Techno Press
Techno Press

Structural Engineering and Mechanics   Volume 51, Number 3, August10 2014, pages 377-402
Minimum dynamic response of cantilever beams supported by optimal elastic springs
Ersin Aydin

Abstract     [Full Text]
    In this study, optimal distribution of springs which supports a cantilever beam is investigated to minimize two objective functions defined. The optimal size and location of the springs are ascertained to minimize the tip deflection of the cantilever beam. Afterwards, the optimization problem of springs is set up to minimize the tip absolute acceleration of the beam. The Fourier Transform is applied on the equation of motion and the response of the structure is defined in terms of transfer functions. By using any structural mode, the proposed method is applied to find optimal stiffness and location of springs which supports a cantilever beam. The stiffness coefficients of springs are chosen as the design variables. There is an active constraint on the sum of the stiffness coefficients and there are passive constraints on the upper and lower bounds of the stiffness coefficients. Optimality criteria are derived by using the Lagrange Multipliers. Gradient information required for solution of the optimization problem is analytically derived. Optimal designs obtained are compared with the uniform design in terms of frequency responses and time response. Numerical results show that the proposed method is considerably effective to determine optimal stiffness coefficients and locations of the springs.
Key Words
    optimal stiffness; beam vibrations; transfer functions; optimal support location; support stiffness
Ersin Aydin : Faculty of Engineering, Department of Civil Engineering, Nigde University, Nigde, Turkey

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