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Articles in press have been peer-reviewed and accepted, which are not yet assigned to volumes/issues, but are citable by Digital Object Identifier (DOI).
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, Available online  , doi: 10.21656/1000-0887.420359
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Abstract:
The event-based state estimation problem is investigated for a class of complex valued neural networks with mixed delays. By utilizing the measurement output, a novel event-triggering scheme is introduced to reduce the frequency of updating while ensuring estimation performance. A waiting time is first employed to avoid the Zeno phenomenon. By using the Lyapunov direct method and some properties of complex-valued matrix, a sufficient criterion is established to guarantee the globally asymptotic stability for the error system. The weighted parameters and gain matrices are designed by resorting to the feasible solution of matrices inequalities. Finally, a numerical example and its simulations are presented to illustrate the effectiveness of proposed approach.
, Available online  , doi: 10.21656/1000-0887.420223
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Abstract:
The complex non-linear coupling generated in spatial cooperation process of mobile manipulators, makes it extremely tedious to model directly for spatial cooperative systems with Lagrange equation or Newton-Euler method. A dynamic modeling method, combining Udwadia-Kalaba (U-K) method with Lagrange equation, for spatial cooperation of dual mobile manipulators is explored. The load was simplified as a connecting link while modeling. The center of load was selected to be disconnected for decomposition, so that the lack of constraint information between the end joint angle and the end link angle caused by disconnecting the end joint of the manipulator is avoided; the segmented two subsystems were modeled with Lagrange equation, thus, the dynamic model of subsystems was obtained. The inherent geometric relationships of cooperative system were introduced in the form of constraints, and the U-K method was applied to obtain the dynamic model of cooperative system. The computation for modeling is reduced. Finally, the accuracy of the model was verified by numerical simulation.
, Available online  , doi: 10.21656/1000-0887.420244
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Structural vibrations of the ultra-large structures during on-orbit assembly should be prevented to the maximum extent, because of the extreme flexibility and low natural frequencies. The assembling process is divided into four stages: grasping stage, position-attitude adjusting and stabilizing stage, mounting stage, and crawling stage. This paper focuses on the mounting stage, and a collinear assembly trajectory planning method is proposed to prevent structural vibrations. First, a dynamic model of the on-orbit assembly system (including the main structure, the space robot, and the assembling structure) is established based on natural coordinate formulation and absolute node coordinate formulation. Second, the requirements of collinear assembly are transformed into a trajectory planning problem of the space robot. The distance from the center of mass of the space robot to the main structure should remain unaltered, which is main idea of the proposed collinear assembly method. Numerical simulation results show that the proposed assembly method can effectively prevent the transverse motions of the ultra-large structure and reduce the required grasping moment. Finally, the influences of the system parameters on the dynamic response of the assembly process are studied, which provides a theoretical basis for the on-orbit assembly of ultra-large spacecraft.
, Available online  , doi: 10.21656/1000-0887.420273
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The nonlinear vibration responses of functionally graded shells with different cone angles under external load are studied in this paper. Firstly, the Voigt model was employed to describe the physical properties along the thickness direction of FGMs conical shells. Then, the motion equations were derived based on the first shear deformation theory, von Kármán geometric nonlinearity and Hamilton’s principle. Next, the Galerkin method was applied to discretize the motion equations and the governing equations was simplified into a single degree of freedom nonlinear vibration differential equation based on the Volmir’s assumption. Finally, the nonlinear motion equation was solved by the harmonic balance method and Runge-Kutta method, and the amplitude frequency response characteristic curves of FGMs conical shell were obtained. The effects of different material distribution function and the ceramic volume fraction exponents on the amplitude frequency response curve of conical shell were discussed. The bifurcation diagrams of conical shells with different cone angles and time process diagrams and phase diagrams with different excitation amplitudes were described. The motion characteristic was characterized by Poincaré map. The results show that FGMs conical shell presents the nonlinear characteristics of "hardening" spring. The chaotic motion of FGMs conical shell is restrained and FGMs conical shell is not prone to produce motion instability with the increase of cone angle. The motion of FGMs conical shell presents a process from periodic motion to multi-periodic motion and then to chaos with the increase of excitation amplitude.
, Available online  , doi: 10.21656/1000-0887.420290
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Many slender robs in engineering can be abstracted as Euler-Bernoulli beams. When analyzing their dynamic behavior, it is necessary to establish the dynamic model of the flexible multi-body systems. Geometric nonlinear elements with absolute nodal coordinates solved a large number of dynamic problems of flexible beams, but it still faces such problems as shear locking, discontinuity of nodal stress and low computational efficiency. In this paper, based on the theory of large deformation beam’s virtual power equation, the functional formula between displacements and rotation angles located at the nodes were established, which can satisfy the deformation coupling relationships and the generalized strains that can describe geometric nonlinear effects in this case were derived. Some parameters of boundary nodes were replaced by axial strain and sectional curvature to obtain a more accurate and concise constraint method for applying external forces. In order to improve the numerical efficiency and stability of the system’s motion equations, a model smoothing method was used to filter out high frequencies from the model. The rationality and effectiveness of the proposed unit were verified.
, Available online  , doi: 10.21656/1000-0887.430197
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In this paper, the Stokes flow in a cylindrical container with rotating ends is studied. Based on the characteristic of the flow, the problem is reduced to the eigenvalue and eigensolution problem of Hamiltonian dual equations by taking axial coordinate in analogy to time. Due to the completeness of the space of symplectic eigensolutions and adjoint relationships of symplectic orthogonality between eigensolutions, the solution of the problem can be obtained, and the numerical method of expansion coefficients is given. When one end rotates or two ends rotate with the same or reverse angular velocity, the flows in cylindrical containers with different geometric aspect ratios (the ratio of length to radius of the container) are investigated. The results show the velocity and stress distributions of these flows, and then the characteristics of the flows under different boundary conditions are revealed.
, Available online  , doi: 10.21656/1000-0887.420200
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The dual-phase-lag thermoelasticity theory with memory-dependent derivative can perfectly describe the phenomenon of non-Fourier heat conduction, nevertheless, it has not been comprehensively considered: the mechanical response of materials aroused by the size-dependent effects and the influence of multiple coupling effects such as magnetic, thermal and elastic fields. A dual-phase-lag thermoelasticity theory considering memory dependent effect and non-local effect is established. Based upon the revised theory, the magneto-thermoelastic coupling problem of a thin plate subjected to a cyclical heat source is investigated. First the governing equations of the problem are formulated. Then combining the boundary conditions and initial conditions, the solution of the problem is obtained by using Laplace transform and inverse transform techniques. Last, the effects of magnetic field, phase lag, time-delay, kernel function, non-local effect and time on the dimensionless quantities were investigated respectively, which provided a powerful reference for the dynamic response of micro-scale materials.
, Available online  , doi: 10.21656/1000-0887.420208
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Based on the boundary element method theory of elasticity, the boundary element method is combined with the dual reciprocity method, and the exponential basis function is used to interpolate the non-homogeneous term to obtain the dual reciprocity boundary integral equation. The boundary integral equation is discretized into algebraic equations, and the equations are solved by using the known boundary conditions and equation special solutions to obtain the displacement and boundary surface force in the domain. The shape parameter of exponential basis function is determined by the minimum value of the nearest distance between interpolation points. Using this shape parameter change scheme, the RBF interpolation accuracy and interpolation stability are analyzed. Thirdly, the exponential basis function is applied to the dual reciprocal boundary element method to analyze the calculation accuracy and stability under the dual reciprocal boundary element method, and verify the effectiveness of the exponential interpolation function as the radial basis function of the dual reciprocal boundary element method to solve the physical force problem in the elastic domain.
, Available online  , doi: 10.21656/1000-0887.410278
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In this paper, a coupled pure meshless finite pointset method (CFPM) is developed for the first time to numerically predict the inelastic collision process of solitary wave described by the time fractional coupled nonlinear Schrödinger (TF-CNLS) equation. Its construction process is as follows: 1) a high-precision difference scheme is used for the Caputo time fractional derivative; 2) FPM discrete scheme based on Taylor expansion and weighted least square method is adopted for spatial derivatives; 3) The region is locally refined and the double cosine kernel function with good stability is used to improve the numerical accuracy. In the numerical study, the one-dimensional TF-CNLS equations with analytical solutions are solved by CFPM, and the error and convergence rate are analyzed when the nodes are uniformly distributed or locally refined, showing that the proposed method has the approximate second-order accuracy and the flexibility of easy local refinement. Secondly, the inelastic collision process of solitary waves, which is described by the one-dimensional TF-CNLS equation without analytical solution, is numerically predicted by CFPM, and the wave collapse phenomenon depicted above is completely different from the multi-wave phenomenon under the integer order. Meanwhile, by comparing the result with that obtained by finite difference method, it suggests that the CFPM is reliable to predict the complex propagation of the inelastic collision process of the solitary waves under the time fractional order.
, Available online  , doi: 10.21656/1000-0887.420231
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The effective bulk modulus and the effective in-plane shear modulus of nano-fiber composites are investigated using interface model and interphase model based on the generalized self-consistent method, the closed-form analytical solutions of effective bulk modulus and all equations for predicting effective in-plane shear modulus by numerical method based on the two models are presented. Using the interface model, interface effects of the effective bulk modulus and the effective in-plane shear modulus are discussed by use of numerical examples. Further research demonstrates that the analytical formula of the effective bulk modulus and the numerical results of the effective in-plane shear modulus derived from the interface model can be obtained again from the interphase model. An example of aluminium containing nano voids shows that the effective bulk modulus and the effective in-plane shear modulus predicted by the interface model have large deviations from that of the interphase model when the void radius is small, however for larger void radius, the difference is small.
, Available online  , doi: 10.21656/1000-0887.430007
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A kind of two-fluid system in plasmas describes rich dynamics of a plasma, including the interactions between the ion acoustic wave and the plasma wave. In order to describe the evolution of the envelope of the small oscillating wave packet solution of the two-fluid model, the nonlinear Schrödinger (NLS) equation is derived as a formal approximation equation by using the multi-scale analysis method, and the uniform energy estimation of the error between the real solution and the approximate solution of the two-fluid model is carried out in Sobolev space. The NLS approximation is finally proved strictly on the time scale ${\cal{O}}(\epsilon^{-2})$.
, Available online  , doi: 10.21656/1000-0887.420267
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In this paper the asymptotic property of the solutions for a class of perturbed stochastic impulsive functional differential equations is investigated. By comparing the solutions for the perturbed equations with the solutions for the corresponding unperturbed ones, we derive sufficient conditions for these solutions to be close on a finite time interval. Then, when small perturbations tend to zero and the length of the time interval goes to infinity, we prove that similar results still hold. Finally,an example is given to illustrate the effectiveness of the results.
, Available online  , doi: 10.21656/1000-0887.430036
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Boussinesq system, as a model to describe many geophysical phenomena, is a zero-order approximation of the coupling between Navier-Stokes equations and thermodynamic equations. In this paper, we consider the multi-dimensional viscous Boussinesq equations. By using the implicit function theorem, we obtain the global well-posedness of the mild solution when the small initial data are in the scaling invariant spaces.
, Available online  , doi: 10.21656/1000-0887.420414
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The projection algorithm is one of the main methods to solve variational inequality problems. At present, the research on projection algorithms usually requires the assumption that the mapping is monotone and Lipschitz continuous, but in practical problems, these assumptions are often unsatisfied. In this paper, a new double projection algorithm for solving non-monotone variational inequality problems is proposed by using the line search method. Under the assumption that the mapping is uniformly continuous, it is proved that the sequence generated by the algorithm strongly converges to a solution of variational inequalities. The numerical experiments illustrate effectiveness and superiority of the proposed algorithm.
, Available online  , doi: 10.21656/1000-0887.420241
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In order to identify the instantaneous frequency of time-varying signals, this paper derives the theoretical relationship between the frequency in a signal and rotational angle α in a fractional Fourier transform. It is demonstrated that the fractional Fourier transform is actually an algorithm of ordinary Fourier transform combined with telescopic translation window. A general expression of signal instantaneous frequency in the fractional Fourier domain is thereafter formulated so that structural instantaneous frequency can be extracted accordingly. The feasibility and reliability of proposed method is verified by a simulated nonlinear frequency modulation signal and a numerical example of a three-degree-of-freedom damped time-varying structure system. The results show that the proposed method is in good agreement with the theoretical values and the method has a certain degree of anti-noise capability. Subsequently, the proposed method is capable of identifying the instantaneous frequency of time-varying structures.
, Available online  , doi: 10.21656/1000-0887.420169
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Based on Lyapunov stability theory, matrix analysis method, linear matrix inequality methods, etc, the generalized H2 control of singularly perturbed uncertain control systems with time-varying delay and control input and disturbance input is studied. A memory state H2 generalized controller is designed, the decision theorem of the specific design method given. Quoting new lemma for delay dependent and delay independent cases, the relatively less conservative stability criterion is derived. The obtained results are linearized, the selected numerical examples are used to verify the effectiveness and feasibility to the derived conclusions. It is pointed out that the closed-loop system is asymptotically stable in the whole range from zero to singular perturbation upper bound, which expands the generalized H2 stability space and reduces the L2-L performance index. By comparing the stability state parameter index with the related literatures, it is shown that the proposed method has certain advantages and less conservatism, and is suitable for standard and non-standard cases.
, Available online  , doi: 10.21656/1000-0887.420245
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The sine-cosine method is applied to the wave equation of nonlinear elastic rod, and some new periodic and soliton solutions of the equation is obtained (material constant n is a constant different from 1). The graphs of some solutions are given through math software. The results are helpful to further research on existence of solitary waves in the nonlinear elastic rod.
, Available online  , doi: 10.21656/1000-0887.420318
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The computation consumption of finite element analysis for structural optimization design of holding pole is large, and it is difficult to determine the feasible region. The response surface method (RSM) was used to simulate the real response of the holding pole, and an improved arithmetic optimization algorithm (IAOA) was proposed to optimize the holding pole. Fractional-order calculus was introduced into arithmetic optimization algorithm (AOA) to improve the exploitation ability of AOA. Latin hypercube sampling was applied to select the test samples of each member of the holding pole, and the least square method was employed to analyze the sample points. Then, the second-order response surface surrogate model of the stress and displacement of the holding pole on the cross-sectional size of each member was established. An optimization model was constructed with the minimum mass as the optimization objective and the allowable stress and displacement as constraints, and the IAOA was implemented to solve the model. The results show that the second-order response surface model can accurately predict the response value of the holding pole. The solution accuracy of the IAOA is significantly improved. The surrogate model can greatly decrease the calculation cost of finite element analysis. The mass of the holding pole is reduced 8.2% after optimization. The RSM and the IAOA can be combined to solve the optimization design problem of large spatial truss structures effectively.