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Large amplitude free vibration analysis of tapered Timoshenko beams using coupled displacement field method

Rajesh K., Saheb K. M.

International Journal of Applied Mechanics and Engineering

2018

Vol. 23, no. 3

673--688

Tapered beams are more efficient compared to uniform beams as they provide a better distribution of mass and strength and also meet special functional requirements in many engineering applications. In this paper, the linear and non-linear fundamental frequency parameter values of the tapered Timoshenko beams are evaluated by using the coupled displacement field (CDF) method and closed form expressions are derived in terms of frequency ratio as a function of slenderness ratio, taper ratio and maximum amplitude ratio for hinged-hinged and clamped-clamped beam boundary conditions. The effectiveness of the CDF method is brought out through the solution of the large amplitude free vibrations, in terms of fundamental frequency of tapered Timoshenko beams with axially immovable ends. The results obtained by the present CDF method are validated with the existing literature wherever possible.

Large amplitude free vibration analysis of tapered timoshenko hinged-hinged beam using coupled displacement field method

Korabathina R., Koppanati M. S.

Vibrations in Physical Systems

2017

Vol. 28

art. no. 2017007

Tapered beams are more efficient compared to uniform beams as they provide a better distribution of mass and strength and also meet special functional requirements in many engineering applications like architecture, aeronautical, civil, mechanical, automobile, nuclear and robotics. The authors proposed a new method called Coupled Displacement Field (CDF) method in which the displacement field such as total rotation is assumed such that the assumed displacement must satisfy the kinematic and force boundary condition of the beam. The lateral transverse displacement is derived from the coupling equation which is derived from the static equilibrium conditions of the beam. By the application of principle of minimum total potential energy for different beam boundary conditions, the fundamental frequency parameter value is calculated in terms of taper ratio and slenderness ratio for various maximum amplitude ratios of the tapered Timoshenko shear flexible hinged-hinged beam boundary condition.