Geometrically non-linear free and forced vibration of a shallow arch
The purpose of this present work is to investigate the geometrical non-linearity in free and forced vibration of a shallow arch elastically restrained at the ends. The non-linear governing equilibrium equation of the shallow arch is obtained after the Euler Bernoulli theory and the Von Karman geomet...
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| Main Authors: | , , , , |
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| Format: | article |
| Language: | EN |
| Published: |
JVE International
2021
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| Subjects: | |
| Online Access: | https://doaj.org/article/f6919096fc7d4024b64a3f291ff46934 |
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| Summary: | The purpose of this present work is to investigate the geometrical non-linearity in free and forced vibration of a shallow arch elastically restrained at the ends. The non-linear governing equilibrium equation of the shallow arch is obtained after the Euler Bernoulli theory and the Von Karman geometrical non-linearity assumptions. After applying the ends conditions, the eigenvalues problem of the generalized trancendant equation have been determined iteratively using the Newton-Raphson algorithm. The kinetic and total strain energy have been discretized into a series of a finite spatial functions which are a combination of linear modes and basic function contribution coefficients. Using Hamilton’s principle energy and spectral analysis, the problem is reduced into a set of non-linear algebraic equations that solved numerically using an approximate explicit method developed previously the so-called second formulation. Considering a multimode approach, the effect of initial rise and concentrated force on non-linear behaviour of system has been illustrated in the backbone curves giving the non-linear amplitude-frequency dependence. The corresponding non-linear deflections and curvatures have been plotted for various vibration amplitudes. |
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