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S. Nicaise and O. Zair, “Determination of Point Sources in Vibrating Beams by Boundary Measurements: Identifiability, Stability and Reconstruction Results,” Electronic Journal of Differential Equations, Vol. 2004, No. 20, 2004, pp. 1-17.

has been cited by the following article:

• TITLE: A Time History Method for Analysing Operational Piping Vibrations

  AUTHORS: Subrata Saha

  KEYWORDS: Vibration; Inverse Problem; Direct Problem; Time History; Fatigue Failure; Vibration Screening Criterion; Integral Equation; Frequency; Damping

  JOURNAL NAME: World Journal of Mechanics, Vol.2 No.6, December 27, 2012

  ABSTRACT: Vibration failure of piping is a serious problem and a matter of concern for safety and reliability of plant operations. Fatigue is the main cause of such failures. Due to the complexity of the phenomenon no closed form design solutions are available. In our study an analytical technique based on the theory of vibrations in the time domain has been presented. Using the inverse theory, the problem has been reduced to a system of Volterra Integral equations to be solved simultaneously at every time step. The solution of the inverse problem may be used in the conventional method to calculate stresses and end reactions which are important from the perspective of engineering design and condition monitoring. The method is robust, simple and can be easily adopted by practicing engineers.