Abstract
The problem of calculating the dynamic response of a one-dimensional distributed parameter system excited by an oscillator traversing the system with an arbitrarily varying speed is investigated. An improved series representation for the solution is derived that takes into account the jump in the shear force at the point of the attachment of the oscillator, which makes it possible to efficiently calculate the distributed shear force and, where applicable, bending moment. The improvement is achieved through the introduction of the “quasi-static” solution, an approximation to the desired one, which makes it possible to apply to the moving oscillator problem the “mode-acceleration” technique conventionally used for acceleration of series in problems related to the steady-state vibration of distributed systems. Numerical results illustrating the efficiency of the method are presented.
Application of reduced models for robust control and state estimation of a distributed parameter system
