2013, 11(4):289-294. DOI: 10.6052/1672-6553-2013-048
Abstract:Based on the theory of impulsive differential equations, this paper studied the asymptotic stability of hyperchaotic complex Lü system under the stochastic impulsive signal. Some criteria were derived for the stabilization of the complex system via an impulsive method. And we also presented the estimate of the stable regions for the equal impulsive intervals. Numerical simulations demonstrated the effectiveness of the theoretical results and also showed that the method was robust against the noise.
2013, 11(4):295-300. DOI: 10.6052/1672-6553-2013-077
Abstract:The mechanical system′s intrinsic structure may influence the long time computation′s accurate and stability. The discrete variation integrators can conserve the energy momentum and the symplectic structure of the system. Combined with the discrete variation principle, the discrete variation integrator method can be obtained through the process of discretization varaiton and integration. This is a recursive algorithm that the time history of the parameters only need the initial condition. According this theory, a sympletic-momentum integrator can be formulated for the holonomic constraint Lagrange system. This method can get the recursive formula of the attitude and the angle velocity direct form the discrete Lagrange function and don′t need complicated iterative computation. The discrete variation integrator method explored in this paper is based on the first Lagrange function. The spherical pendulum is a Lagrange system with holonomic constraints. The simulation result states that the energy be conserved in a long time simulation, and the accuracy of the computation presents a quadratic relation with the time step. The angle velocity and the attitude also present different character under two different algorithm.
2013, 11(4):301-305. DOI: 10.6052/1672-6553-2013-067
Abstract:The collinear collision dynamics of the three ball chain is able to demonstrate one of the difficulties of the problem of collisions of multi body system:non unique solution.The paper presents three ball chain collision is modeled by Hertz contact, numerical algorithm is found to solve the contact model, the finite element model is used to verified it.Research shows:compared with linear model, the contact forces between three balls by Hertz model are closer to the finite element results;based on the Hertz model,the change of the contact forces is analyzed during the collision process;it is researched that the stiffness ratio and mass ratio affect the state of motion of each ball after the collision,and study the established condition of two girid body models collision orders.
2013, 11(4):306-313. DOI: 10.6052/1672-6553-2013-044
Abstract:It is difficult to express analytically potential mode shapes and free surface mode shapes of sloshing liquid in cylindrical container in microgravity. To discover nonlinear behaviors, generally, potential mode shapes and free surface mode shapes in normal gravity are taken to approximate those in microgravity. The sloshing of liquid in cylindrical container in microgravity is analyzed using mode expanding method. Dimensionless form of nonlinear dynamic equations of the fluid structure coupling system are derived by Lagrange principle and numerically solved. It is found that this coupled system presents resonance in some ranges of parameters of the external excitation. If the system does not resonate, in plane modes and out plane modes behave respectively the same kind stable motion and their types of stable motion change when parameters of the external excitation are different. These types of stable motion contain stillness, periodic motion, quasi periodic motion and chaotic motion.
2013, 11(4):314-319. DOI: 10.6052/1672-6553-2013-038
Abstract:The transverse vibration of an axially moving viscoelastic sandwich beam with small deflection was investigated. Based on the Kelvin differential constitutive equation, the transverse controlling equation was established. The eigenfunctions of the axially moving viscoelastic sandwich beam with simple supported boundary condition were obtained by using Galerkin truncation and complex mode analysis. The influence of the ratio of the core layer, axially moving velocity and axial tension on the natural frequencies and critical velocity were discussed by using numerical method.
2013, 11(4):320-328. DOI: 10.6052/1672-6553-2013-047
Abstract:In this study, based on the complete nonlinear mathematical model obtained from the generalized Hamilton principle of isotropic thermoelastic beams with voids and the aerodynamic pressure loading presented by the first order modified piston theory, the governing differential equations and the deterministic conditions of solutions for a thermoelastic beam with fixed ends and located in a high speed or an ultra high speed flow are presented, which are expressed by the axial and lateral displacements and the two “moments” defined by changes of the volume fraction of voids and the temperature field. In order to consider the nonlinear aeroelastic characteristic of the thermoelastic beam with voids subjected to the transverse loading and aerodynamic pressure loading, the differential quadrature method is applied to discretize the governing differential equations on the spatial domains, and a system of ordinary differential equations with respect to time is yielded and solved through the fourth order Runge Kutta method. From this, the aeroelastic characteristic of the beam is studied and the effect of parameters is considered as well.
2013, 11(4):329-335. DOI: 10.6052/1672-6553-2013-042
Abstract:The rigid flexible coupling dynamics of a rectangular functionally graded thin plate undergoing large overall motion is investigated.Based on continuum medium mechanics, The governing equations of motion are established using assumed mode method and Lagrange′s equations, for the rectangular functionally graded thin plates undergoing large overall motions. The second order coupling deformation variable, which is ignored in traditional method, is considered in this paper. The dynamics of cantilever plates with different functionally graded coefficiernt undergoing rotation are simulated and the deformation results of first order approximation model are compared with those of traditional zero order appoximation model. It is shown that, as the rotating velocity increase,the traditional model divergences while the first order model converges.The first order model describes the dynamic behavior of the system better. The effects of the functionally graded index on the deformation of plates are studied. Studies have shown that, with the increases of the functionally graded index, the greater the lateral deformationthe of plate. By solving the natural frequencies of rotating FGM plate under a constant speed,the impact of of changes in the material composition of FGM plates on the plate vibration characteristics is further studied.
2013, 11(4):336-342. DOI: 10.6052/1672-6553-2013-040
Abstract:Free vibration characteristics of viscoelastic sandwich circular plate is presented. Based on the basic assumption of elastic thin plate and Kelvin Viogt constitutive equation, the vibration control equation of the viscoelastic circular plate is established. The analytical expression of natural frequency and modes of free vibration is derived by employing the method of separated variables. The natural frequency of fixed and simply supported sandwich circular plate are calculated respectively. The results are compared with finite element method. The influence of core ratio on natural frequency and damping coefficient is discussed. Conclusions are as follows: (1) The natural frequency increases at first, then decreases with the increase of core ratio. It is more obvious for high order frequency. (2) The damping coefficient always increases with the increase of core ratio.
2013, 11(4):343-349. DOI: 10.6052/1672-6553-2013-091
Abstract:With the high pressure rotor system of an aero engine as the object of study, in the context of uneven radial distribution of steady state temperature field, this paper establishes FEM model of 3D solid elements of a high pressure rotor system and vibration equation of thermal structural coupling model of 3D solid rotor system in the steady state temperature field, it first makes an analysis of the steady state temperature field by indirect coupling method using thermal structural dynamic coupling theory, and then makes a static analysis to generate thermal stress, and then generates global stiffness matrix by setting prestress option to make a modal analysis, and finally makes an analysis of coupling response of unbalance and thermal bending by modal superposition method to realize thermal structural dynamic coupling computation. Through the analysis of the effect of steady state temperature field on steady state response of typical stage discs and analysis of steady state response of coupling of unbalance and thermal bending, this paper finds coupling response has a big effect on vibration response of different stage discs of the rotor system.
2013, 11(4):350-356. DOI: 10.6052/1672-6553-2013-054
Abstract:In consideration of shear deformation and shear lag effects, A new warping displacement mode of T beams is chosen to meet the axial self equilibrium condition for corresponding stress, this paper proposes an approach of analyzing the dynamic characteristics of thin walled T beams with wide flanges generally used in engineering. three generalized displacement functions are employed in analyzing dynamic response of the thin walled T beams by calculus of variations, the differential equations and the corresponding natural boundary conditions of the T beams are induced based on the minimum potential principle, and the dynamic characteristics of thin walled T beams are discussed. The calculation examples compare the finite solid element solutions with the analytical solutions, and the analytical solutions in consideration of the axial self equilibrium condition is still more identical with the finite solid element solutions, the formulas obtained in this study strengthen the theoretical foundation for further research of dynamic characteristics of the structures.
2013, 11(4):357-362. DOI: 10.6052/1672-6553-2013-041
Abstract:At present, the main task of designing a mounting system of automotive engine powertrain is to select appropriate stiffness, position and angle of mounting components so that free-vibration modal frequency of the mounting system can avert from the exciting-force frequency at the idle speed of the engine and the natural frequency of vibration of the vehicle body and that the decoupling degree of each mode shape is increased as far as possible, so as to improve the vibration-isolation effect of the mounting system. The design of a mounting system based on strict decoupling at predetermined frequencies is to make the modal frequencies of the designed mounting system completely equal to the frequencies predetermined in accordance with the frequency planning of automotive design, and to enable strict decoupling of each mode shape of each mode, i.e., the decoupling degree of vibration energy in every direction equals to 1. Based on a free-vibration equation for a mounting system, this paper presents an equation system for designing a mounting system with strict decoupling at predetermined frequencies, provides a solving method for this equation system by using the theory of generalized inverse matrix or method of constructing function, so as to provide an optimal design method more efficient and simpler than the current modal optimization method of mounting system. Relevant example has validated the correctness of equations and solving method of the strict-decoupling design at predetermined frequencies.
2013, 11(4):363-368. DOI: 10.6052/1672-6553-2013-037
Abstract:The CFD/CSD algorithm which is a two way fluid structure coupling algorithm is used to study the aeroelastic coupliing characteristics of plate structures. Firstly, the CFD/CSD algorithm is employed to compute the flutter critical velocity of plate structure. The results obtained by the CFD/CSD are verified by the comparison with the experiment results in the open literature. Secondly, the aeroelastic characteristics for three dimensional plate structures with simply supported and clamped edges are analyzed. The variation of flow field distribution and the plate displacement responses under different restricted conditions are claculated. Meanwhile, the influences of the stiffener and structural material parameters on the aeroelastic characteristices of the plate structure are also considered.
2013, 11(4):369-374. DOI: 10.6052/1672-6553-2013-043
Abstract:The vibration characteristic of the bi-material cantilever beam with graded interface layer was studied by Timoshenko beam corrective theory. The neutral axis site of the bi-material cantilever beam with graded interface layer was determined by the static equilibrium equations and the vibration equations of bi-material cantilever beam with graded interface layer were also established by Timoshenko beam corrective theory, the expression for natural frequency of it and the analytical solution for forced vibration of it under the action of harmonic load were obtained. The effect of neutral axis site to vibration characteristic of bi-material cantilever beam with graded interface layer was discussed. Analysis of examples indicates that the height of graded interface layer had more greatly influence on vibration characteristic of bi-material cantilever beam with graded interface layer.
2013, 11(4):375-380. DOI: 10.6052/1672-6553-2013-049
Abstract:The flutter of two dimensional sandwich panel with supersonic aerodynamic loading on one side is studied. The flutter critical Mach number and the effect of viscous damping are studied by using the Galerkin method and the complex modal method. The results show that the flutter occurs when the first and the second mode natural frequency coalesce, where the vibration energy accumulation starts to be positive. Considering the viscoelasticity of the mid layer, the results show that with the increase of viscous damping, the critical flutter Mach number and the corresponding critical flutter frequency of the system will decrease at first and then increase. It is concluded that the reason for this phenomenon is due to the dual effect of the viscous damping. The viscous damping can reduce the natural frequency to make the system less stable at one hand, and absorb energy which enhances the stability at the other hand. The system appears complex phenomenon as the result of dual effects of the viscous damping. The conclusions of this research will be meaningful in the design of composite panels in supersonic flow.
2013, 11(4):381-384. DOI: 10.6052/1672-6553-2013-050
Abstract:In this paper, the logic stochastic resonance (LSR) phenomenon in a triple well potential system is investigated by performing Simulink simulation. When the additive noise and multiplicative noise are uncorrelated, it is shown that LSR can be successfully induced by multiplicative Gaussian colored noise instead of additive noise. Compared with the Gaussian white noise, the reliable region in plane (D,Q) expands with increasing noise color. Furthermore, we find that the LSR is destroyed by the correlation between the additive noise and multiplicative noise.