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Simulation Study on Effect of Variable Curvature on the Modal Properties of Curved Cantilever Beams

  • Aqleem SiddiquiEmail author
  • Girish Dalvi
  • Akshay Patil
  • Surabhi Chavan
Conference paper
  • 13 Downloads
Part of the Lecture Notes in Mechanical Engineering book series (LNME)

Abstract

Curved beams are widely used in many engineering fields due to the high-strength capacity compared to their straight forms. It is essential that curved beams be analyzed for their modal properties as structures should have the natural frequency away from that which occurs in their working condition to avoid resonance. In the last few decades, many researchers had carried out investigation on several parameters of the curved beam. The present research work proposes a generalized mathematical equation for predicting mode shapes of curved cantilever beams, which take into account the change in length and curvature of the beam. Modeling of curved beam subjected to cantilever boundary condition is done by using ANSYS software. Twelve cases of cantilever beams, each having different curvature and length, were created. The mode shapes of the curved beams were obtained using the normalization method for each mode shape. The effect of the variation of the curvature on the mode shapes and natural frequency was analyzed for the first six transverse modes. It is found that the frequency of vibration and amplitude of vibration increase as the radius of curvature of the beam increases. Curve fitting equations for these mode shapes were obtained using MATLAB software. The generalized equation obtained for the mode shapes of the curved cantilever beams generates the mode shapes which are in good agreement with those obtained from ANSYS.

Keywords

Modal analysis Curved beams Variable curvature 

References

  1. 1.
    Lee BK, Wilson JF (1989) Free vibrations of arches with variable curvature. J Sound Vib 136(l):75–89Google Scholar
  2. 2.
    Gutierrez RH, Laura PAA, Rossi RE, Bertero R, Villaggi A (1989) In-plane vibrations of non-circular arcs of non-uniform cross-section. J Sound Vib 129(2):181–200CrossRefGoogle Scholar
  3. 3.
    Kang K, Bert CE, Striz AG (1995) Vibration analysis of shear deformable circular arches by the differential quadrature method. J Sound Vib 353–360Google Scholar
  4. 4.
    Oh SJ, Lee BK, Lee IW (1999) Natural frequencies of non-circular arches with rotatory inertia and shear deformation. J Sound Vib 219(1):23–33CrossRefGoogle Scholar
  5. 5.
    Raveendranath P, Singh G, Pradhan B (2000) Free vibration of arches using a curved beam element based on a coupled polynomial displacement field. Comput Struct 78:583–590Google Scholar
  6. 6.
    Yang F, Sedaghati R, Esmailzadeh E (2008) Free in-plane vibration of general curved beams using finite element method. J Sound Vib 318:850–867CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2021

Authors and Affiliations

  1. 1.Fr. C. Rodrigues Institute of TechnologyVashi, Navi MumbaiIndia

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