The exact solution of the differential equation of mtion of a single degree of freedom system with cubic forces in the form of a combination of different displacement, velocity and acceleration exposed to a periodic excitation, is determined directly in the frequency domain. For this purpose, the well known harmonic balance method is improved. A system of algebraic equations is derived in an explicit form and solved by a recurrent and simultaneous procedure for the case of monoharmonic and polyharmonic excitation respectively. In addition, the latter procedure is employed to analyse the random oscillations caused by a periodic excitation with different phase angles. Some nonlinear effects are illustrated within numerical examples, as for instance jumping phenomenon and nonstationarity of deterministic and random response.
Nonlinear Deterministic and Random Oscillations of Cubic Dynamical Systems
FRANCESCUTTO, ALBERTO
1993-01-01
Abstract
The exact solution of the differential equation of mtion of a single degree of freedom system with cubic forces in the form of a combination of different displacement, velocity and acceleration exposed to a periodic excitation, is determined directly in the frequency domain. For this purpose, the well known harmonic balance method is improved. A system of algebraic equations is derived in an explicit form and solved by a recurrent and simultaneous procedure for the case of monoharmonic and polyharmonic excitation respectively. In addition, the latter procedure is employed to analyse the random oscillations caused by a periodic excitation with different phase angles. Some nonlinear effects are illustrated within numerical examples, as for instance jumping phenomenon and nonstationarity of deterministic and random response.Pubblicazioni consigliate
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