Dynamic analysis and optimum design for control of beams with time-dependent changes of length

Structural systems with longitudinal mass flow can be seen in belt-conveyers, running magnetic tapes and flexible manipulators, etc. Transverse vibration problems of flexible longitudinally extensible beams are considered as a special class of vibration problems of structural systems with longitudinal mass flow. The optimum design problem to control the dynamic response of such structural systems is very important from engineering and practical viewpoints, but until now it has not been the subject of much study. Based on the method of dynamic response analysis of extensible beams presented in the author's previous studies, a method of sensitivity analysis of dynamic response is presented in this paper. Utilizing the obtained sensitivities of the response with respect to design parameters, such as mass flow velocity, tension and rigidity etc., a new optimum design method to control the responses of such structural systems is also presented.