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Structural Engineering and Mechanics Volume 62, Number 2, April25 2017 , pages 171-178 DOI: https://doi.org/10.12989/sem.2017.62.2.171 |
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Vibration analysis of a beam on a nonlinear elastic foundation |
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M.M. Fatih Karahan and Mehmet Pakdemirli
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| Abstract | ||
| Nonlinear vibrations of an Euler-Bernoulli beam resting on a nonlinear elastic foundation are discussed. In search of approximate analytical solutions, the classical multiple scales (MS) and the multiple scales Lindstedt Poincare (MSLP) methods are used. The case of primary resonance is investigated. Amplitude and phase modulation equations are obtained. Steady state solutions are considered. Frequency response curves obtained by both methods are contrasted with each other with respect to the effect of various physical parameters. For weakly nonlinear systems, MS and MSLP solutions are in good agreement. For strong hardening nonlinearities, MSLP solutions exhibit the usual jump phenomena whereas MS solutions are not reliable producing backward curves which are unphysical. | ||
| Key Words | ||
| beam on elastic foundation; direct perturbation method; Multiple Scales Lindstedt Poincare (MSLP) method; forced vibrations; strongly nonlinear systems | ||
| Address | ||
| M.M. Fatih Karahan and Mehmet Pakdemirli: Department of Mechanical Engineering, Manisa Celal Bayar University, Muradiye 45140, Manisa, Turkey | ||