Papers by Keyword: Nonlinearity

Abstract: This paper presents theory, experiments and numerical approaches suitable for the solution of straight plane beams rested on an elastic (Winkler's) foundation, including nonlinearities. The nonlinear dependence of the reaction force on displacement in the foundation (i.e. the experimental data) can be described via bilateral linear or bilateral linear + cubic or bilateral linear + cubic + quintic approximations, or by unilateral approximation (i.e. by using the Least Squares Method). These applications lead to linear or nonlinear differential 4^th-order equations. For solutions of nonlinear problems of mechanics, the Finite Difference Method (i.e. the Central Difference Method) and boundary conditions are applied. The solution and its evaluation is performed in second part of this article.

Abstract: Usually, a large horizontal force will be generated to the pier in the construction process, which may induce significant influence on the pier‘s safety, especially in the case of the bridges with high piers and long span. Some cracks ermerged in the foot part of a pier in the construction stage and a horizontal force was believed to have been load on it, hence its reliability was douted.The pier was simulated with virtual laminated element program, and its mechanical performance under a horizontal force was calculated with both geometrical and material nonlinearity are considerd, thus its whole loading and failure process was illustrated and the pier’s safety was assessed.

Abstract: In this paper, the magneto-elastic nonlinear random vibration of a clamped rectangular thin plate in magnetic field is studied. According to the magneto-elastic theory of plates and shells and the theory of structural random vibration, the magneto-elastic nonlinear random vibration equation of a clamped rectangular thin plate in a magnetic field is derived. Then the nonlinear random vibration equation is transferred into the Ito differential equation, and the Ito differential equation is solved using FPK equation method. Thus the numerical characteristics of displacement response and velocity response of the rectangular thin plate are obtained. Finally, through a numerical example, the influences of magnetic field parameters on the numerical characteristics are discussed, and some methods which can be used to effectively control the random vibration responses of the plate are given.

Abstract: It is introduced that three main factors cause geometric nonlinear effects of long span cable-stayed bridge: large displacement effect, cable sag effect, and the combination of bending moment and axial force effect. The iteration method of geometrical nonlinear problem is also introduced. The bridge deformation was calculated by establishing a plane truss finite element model of a long-span single tower cable-stayed bridge under consideration of nonlinearity and compared with that done with linear method. It is concluded that nonlinearity influenced differently to the bending moment of main girder, the displacement of tower root and the vertical displacement of girder.

Abstract: Firstly, the origin and mathematical mechanism of freeplay nonlinearity ,cubic nonlinearity, hysteresis nonlinearity was analyzed in this paper , and the importance of nonlinear aeroelasticity on structure was pointed out .On the current system of nonlinear aeroelasticity for the method of flutter analysis was summarized. Meanwhile on the mechanism of geometric nonlinearity and analytic methods have been studied, the future direction of the nonlinear aeroelasticity was concluded .

Abstract: To improve the vehicle comfort, Magnetorheological damper is installed on the vehicle suspension system. So the system with hysteretic nonlinearity is a typical nonlinear system. First, the behavior of system under the periodic excitation force is analyzed, and the possibility of chaos is proved in the paper. Then, with piecewise-quadric function employed, the nonlinear feedback controller can be used to control the chaos. At the same time, Melnikov’s method is used to gain coefficient of controller. Numerical simulation shows that this method can the effectively guide chaotic motions toward regular motions. This control method is quite simple and effective without affecting the system properties. The results may supply theoretical bases for analysis and optimal design of vehicle suspension systems.

Abstract: Layered shallow shells based on rectangular plan variation form are considered. Middle surface of shells depends on the high of supporting arches, the boundary conditions, and the thickness. Form of shall variation on the critical force coefficient and stress of shell are investigate with the help of Bubnov-Galerkin method. The calculation method has done in the Maple program complex.

Abstract: Nonlinear dielectric lines have been tested for use in RF generation. Although they have presented a reasonable success in the frequency range between 250 and 400 MHz, their main limitation is the dielectric losses of barium titanate (BT) tiles used as nonlinear medium in these lines, which prevents from achieving higher frequencies. The solution for this appears to be the search for a new dielectric. Herein, we are proposing the use of a piezoelectric titanate-based ceramics known as PZT (lead zirconate titanate), which appears to have lower dielectric losses than BT slabs. In this paper, loss characterization tests of the PZT ceramics are compared with BT in the MHz frequency range. Also, we have investigated and compared the nonlinearity properties of the dielectrics by varying the DC applied voltage and temperature.

Abstract: A large horizontal force will be generated to the pier when the movable die carrier walks to the next span, especially for the high-pier bridges. thus a horizontal deflection will be produced as well as cracks developed. With solid degenerated virtual laminated element program, considering both geometrical and material nonlinearity, the mechanical performance of the pier under a horizontal force on the top of the pier is simulated and illustrated, and the cracks emerged at the bottom part of a high pier in the process of the movable die carrier walking to the next span is analyzed. The results show that when the cracks emerged, the stress of the bars and the stress of the concrete in the compression zone is quite small, hence the safety of the bridges in the construction stage is confirmed.

Abstract: Bearing capacities and operating characteristics cover of a building deteriorate since time. Reconstruction of shallow shells cover by increase of their thickness in the center or at the edge. Critical force and stress of shell are considered with the geometric nonlinearity consideration. Vertical static loading and various types of a fixing are investigated. The method allows to describe various forms of shells with defects.