Narrow Results

This paper focuses on the classification of the bifurcation modes of a Duffing system under the combined excitations of constant force and harmonic excitation. The Harmonic Balance method combined with the arc-length continuation is used to obtain the periodic solutions of the system, and the Floquet theory is employed to analyze the stability of the corresponding solutions. Accordingly, the frequency-response curves affected respectively by the constant force and the magnitude of the harmonic excitation are analyzed to show the basic dynamical properties of the system. Afterwards, the bifurcation investigations are carried out with the aid of the two-state variable singularity method. It is derived that there are a total of six different types of bifurcation modes due to the effects of the constant force and the magnitude of the harmonic excitation. At last, the effects of the nonlinearity parameter and the damping ratio on the bifurcation modes of the system are also discussed. The results obtained in this paper extend the findings in reference that the system can have markedly three types of frequency-response curves: with only one solution, or with maximum three or five solutions for a certain excitation frequency, and contribute to a better understanding of the significant influence of the constant force.

Constant force component is very useful in medical device, such as forceps with constant force, which may prevent soft tissues from injures due to overloading. This paper studied the optimization procedure in constant force component for superelastic shape memory alloy, and tried to find the rule of obtaining constant force within a relatively large deformation range for superelastic C-shaped shape memory alloy sheet. The optimization concept of combing finite element analysis in ANSYS with genetic algorithm in MATLAB was presented for designing constant force component using superelastic SMA. The computational optimization and experimental results of the C-shaped shape memory alloy sheet showed that the proposed optimization method was potential for superelastic shape memory alloy. The optimization results were consistent with the experimental results. It was demonstrated that constant force could be obtained within a relatively large deformation range by varying the initial shape of the superelastic SMA component.