The bifurcate solutions and the stability criteria are obtained, Then the important relationships between vibration and the bifurcation parameter are revealed.

It couldbe found in the bifurcate equation of the ring catastrophic mold that ringsmight lose stability under pressure higher than critical pressure correspondingto wave numbers.

In order to predict the fatigue life of the cracked bodies, it is necessary, first of all, to find cot the whole process of the crack growth. Because the crack can not only kink out of the interface but also bifurcate in the laminated composites, its growing path is very complicated.

nonlinearity and discreteness, have been approximately solved by the above-mentioned means. The bifurcated solution leading to transition and turbulence is meaningful, which embraces all the effects of nonlinearity and discreteness, including shearing, stretching, rotation, dispersion, pressure-strain interaction and memory.

It is demonstrated that the system can exhibit unstable periodic 3 3 motion bifurcated from periodic 1 1 motion on the resonance condition, and the transition from subharmonic impacts to chaos is disscussed.

For η <1, the shock wave will be bifurcated to form a λ shock wave, under which two vortexes with different spin wise exist, and the pressure on the wall is lower than the case when η =1.

If the vibration amplitude is increased further, the streets bifurcate.

The coordination polyhedron of Ca2+ in ion I1 (CN = 7) is a distorted octahedron with a bifurcate vertex.

9) is a distorted pentagonal bipyramid with two O atoms of two nitrato ligands as two bifurcate vertices and five O atoms of five water molecules as the base.

In the crystal structure I, four bifurcate positions of Br and Cl in the tetrahedral anion [FeBr2Cl2]- are a randomly disordered mixture of these atoms.

In crystal, complexes I are united, due to the slip plane a, through bifurcate hydrogen bonds into infinite chains along the direction [100].

The asymptotic expressions of the steady state solutions bifurcated from the trivial solution near α=2 and α=5 are given.

And the stability of the nontrival solutions bifurcated from α=2 is studied.

The bifurcated self-excited oscillation modes are determined, and the effect on the branching of the Reynolds numbers Re and, moreover, the compliance and internal viscosity of the pipe material is analyzed.

The independent cation Na+ of the centrosymmetric binuclear complex anion I2 is coordinated by one bifurcated O atom of the disordered water molecule and by three N atoms of the SCN- ligands (including two bridging ligands).

Molecule-Based Magnets with 1D Chain Structure of Bifurcated H-Bonding: Syntheses, Structure, and Magnetic Properties

In this paper, the brachial artery branched from arch of aorta to radial artery is assumed to he an elastic tube with uniform cross-section and homogenous elastic modulus. The pressure waver, recorded at the crossing of the arch of aorta and the brachial artery are taken as the input to the segment of the brachial artery. The incoming waves are described by about 20 small. steps. Then the transient pressure expression at the radial artery is found under the linear assumption. The influence of the duration of...

In this paper, the brachial artery branched from arch of aorta to radial artery is assumed to he an elastic tube with uniform cross-section and homogenous elastic modulus. The pressure waver, recorded at the crossing of the arch of aorta and the brachial artery are taken as the input to the segment of the brachial artery. The incoming waves are described by about 20 small. steps. Then the transient pressure expression at the radial artery is found under the linear assumption. The influence of the duration of systole, the elastic modulus of arterial wall and the end resistance of the brachial artery on the pressure waves of radial artery is described in full. Comparisons with the experimental pressure waves obtained in test model is made and the experimental results show satisfactory agreement with theoretical results.

In the present paper, the resonant response of a vertical mooring-line in case of neutrally buoyancy, for a given harmonic longitudinal excitation, is discussed. The law of stress-strain is nonlinear. For the above case, a nonlinear equation and corresponding boundary conditions are given. Based on the singular perturbation method, a quasi-periodic solution is obtained. It exists bifurcations throns through the resonant region. The stability of the bifurcation solutions is investigated. The method in the present...

In the present paper, the resonant response of a vertical mooring-line in case of neutrally buoyancy, for a given harmonic longitudinal excitation, is discussed. The law of stress-strain is nonlinear. For the above case, a nonlinear equation and corresponding boundary conditions are given. Based on the singular perturbation method, a quasi-periodic solution is obtained. It exists bifurcations throns through the resonant region. The stability of the bifurcation solutions is investigated. The method in the present paper can be extended for solving the subharmonic response.

Solutions for creep buckling problems can be converted to elastic-plastic buckling analyses, as formerly explained by the ratio stress-strain method, which is based on the geometric similarities of isochronic creep curves at each constant temperature. Large deflection equilibrium equations and buckling equations of stiffened cylindrical shells are presented with their corresponding variational solution methods. For the ease of pure bending, a simplified method is proposed accounting for both bifurcation type...

Solutions for creep buckling problems can be converted to elastic-plastic buckling analyses, as formerly explained by the ratio stress-strain method, which is based on the geometric similarities of isochronic creep curves at each constant temperature. Large deflection equilibrium equations and buckling equations of stiffened cylindrical shells are presented with their corresponding variational solution methods. For the ease of pure bending, a simplified method is proposed accounting for both bifurcation type and limit type of buckling. Shells of various radius-thickness ratios and with several stiffening conditions are computed. The results are compared indirectly with some existing experimental data. .....