Structural Engineering and Mechanics

  • 제51권3호
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  • Pages.377-402
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  • 2014
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Minimum dynamic response of cantilever beams supported by optimal elastic springs

  • Aydin, Ersin (Faculty of Engineering, Department of Civil Engineering, Nigde University)
  • 투고 : 2012.04.17
  • 심사 : 2014.04.04
  • 발행 : 2014.08.10
⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

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피인용 문헌

  1. Optimization of elastic spring supports for cantilever beams vol.62, pp.1, 2014, https://doi.org/10.1007/s00158-019-02469-3
  2. Exact closed-form solution for free vibration of Euler-Bernoulli and Timoshenko beams with intermediate elastic supports vol.213, pp.None, 2014, https://doi.org/10.1016/j.ijmecsci.2021.106842