Publisher : The Korean Society for Noise and Vibration Engineering
DOI : 10.5050/KSNVE.2016.26.2.217
Title & Authors
Analysis of Vibration for the Pre-twisted Beam Considering the Effect of Rotary Inertia Using the Transfer Matrix Mathod Lee, Jung Youn;
In this study, a transfer matrix method (TMM) for a twisted uniform beam considering the effect of rotary inertia is developed, and the differential equation and the displacements and forces are derived from Hamilton`s principle. The particular transfer matrix is derived by applying the distributed mass and transcendental function while using a local coordinate system. In addition, the results obtained from this method are independent for a number of subdivided elements, and this method can determine the exact solutions for the free vibration characteristics of a twisted uniform Rayleigh beam. To validate the accuracy of the proposed TMM, the computed results are compared with those reported in the existing literature, and the comparison results indicate notably good agreement. In addition, the method is used to investigate the effects of rotary inertia for a twisted beam.
Transfer Matrix Method;Coupled Bending-bending Vibration;A Twisted Rayleigh Beam;Hamilton`s Principle;Rotary Inertia;
Murthy, V. R., 1976, Dynamic Characteristics of Rotor Blades, Journal of Sound and Vibration, Vol. 49, No. 4, pp. 483~500.
Banerjee, J. R., 2001, Free Vibration Analysis of a Twisted Beam Using the Dynamic Stiffness Method, International Journal of Solids and Structures, Vol. 38 No. 38-39, pp. 6703~6722.
Lin, S. M., 1997, Vibrations of Elastically Restrained Nonuniform Beams with Arbitrary Pretwist, AIAA, Vol. 35, No. 11, pp. 1681~1687.
Rosen, A., 1991, Structural and Dynamic Behavior of Pretwisted Rods and Beams, Applied Mechanics Reviews, Vol. 44, No. 12, pp. 483~515.
Yoo, H. H, Kwak, J. Y. and Chung, J., 2001, Vibration Analysis of Rotating Pre-twisted Blades with a Concentrated Mass, Journal of Sound and Vibration, Vol. 240, No. 5, pp. 891~908.
Yardimoglu, B. and Yildirim, T., 2004, Finite Element Model for Vibration Analysis of Pre-twisted Timoshenko Beam, Journal of Sound and Vibration, Vol. 273, No. 4-5, pp. 741~754.
Ho, S. H. and Chen, C. K., 2006, Free Transverse Vibration of an Axially Loaded Non-uniform Spinning Twisted Timoshenko Beam Using Differential Transform, International Journal of Mechanical Sciences, Vol. 48, No. 11, pp. 1323~1331.
Attar, M. A., 2012, Transfer Matrix Method for Free Vibration Analysis and Crack Identification of Stepped Beams with Multiple Edge Cracks and Different Boundary Conditions, International Journal of Mechanical Sciences, Vol. 57, No. 1, pp. 19~33.
Hallauer, Jr. W. L. and Liu, R. Y. L., 1982, Beam Bending-torsion Dynamic Stiffness Method for Calculation of Exact Vibration Modes, Journal of Sound and Vibration, Vol. 85, No. 1, pp. 105~113.
Gupta, K. K., 1976, On a Finite Dynamic Element Method for Free Vibration Analysis of Structures, Computer Methods in Applied Mechanics and Engineering, Vol. 9, No. 1, pp. 105~120.
Lee, J. W. and Lee, J. Y., 2016, Development of a Transfer Matrix Method to Obtain Exact Solutions for the Dynamic Characteristics of a Twisted Uniform Beam, International Journal of Mechanical Sciences, Vol. 105, pp. 215~226.