Transverse vibrations of a single-span beam with the motion of a bending moment

Conclusions

Analysis of the dynamic action of a moving bending moment on a single-span beam-type system showed that, with v=(0.2–0.8v ⁰₁ , taking account of the inertial forces of the load does not enter into the margin of strength of the construction, and these forces must be taken into consideration in dynamic calculations. The greatest deflections of the beam, when the mass of the load M=0.5ml, exceed the static deformations, taking account of the inertial forces of the load, by 2.5 times. The value of the velocity here is v=0.6v ⁰₁ .

The maximal coefficient of the dynamics, calculated without taking account of the weight of the load, is equal to 1.95 and occurs with v=0.8v ⁰₁ . We note that, with the motion of a vertical force along the beam, the maximal value of the dynamic coefficient is equal to 1.77 and is observed with v=0.6v ⁰₁ [3].

If v<0.6v ⁰₁ , where the mass of the load is not introduced into the calculations, and v<0.4v ⁰₁ , where account is taken of the inertial forces of the load, then the maximal deformations of the beam take place during the process of forced vibrations at the moment that the load is located in the construction. With large values of v, the greatest deflections are observed after passage of the load, during the period of free vibrations of the system.

In distinction from the solution of the problem of the vibrations of a beam under the action of a moving force (load), where a sufficient degree of exactness of the computations assures taking account of the first form of the vibrations of the construction, with an analysis of dynamic deformations of a beam, brought about by the action of a moving bending moment, the higher forms of the vibrations of the system must be taken into consideration.