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A New Differential Operator Method to Study the Mechanical Vibration
Shandong Iron and Steel Company Ltd., Jinan, China
Department of Mathematical Sciences, Yeshiva University, New York, USA
The State Key Laboratory of Tribology, Tsinghua University, Beijing, China
Department of Mathematical Sciences, Yeshiva University, New York, USA
- 1 Shandong Iron and Steel Company Ltd., Jinan, China
- 2 Department of Mathematical Sciences, Yeshiva University, New York, USA
- 3 The State Key Laboratory of Tribology, Tsinghua University, Beijing, China
- 4 Department of Mathematical Sciences, Yeshiva University, New York, USA
Modern Mechanical Engineering·Volume 02 (2012)·Pages 65–70·Published 31 August 2012·DOI10.4236/mme.2012.23009
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Abstract
In this paper, we propose a unified differential operator method to study mechanical vibrations, solving inhomogeneous linear ordinary differential equations with constant coefficients. The main advantage of this new method is that the differential operator D in the numerator of the fraction has no effect on input functions ( i.e. , the derivative operation is removed) because we take the fraction as a whole part in the partial fraction expansion. The method in various variants is widely implemented in related fields in mechanics and engineering. We also point out that the same mistakes in the differential operator method are found in the related references [1-4].
KeywordsNew Differential Operator MethodMechanical Vibration (Torsional Vibration of Rolling-Mill)Torque Amplification FactorModel Analysis MethodLaplace Transform
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