particle in fig.1.5 can be expressed in terms of two indenpent virtual displacements—say one in the x direction and one in the y direction—and that when the virtual work done during these displacements is zero that we can conclude that the particle is in equilibrium. The use of two independent virtual displacements corresponds to the two degrees of freedom of a single particle in the plane. A particle in speace, for example, has three degrees of freedom and, consequently,the virtual work done during three independent virtual displacements must vanish for equilibrium, ΔW must vanish for any four independent virtual displacements. In view of thi, we now write a useful corollary to Theorem Ⅰ：
A system of particles is in equilibrium if the total virtual work done is zero for every independent virtual displacement.(THEOREM Ⅱ )
The converse of this true;but we cannot conclude that a system is in equilibrium just because the viatual work is zero due to a specific virtual displacement.this fact is amply demonstrated bu the particle showm in fig.1.5,which , even though a displacement parallel to the x axis results in zero work,is obviously not in equilibrium. It may appear that all possible virtual displace must be investigated in order to estabilsh the equilibrium of a particle. If this is were true,to use the principle to study equilibrium would be an extremely laborious an impractical task, since, even for a single particle, the number of possible virtual displacements is infinite. Fortunately , this is not the case. A quick calculation will show that every possible displacement of the particle in fig.1.5 can be expressed in terms of two indenpent virtual displacements—say one in the x direction and one in the y direction—and that when the virtual work done during these displacements is zero that we can conclude that the particle is in equilibrium. The use of two independent virtual displacements corresponds to the two degrees of freedom of a single particle in the plane. A particle in speace, for example, has three degrees of freedom and, consequently,the virtual work done during three independent virtual displacements must vanish for equilibrium, ΔW must vanish for any four independent virtual displacements. In view of thi, we now write a useful corollary to Theorem Ⅰ：
A system of particles is in equilibrium if the total virtual work done is zero for every independent virtual displacement.(THEOREM Ⅱ )
这种真正的交谈,但我们不能断定是一个系统的平衡只是因为viatual工作是零,由于特定的虚拟位移.这个事实充分表明布图粒子showm.1.5,其中,即使位移平行于X轴在零工作的结果,是明显不均衡.它可能出现的所有可能的虚拟取代,必须予以追究,以estabilsh粒子的平衡.如果这是属实的,要使用平衡的原则,研究将是非常艰苦的不切实际的任务,因为即使是单粒子,虚位移的可能数是无限的.幸运的是,情况并非如此.一个快速计算将显示每一个可能位移粒子图.1.5可以表示成两个indenpent虚位移,说的是在x方向,一个在y方向上,而当虚功做的是在这些位移为零,我们可以得出这样的结论粒子在平衡状态.两个独立的虚拟位移使用对应于一个平面上的单粒子自由的两个学位.以speace粒子,例如,具有三个自由度,因此,虚拟工作在三个独立的虚拟位移做必须为平衡消失,ΔW必须消失的任何四个独立的虚拟位移.在氏认为,我们现在写一个定理Ⅰ有用的推论：..
的粒子系统的平衡如果总虚功做的是为每个独立的虚拟位移为零.（定理Ⅱ）..
的粒子系统的平衡如果总虚功做的是为每个独立的虚拟位移为零.（定理Ⅱ）..
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