The principal resonance of Duffing oscillator to combined deterministic and random external excitation was investigated. The random excitation was taken to be white noise or harmonic with separable random amplitude and phase. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The one peak probability density function of each of the two stable stationary solutions was calculated by the linearization method. These two one-peak-density functions were combined using the probability of realization of the two stable stationary solutions to obtain the double peak probability density function. The theoretical analysis are verified by numerical results.
This paper gives the direct formulas of stiffness matrixes of two'kinds of Kirchboff nonlinear elements under total-Lagrangecoordinate. For the first one, it includes not only the quadric terms of increments of strain and displacegnent but aiso.th e influence of rotations. For the second one, it is simpllfied ~ut its nonlinear ts cor~idered by taking into account the influence of axial force on the equilibrium equation in the litwar beam .theory. The nonlinear equation obtained from both of the above,said elements is SOlved by mixed Newton-Raphson method, and by comparing the results obtained from two kinds of nonlinear beam some important conclusions that we can know how to use them right are given in our paper.
Communicated by LIU Zeng-rong) Absl~act: The response of visco-elastic system to combined deterministic harmonic and random excitation was investigated. The method of harmonic balance and the method of stochastic averaging were used to determine the response of the system. The theoretical analysis was verified by numerical results. Theoretical analyses and numerical simulations show that when the intensity of the random excitation increase, the nontrivial steady state solution may change from a limit cycle to a diffused limit cycle. Under some conditions the system may have two steady state solutions and jumps may exist.
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