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1/2 SUBHARMONIC SOLUTION OF A CIRCULAR PLATE WITH QUADRATIC NONLINEAR

Yinshan Li

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Abstract

The nonlinear dynamic equation of a circular plate subject to a harmonic force is derived, with the viscoelastic effects taken into account. A superpositive iterative harmonic balance method(SIHB) is presented for the steady state analysis of strongly nonlinear oscillators. In a periodic oscillation, the periodic solutions can be expressed in the form of basic harmonics and bifurcate harmonics. Thus, an oscillation system which is described as a second order ordinary differential equation, can be expressed as basic differential equation with basic harmonics and the incremental differential equation with bifurcate harmonics. The 1/2 superharmonic solution for a circular plate is investigated by using SIHB. The SIHB is compared with the numerical integration method. Finally, asymptotical stability of the 1/2 subharmonic oscillations is inspected.

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What this paper is about

The nonlinear dynamic equation of a circular plate subject to a harmonic force is derived, with the viscoelastic effects taken into account. A superpositive iterative harmonic balance method(SIHB) is presented for the steady state analysis of strongly nonlinear oscillators. In a periodic oscillation, the periodic solutions can be expressed in the form of basic harmonics and bifurcate harmonics. Thus, an oscillation system which is described as a second order ordinary differential equation, can be expressed as basic differential equation with basic harmonics and the incremental differential equation with bifurcate harmonics. The 1/2 superharmonic solution for a circular plate is investigated by using SIHB. The SIHB is compared with the numerical integration method. Finally, asymptotical stability of the 1/2 subharmonic oscillations is inspected.

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Available abstract

The nonlinear dynamic equation of a circular plate subject to a harmonic force is derived, with the viscoelastic effects taken into account. A superpositive iterative harmonic balance method(SIHB) is presented for the steady state analysis of strongly nonlinear oscillators. In a periodic oscillation, the periodic solutions can be expressed in the form of basic harmonics and bifurcate harmonics. Thus, an oscillation system which is described as a second order ordinary differential equation, can be expressed as basic differential equation with basic harmonics and the incremental differential equation with bifurcate harmonics. The 1/2 superharmonic solution for a circular plate is investigated by using SIHB. The SIHB is compared with the numerical integration method. Finally, asymptotical stability of the 1/2 subharmonic oscillations is inspected.

Key concepts: Subharmonic function, Harmonics, Harmonic balance, Mathematics, Mathematical analysis, Nonlinear system, Oscillation (cell signaling), Harmonic

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