2014, 12(1):1-8. DOI: 10.6052/1672-6553-2013-106
Abstract:The development of analytical mechanics involves many aspects of theory and application. This paper summarizes the recent progress of analytical mechanics in three problems on the interdisciplinarity between analytical mechanics and mathematics. The first is to study the integration problem of equations of analytical dynamics by using some results of Lie groups and Lie algebras. The second is to apply the classical and modern integration methods of analytical mechanics to the integration problem of general differential equations. The third is to transform the equations of analytical dynamics into the equations of gradient system under certain conditions and then discuss the dynamical behaviors of the mechanical system by using the properties of gradient system.
2014, 12(1):9-12. DOI: 10.6052/1672-6553-2013-094
Abstract:Focusing on the conservation properties, the symplectic Euler scheme of the harmonic oscillator was constructed to analyze its vibration properties. Firstly, three conservation laws, including the square conservation law, the period conservation law and the phase difference conservation law, were presented for the harmonic oscillator. And then, the common Euler scheme and the symplectic Euler scheme were constructed to study the above three conservation laws. The numerical results imply that the symplectic Euler scheme can preserve the conservation law in time domain (the square conservation law) exactly, but can’t preserve the conservation laws in phase domain (the period conservation law and the phase difference conservation law), which is the shortcoming of the symplectic method but can be overcome by the modification method presented by Prof. Xing.
2014, 12(1):13-17. DOI: 10.6052/1672-6553-2013-069
Abstract:This paper studied a type of conserved quantity deduced by the Lie symmetry for nonholonomic system with Chetaev type of the Nielsen equation. Firstly, the determining equations of the Lie symmetry for nonholonomic system with Chetaev type of the Nielsen equation were given under the infinitesimal transformation of groups. Secondly, the conditions of the existence of the type of conserved quantity of the system as well as its forms were obtained. And finally, an example was given to illustrate the application of the results.
2014, 12(1):18-23. DOI: 10.6052/1672-6553-2013-068
Abstract:The electromechanical coupling model of cantilevered piezoelectric harvester was developed by considering the nonlinearities of piezoelectric material, based on Hamilton theory, Rayleigh-Ritz method, Euler-Bernoulli beam theory and constant electrical field across the piezoelectric element. The response characteristics of the system were investigated numerically, and the influences of piezoelectric material nonlinear coefficient on the system response were analyzed. By exploring the nonlinear characteristics of the piezoelectric vibrator near the resonant frequency, the nature of the multi-solutions and jump phenomena in the resonance region was revealed. The results were verified experimentally. which provides a theoretical basis for the study of nonlinear mechanism of piezoelectric power generation system.
2014, 12(1):24-29. DOI: 10.6052/1672-6553-2013-115
Abstract:Firstly, based on the Reddy higher-order shear deformation theory and the pneumatic elastic piston theory, the nonlinear governing equations of motion for an axially moving cantilever beam were established by using the generalized Hamilton’s principle, and the first order nonlinear aerodynamic force and parametric excitation in-plane were obtained. After introducing dimensionless variables and parameters, the nonlinear governing equations became dimensionless equations. At last, according to Galerkin’s approach, the governing equations of motion were simplified to three ordinary differential nonlinear dynamic equations. As long as the suitable composite material and relevant parameters are given, the relevant vibration characters of the modeling during deployment and retrieval can be analyzed by using numerical method.
2014, 12(1):30-35. DOI: 10.6052/1672-6553-2013-073
Abstract:The dynamic behaviors of a flexible multi rotor system supported on journal bearing with a misaligned coupling were investigated. Firstly, the dynamic model of a rotor system under the action of the nonlinear oil film forces was developed after taking into account the movement relationships and displacement constraint, which describes the misalignment relation between two rotors, and the theoretical analysis reveals that the system with eleven DOF is of strong nonlinear properties and time varying parameter. Then, the nonlinear dynamic characteristics, such as steady state response, rotor orbit, Poincaré section and the largest Lyapunov exponent, were studied. The results show that, at low speed, the orbit synchronously oscillates within a small zone; as the speed increases, the dynamic characteristics become complicated, and the period doubling, quasi period and chaotic oscillations occur. Finally, the effects of the bolt stiffness on dynamic behaviors were also discussed.
2014, 12(1):36-43. DOI: 10.6052/1672-6553-2013-110
Abstract:The coupling nonlinear dynamic model of dual rotor system was established by using finite element method, and then the critical speed of revolution and mode shape were calculated by using the software MATLAB. In addition, the unbalance responses of dual rotor system were studied, and the vibration performances in different speeds of dual rotor casing systems were obtained. The research provides a theoretical basis for the design of the dual rotors system in engineering.
2014, 12(1):44-49. DOI: 10.6052/1672-6553-2013-051
Abstract:The flight dynamics of a morphing aircraft is obviously depended on the wing shape, because it results in different aerodynamic properties due to the mass reallocation and inertia change. This paper studies the flight dynamics of a changeable wingspan aircraft in low speed flight. Starting with the modeling of the morphing aircraft on the basis of Lagrange's equation, a set of longitudinal dynamic equations for a planar deployable wing is established. At the same time, the low speed aerodynamic parameters for fixed wingspan are calculated with the vortex lattice method. Afterward, the corresponding aerodynamic coefficients versus the wingspan changes are determined through the use of linear interpolation method. The effect of wingspan changes on the flight dynamics of the simplified morphing aircraft are analyzed for different flight status such as level flight, climbing, diving and turning. The results show that wingspan change would influence the flight status of morphing aircraft especially in the longitudinal flight so that the relevant control must be taken in order to keep the stability of the flight of a morphing aircraft.
2014, 12(1):50-55. DOI: 10.6052/1672-6553-2013-059
Abstract:The effect of the transverse shear deformation for Reddy plates or laminated plates is significant. In this case,it can meet the requirements for calculate precision better to use the third order shear deformable theory than to use the classical thin plate theory and the first order shear deformation theory. And it is better to describe the distribution of the plate shear deformation and shear stress varying through the thickness when using the third order shear deformation theory. In this paper,an analytical method is presented for studying the free vibration characteristic of plate using the third order shear deformation theory on different boundary conditions,which are the any combinations of simply supported,free and clamped. Hamilton principle is used to formulate the free vibration equations. Then,by introducing the intermediate variable the original coupling free vibration equations are decoupled and simplified. The fundamental function expressions are obtained basing on the method of separation of variables and the boundary conditions. And the natural frequencies and modal functions are obtained by using the Rayleigh-Ritz method. The method in this paper has a good generality for solving the vibration problems of thick plates under different boundary conditions. The result obtained in this paper can provide a theoretical basis for thick plate's application in engineering,and it has relatively high application value.
2014, 12(1):56-61. DOI: 10.6052/1672-6553-2013-052
Abstract:With the increasing of the vehicle speed, traffic volume and moving loads, the dynamic response of bridges under moving loads attracts more and more attentions. If one considers the inertia effect of moving vehicle and the damping effect of bridges, the moving vehicle could be modeled as a moving mass. Its govern equation is a partial differential equation with variable coefficients. The equation is usually difficult to solve exactly in mathematics. Using the variable separation and modal superposition method, the partial differential equation is reduced as an ordinary equation with variable equation set. Using the method of WKB method, an approximate solution of the problem is obtained, which is compared with the results of numerical simulation, the solutions of moving constant forces and Inglis.
2014, 12(1):62-66. DOI: 10.6052/1672-6553-2013-097
Abstract:A spline finite point method was presented to study the natural frequency of arch. The displacement mode shape function of the arch free vibration was simulated with a linear combination of cubic B spline. The free vibration frequency equation of arch structures was derived according to Hamilton principle, in which the effect of the dead load was considered. Meanwhile, the effect of the dead load on the natural frequency of arch structures was analyzed. The results show that the natural frequency of arch is reduced. The effect of influence depends on the stiffness of the arch itself. When the arch stiffness is certain, the bigger the rise span ration and the radius to thickness ration, the higher the effect of the dead load on the natural frequency of arch structures.
2014, 12(1):67-73. DOI: 10.6052/1672-6553-2013-071
Abstract:By using Lagrangian methods, the rigid body dynamics model was established for a planar 3 DOF controllable excavating mechanism. Based on the system generalized forces of the three driven bars, the control strategy of the semi closed loop control system was studied. A Fuzzy PID dual mode controller was introduced and analyzed by using fuzzy algorithm based on the mathematical model of mechanism driven components AC servo motors. The simulation results indicate that the proposed controller has better performance in overshoot, adjusting time, rise time and anti interference ability, which can satisfy the control requirements of the system.
2014, 12(1):74-78. DOI: 10.6052/1672-6553-2013-086
Abstract:This paper introduced the adaptive multi-scale entropy (AME) measures, in which the scales are adaptively derived from the data by virtue of recently developed empirical mode decomposition. By removing the low or high frequency components from the raw data, the AME can be estimated at either coarse-to-fine or fine-to-coarse scales, over which the sample entropy is performed. Simulations illustrate its effectiveness and promising application in brain death diagnosis to discern the states of the coma and the brain death.
2014, 12(1):79-85. DOI: 10.6052/1672-6553-2013-070
Abstract:An SIRS epidemic model with nonlinear saturation incidence rate and time delay was investigated. By analyzing the corresponding characteristic equations, the local stability of disease free equilibrium and endemic equilibrium was discussed. The bifurcation property was obtained as the time delay passed through a critical value. Applying the center manifold argument and normal form theory, some local bifurcation results were obtained and the formulas for determining the bifurcation direction and stability of the bifurcated periodic solution were derived. Numerical simulations were presented to illustrate the theoretical analysis.
2014, 12(1):86-91. DOI: 10.6052/1672-6553-2013-096
Abstract:A model of scale-free neuronal networks, which consists of heterogeneous Fitzhugh-Nagumo neurons and time-delayed coupling, was constructed. Then, we explored the nontrivial effects of heterogeneity and time-delayed coupling on the resonance dynamics by numerical simulation in this model. When the delays in the coupling are absent, the result has shown that the response of the neuronal networks to an external subthreshold periodic signal is optimized at an intermediate heterogeneity, namely, an appropriate tuned level of heterogeneity can induce resonance in the neuronal networks. This phenomenon was also confirmed to be robust to the changes of the coupling strength. Most importantly, we find that the delays in the coupling have significant influences on the resonance dynamics. It is revealed that proper delays can induce multiple resonances in the neuronal networks, which appears at each multiple of the oscillation period of the signal. Moreover, the performance of fine tuned delays in inducing multiple resonances can also be clearly observed when the heterogeneity is within an appropriate range.
2014, 12(1):92-96. DOI: 10.6052/1672-6553-2013-084
Abstract:This paper investigated the time derivative of entropy for a dissipative dynamical system driven by non Gaussian noise. The dimension of Fokker Planck equation was reduced by the way of linear transformation. Based on the definition of Shannon′s information entropy, the exact time dependence of the entropy was calculated. The relationship between the properties of non Gaussian noise and dissipative parameters and their effect on the information entropy were also discussed.