Papers by Keyword: Nonlinear Stability

Abstract: On the basis of nonlinear features analysis of restoring torque, damping torque and especially hull deformation, a nonlinear roll equation of rotary molding boats has been established. The equation includes elastic deformation term which differs from existing ones usually borrowing ideas of steel boats. By numerical simulation, it’s found roll frequency and velocity increase when elastic deformation occurs, i.e. the roll stability margin shrinks which can underlie how to amend the stability evaluation criteria on rotary molding boats.

Abstract: The weakly nonlinear stability of a thin Ostwald de-Waele power-law fluid during spin coating is investigated. Long-wave perturbation analysis is proposed to derive a generalized kinematic model of the physical system with a small Reynolds number. The study reveals that the rotation number generates a destabilizing effect either in pseudoplastic fluid or in dilatant fluid. Further, it is shown that the degree of power-law index n plays a vital role in stabilizing the film flow.

Abstract: The nonlinear stability of three main piers of Xiniu bridge was analysed with RM Bridge V8i in this paper. The change of high pier’s nonlinear stability with the strength decline of high pier’s local concrete and variation of high pier’s height were also respectively researched.The results show that nonlinear stability coefficients will be lower if one segment of high pier’s concrete strength declines. It also indicate that the nonlinear stability coefficients drop is related to the decrease of the concrete strength, the distance between the segment at the bottom of pier, and the height of pier.

Abstract: The linear and nonlinear stability of continuous rigid frame bridge with thin-wall piers is analyzed by using the current FEM software. Linear stability analysis indicates that coefficient of stability in cantilever stage is poorest. Two aspects are included in nonlinear stability analysis. The first one, only geometric nonlinearity is considered and the other one, geometric nonlinearity and material nonlinearity are considered simultaneously. The results show that material nonlinearity is a factor to stability coefficient that can not be overlooked. Considered the dual non-linearity, the stability coefficient descends consumedly.

Abstract: Based on the Von Karman large deflection theory of shallow shell, the problem of nonlinear stability of symmetrically FGM shallow conical shells under the action of mechanical and thermal loads is investigated. The nonlinear governing equation under the united action of mechanical and thermal loads of FGM shallow conical shells whose physical parameters change with the power rate is derived and solved by the modified iteration method. The nonlinear characteristic relation of load, deflection and temperature is obtained. The extremum buckling principle is employed to determine the critical buckling load. The influences of gradient constants, geometric parameters and temperature differences on buckling are discussed as well.

Abstract: Based on theory of Lematire’s equivalent strain of the damage and with the damage of bars of the shallow reticulated spherical shell, on the basis of the nonlinear dynamical foundational equations and introducing dimensionless quantity of shells with uniform thickness, the nonlinear dynamic equation of the shallow spherical shells with initial damage were established by the method of quasi-shells. Then, the critical conditions of that chaos motion of the structure with initial damage are given by the Melnikov function. Finally, further using the digital simulation plotted the plane phase and it approved existence of the chaotic motion. It is found that the natural frequency of shallow reticulated spherical shells considering initial damage becomes bigger and the critical value of chaotic motion is smaller.

Abstract: Based on the nonlinear bending theory of double-deck reticulated shallow shells, the nonlinear buckling problem of cylindrical double-deck reticulated shallow shells under wind pressure is studied. An analytic solution for simply supported edges is obtained by using Galerkin’s method. The results of numerical calculations are presented in diagram and table, which show the influence of geometrical parameters on the buckling behavior.

Abstract: The nonlinear chatter in grinding machine system is discussed analytically in the paper. In higher speed grinding process, the self-excited chatter vibration is mostly induced by the change of grinding speed and grinding wheel shape. Here the grinding machine tool is viewed as a nonlinear multi-D.O.F. autonomous system, in which hysteretic factors of contact surfaces are also introduced. Firstly, the DOFs of the above system are reduced efficiently without changing its dynamic properties by utilizing the center manifold theorem and averaging method. Then, a low dimensional system and corresponding averaging equations are obtained. The stability and bifurcation of chatter system are discussed on the base of deduced averaging equations. It is proved that chatter occurs as a Hopf bifurcation emerging from the steady state at the origin of system. The theoretical analyses on the multi-DOF chattering system will lead to further understanding of the nonlinear mechanisms of higher speed grinding processes.