Response of Elastic Continuum Carrying Moving Linear Oscillator

Revisiting the moving force problem

“…(4) and (A.1) at t ¼ T p [5] with regard to the orthogonality of the eigenfunctions: A n ¼ q n ðT p Þ and B n ¼ ' q n ðT p Þ=o n : Using Eq. (8) and the equality a n T p ¼ np and denoting g n ¼ ffiffi ffi 2 p a n =o n ða…”

“…[1,2]; and references therein). One of the most well-known techniques is to represent the solution in a series form in terms of the eigenfunctions of the beam [2][3][4][5]. If the travelling force is constant, the time-dependent coefficients can be obtained in an analytical form [2][3][4], which makes it easy to find a solution to any particular problem.…”

Experimental and numerical investigation of the earthquake response of crane bridges

“…It is well known that the main drawback of this similarity law is that, since the Froude number similitude is not satisfied, the ratio between dynamic and static stresses of the model is not the same as in the prototype . Moreover, in the present case, where the importance of friction phenomena is crucial, if the same coefficient of friction μ, is used for both the prototype and the model, it is not possible to respect 4  similarity. Therefore, similarity of the friction forces with respect to the seismic excitation forces cannot be achieved unless specific interface materials are used with a friction coefficient times the friction coefficient of the prototype.…”

“…Surprisingly, to the authors' knowledge, a very few experimental and analytical research work in this field has been done in the past. The dynamics of elastic continua with moving loads has been covered by Fryba [1] and more recent work presents the approximate analytical solutions [2][3][4][5][6] and finite element solutions [7,8] to similar problems. Regarding the earthquake response of these structures, not many publications can be found in the literature.…”

Interaction of a non-self-adjoint one-dimensional continuum and moving multi-degree-of-freedom oscillator

“…Pesterev and Bergman [10] considered the problem of the vibrations of a general category of linear, conservative, one-dimensional (1D) continua carrying a moving, linear, conservative, one-degree-of-freedom (1DOF) oscillator. They established the solution of the interaction problem in the form of a series in terms of the eigenfunctions of the isolated continuum.…”