Structural Engineering and Mechanics

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An asymptotic analysis on non-linear free vibration of squarely-reticulated circular plates

  • Nie, G.H. (Department of Engineering Mechanics, Tongji University)
  • Published : 1999.12.25
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Abstract

In this paper an asymptotic iteration method is adopted to analyze non-linear free vibration of reticulated circular plates composed of beam members placed in two orthogonal directions. For the resulting linear ordinary differential equations in the process of iteration, the power series with rapid convergence has been applied to obtain an analytical solution for non-linear characteristic relation between the amplitude and frequency of the structure. Numerical examples are given, and the phenomena indicating hardening of such structures have been presented for the (immovable or movable) simply-supported and clamped circular plates.

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References

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  2. Snap-through buckling of single-layer squarely-reticulated shallow spherical shells continuously supported on springs vol.10, pp.2, 2000, https://doi.org/10.12989/sem.2000.10.2.111
  3. Nonlinear analysis of imperfect squarely-reticulated shallow spherical shells vol.50, pp.1, 2007, https://doi.org/10.1007/s11433-007-0001-6
  4. Non-linear Free Vibration of Single-layer Reticulated Shallow Spherical Shells vol.15, pp.1, 2000, https://doi.org/10.1260/0266351001494964
  5. Nonlinear free vibration of reticulated shallow spherical shells taking into account transverse shear deformation vol.39, pp.12, 1999, https://doi.org/10.1007/s10483-018-2399-9