Free Vibration Analysis of Elastically Connected Beams with Step

Subject Areas : Applied Mechanics

H  Nayebi ¹ (Department of Mechanical Engineering, Arak Branch, Islamic Azad University, Arak, Iran)
M.M  Najafizadeh ² (Department of Mechanical Engineering, Arak Branch, Islamic Azad University, Arak, Iran)

Received: 2023-03-29 Accepted : 2023-05-24 Published : 2023-09-01

Keywords: Parallel beams, Winkler-type elastic layer, Differential transform method, Stepped beam,

Abstract :

In this study, free vibration of stepped beam which is parallel to a uniform beam with same length and elastically connected to it, is considered. Euler-Bernoulli beam theory has been applied to drive equations of motion, abrupt change in height of beam considered as step and Winkler-type elastic layer model serve as connection between beams. The differential transform method (DTM) is applied to determine dimensionless frequencies and mode shapes. In the case of two uniform parallel beams accuracy of solution is verified by comparing with results reported by other methods. It is assumed all supports have one type and fully clamped and fully hinged supports considered for boundary conditions. The effects of different parameters such as: step location and ratio, connecting layer coefficient and boundary conditions on dimensionless frequencies and mode shapes investigated and discussed. This problem handled for first time in present study and results are completely new.

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