Authors: Y.T. Yu, Wei Zheng Yuan, D.Y. Qiao

Abstract: Bifurcation of multi-layer microstructures subjected to thermal loading can be harmful
for reliability and stability of MEMS structures. In this paper, three imperfections of geometry,
coefficient of thermal expansion and thermal loading were introduced to investigate their effects on
structural bifurcation by finite element simulation. Results show that bifurcation is strongly
influenced by the imperfections. With larger deviation of imperfections, it results in a decreasing
temperature to trigger the bifurcation and a gradual beginning of it.

276

Authors: Masami Kobayashi, Koji Uetani, Tomohiro Mikami

Abstract: The symmetry limit theory for 3-D continua developed by the authors, is applied to
predictions of the occurrence limit of nonuniform strain in cylinders subjected to cyclic torsion.
Bifurcation analysis of a steady-state path, which was defined as a continuous sequence of steady
states generated under continuous increasing amplitude cyclic loading, is performed for the cylinder
model. The deformation mode with very short wavelength in the circumferential direction is
obtained, analogous to that in the internal buckling of a rigidly confined continuum shown by Biot.
It is shown that this circumferential short-wave mode occurs at much smaller amplitude than the
bifurcation under monotonic torsion.

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Authors: Zhi Wen Zhu, Chang Wei Sui, Jia Xu

Abstract: In this paper, the nonlinear dynamic characteristics of vehicle semi-active suspension
system with SMA spring were studied in hysteretic nonlinear theory. SMA spring was applied in
semi-active suspension system to control vibration. Von del Pol hysteretic cycle model were
introduced to set up a new kind of continuous SMA strain-stress model, based on which the nonlinear
dynamic model of vehicle semi-active suspension system with SMA spring was developed. The
first-order nonlinear approximate solution of suspension system was obtained, the stability and
bifurcation characteristic of suspension system were analyzed. The result of analysis shows that the
nonlinear stiffness parameters can not cause the bifurcation of suspension system, and the qualitative
change of the dynamic characteristic of suspension system has relationship with the nonlinear
damping parameters. Finally, the result of analysis was proved by simulation.

265

Authors: Yu Zhi He, Chang Yun Liu, Zhen Hua Hou, Guang Kui Zhang, Xing Hua Chen, Zi Chen Lin, Jin San Ju

Abstract: The out-of-plane secondary bifurcation buckling load-displacement equilibrium paths of the elastic circle pipe arch with and without out-of-plane brace at the top of the arch are traced using a new numerical tracing strategy. The out-of-plane secondary bifurcation buckling loads of the arch with the same sections and different rise-span ratios are obtained under the concentrated load at the top of the arch and the full span uniformly distributed load, which are compared with out-of-plane linear buckling load and in-plane primary buckling load. The calculation results show: for the same section circle pipe arches without the out-of-plane brace and under the concentrated load at the top the arch, the out-of-plane secondary buckling load is always less than the in-plane primary buckling load and the out-of-plane buckling will occur before the in-plane primary buckling. The out-of-plane secondary bifurcation buckling load of the arch with 0.2 rise-span ratio is the biggest. The bigger the rise-span ratio is, the bigger the difference between out-of-plane and in-plane buckling load. When the arch is subjected to full span uniformly distributed load, the out-of-plane buckling will also occur before the in-plane primary buckling and the out-of-plane secondary bifurcation buckling load of the arch with 0.4 rise-span ratio is the biggest. The difference between out-of-plane and in-plane buckling load of the arch with 0.2 rise-span ratio is the biggest. For the circle pipe arch with the out-of-plane brace at the top of the arch, the out-of-plane buckling load of the arch with 0.4 rise-span ratio is the biggest under the two load conditions. The brace can raise the out-of-plane buckling load significantly especially for the arch with big rise-span ratio and under full span load. The out-of-plane buckling will occur before the in-plane primary buckling when the arch is under full span uniformly distributed load. The out-of-plane buckling will occur before the in-plane primary buckling only when the arch is under concentrated load and the rise-span ratio of the arch is less than 0.3. No matter there is or not brace for the arch, the ultimate load carry capacity of the arches increase a little bit after the out-of-plane secondary buckling occurs.

271

Authors: Ze Jin Shang, Zhong Min Wang

Abstract: The recovery force of shape memory alloy spring is described by using polynomial constitutive equation. The nonlinear dynamic model of forced vibration for the shape memory alloy spring oscillator is derived. Numerical simulations are performed by a fourth-order Runge-Kutta method. The bifurcation diagram and Lyapunov-exponent spectrum are presented while the dimensionless temperature, the dimensionless damping coefficient or the dimensionless amplitude of exciting force is varied respectively, thus the bifurcation of the system is investigated. Furthermore, the periodic and chaotic motions of the system are analyzed by means of the displacement time history diagram, the phase portrait, the Poincare section diagram and the power spectrum with different parameters. The results show that the periodic or chaotic motion of the system occur by changing temperature, damping coefficient and amplitude of exciting force, thus the vibration of the system could be controlled.

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