形状记忆合金层合梁的非线性振动和分岔分析

mplitude-frequency response and bifurcation analysis of simple supported beam laminated with shape memory alloy (SMA) films under harmonic excitation are studied in this paper. The partial differential equation is deduced at first, of which discontinuous on space and non-smooth on time properties caused by piecewise linear characteristic of the bilinear constitutive model of superelastic SMA is pointed out, subsequently, the piecewise nonlinear hysteretic relationship between generalized restoring force caused by SMA layers and the beam deformation is deduced by subsection integration method along the axial direction of beam while the equation is discretized as the beam vibrating under the first mode by galerkin's method. Then amplitude-frequency response equation is solved by average method for the singe-freedom system. In order to investigate the influence of amplitude of harmonic excitation and elastic modulus of matrix on the amplitude-frequency response, the constrained bifurcation theory is introduced to access the different qualitative kinds of amplitude-frequency response curves.