CHEN Xiao-chao, MAO Qi-bo, XUE Xiao-li. Free Vibration Analysis of Elastic Foundation Euler Beams With Different Discontinuities Based on Generalized Functions[J]. Applied Mathematics and Mechanics, 2014, 35(1): 81-91. doi: 10.3879/j.issn.1000-0887.2014.01.009
 Citation: CHEN Xiao-chao, MAO Qi-bo, XUE Xiao-li. Free Vibration Analysis of Elastic Foundation Euler Beams With Different Discontinuities Based on Generalized Functions[J]. Applied Mathematics and Mechanics, 2014, 35(1): 81-91.

# Free Vibration Analysis of Elastic Foundation Euler Beams With Different Discontinuities Based on Generalized Functions

##### doi: 10.3879/j.issn.1000-0887.2014.01.009
Funds:  The National Natural Science Foundation of China(51265037); The Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry
• Rev Recd Date: 2013-09-23
• Publish Date: 2014-01-15
• The general governing differential equations for the vibration of elastic foundation Euler-Bernoulli beams with different discontinuities subject to axial forces were established based on generalized functions. For each discontinuity at a given location, a basic modal displacement function (Dirac delta function) starting at that location was introduced. The differential equations were then solved by means of Laplace transformation. Unlike the classical vibration solutions to problems of beams with discontinuities, the generalized solution was in a single unified expression for the whole beam. Due to unification of the modal function and degeneration of the compatibility conditions, solution of the eigenvalues was greatly simplified. Finally, the free vibration problems of (a) an elastic foundation beam with multiple masses and corresponding rotary inertias, and (b) an elastic foundation beam with multiple cracks under axial force, were solved with the proposed method. Results show that the present method is accurate and effecient for free vibration analysis of beams with different discontinuities.
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