TY - JOUR

T1 - On asymptotics of the solution of the moving oscillator problem

AU - Pesterev, A. V.

AU - Bergman, L. A.

AU - Tan, C. A.

AU - Tsao, T. C.

AU - Yang, B.

N1 - Funding Information:
The authors wish to acknowledge the support of the Civil and Mechanical Systems Division of the National Science Foundation through grant number CMS-9800136.The first author especially acknowledges the International Programs Division of the National Science Foundation for providing the grant supplement necessary to facilitate his extended visit to the United States and this collaboration.

PY - 2003/2/20

Y1 - 2003/2/20

N2 - Asymptotic behavior of the solution of the moving oscillator problem is examined for large and small values of the spring stiffness for the general case of non-zero beam initial conditions. In the limiting case of infinite spring stiffness, it is shown that the moving oscillator problem for a simply supported beam is not equivalent, in a strict sense, to the moving mass problem. The two problems are shown to be equivalent in terms of the beam displacements but are not equivalent in terms of stresses (the higher order derivatives of the two solutions differ). In the general case, the force acting on the beam from the oscillator is shown to contain a high-frequency component, which does not vanish and can even grow when the spring coefficient tends to infinity. The magnitude of this force and its dependence on the oscillator parameters can be estimated by considering the asymptotics of the solution for the initial stage of the oscillator motion. It is shown that, for the case of a simply supported beam, the magnitude of the high-frequency force depends linearly on the oscillator eigenfrequency and velocity. The deficiency of the moving mass model is principally that it fails to predict stresses in the supporting structure. For small values of the spring stiffness, the moving oscillator problem is shown to be equivalent to the moving force problem. The discussion is amply illustrated by results of numerical experiments.

AB - Asymptotic behavior of the solution of the moving oscillator problem is examined for large and small values of the spring stiffness for the general case of non-zero beam initial conditions. In the limiting case of infinite spring stiffness, it is shown that the moving oscillator problem for a simply supported beam is not equivalent, in a strict sense, to the moving mass problem. The two problems are shown to be equivalent in terms of the beam displacements but are not equivalent in terms of stresses (the higher order derivatives of the two solutions differ). In the general case, the force acting on the beam from the oscillator is shown to contain a high-frequency component, which does not vanish and can even grow when the spring coefficient tends to infinity. The magnitude of this force and its dependence on the oscillator parameters can be estimated by considering the asymptotics of the solution for the initial stage of the oscillator motion. It is shown that, for the case of a simply supported beam, the magnitude of the high-frequency force depends linearly on the oscillator eigenfrequency and velocity. The deficiency of the moving mass model is principally that it fails to predict stresses in the supporting structure. For small values of the spring stiffness, the moving oscillator problem is shown to be equivalent to the moving force problem. The discussion is amply illustrated by results of numerical experiments.

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U2 - 10.1016/S0022-460X(02)00953-7

DO - 10.1016/S0022-460X(02)00953-7

M3 - Article

AN - SCOPUS:0037456478

SN - 0022-460X

VL - 260

SP - 519

EP - 536

JO - Journal of Sound and Vibration

JF - Journal of Sound and Vibration

IS - 3

ER -