双E型弹性体六维力传感器薄矩形板AWGN-Kalman滤波

针对六维力传感器采集信号中存在复杂噪声干扰的问题,为有效地对系统降噪和提高传感器的分辨率,本文以六维力传感器薄矩形板为研究对象,引入应变片热噪声与信号处理电路的散粒噪声信号,分析其窄带高斯统计特性,融入系统状态方程,生成状态加性高斯白噪声﹒借鉴Box-Muller变换法,验证了状态噪声的高斯统计特性,进而构建了线性离散时间系统状态模型,并详细推导了AWGN-Kalman滤波公式﹒通过EKF和UKF算法滤波实例,验证了该模型降噪的有效性,且选择合适的滤波方法,能更有效地对六维力传感器的薄矩形板进行滤波.

缺陷对薄板结构振动模态影响的数值与实验分析

利用有限元法和电子散斑干涉技术研究了缺陷对矩形薄铝板的振动模态的影响。通过数值模拟和实验测量同时得到了1块完整和4块带有缺陷大小与位置均不同的铝板1~10阶的振型图;铝板的边界条件为长对边自由,短对边固支。结果表明:缺陷的存在对薄板结构的共振振型影响较大,而对共振频率的影响较小。共振振型随裂缝的大小、位置和方位的不同而有所变化。研究也表明,有限元计算出的模态形状与实验测量得到的结果一致性较好。

Unified Solution Method of Rectangular Plate Elastic Bending

The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition at the corner point. The former can be solved directly by the equilibrium differential equation and the boundary conditions of four edges of the plate. The latter can be solved by using the superposition principle. Making use of the recommended method, the bending of the plate with all kinds of...

Local Bifurcation of a Thin Rectangle Plate with the Friction Support Boundary

The dynamical equations of a thin rectangle plate subjected to the friction support boundary and its plane force are established in this paper. The local bifurcation of this system is investigated by using L S method and the singularity theory. The Z 2 bifurcation in non degenerate case is discussed. The local bifurcation diagrams of the unfolding parameters and the bifurcation response characters referred to the physical parameters of the system are obtained by numerical simulation. The results of the computer simulation are coincident with the theoretical analysis and experimental results.

L~∞-Error Estimate of a Nonconfoming Rectangular Plate Element

In this paper,a nonconforming rectangular plate element,the modified incomplete biquadratic plate element,is considered. The asympotic optimal L~∞-error estimate is obtained for the plate bending problem. This proof is based on the method of regularized Green's function and 'the trick of auxiliary element'.

Numerical simulation of wrinkle phenomenon during multi-point forming process of shallow rectangle cup

In this paper, the principle of multi-point forming (MPF) technique is presented. One of the most serious defects, wrinkling, during the multi-point forming process of a shallow rectangle cup is discussed by means of numerical simulation on the shallow rectangle cup forming process. The effects of thickness, material of sheet metal and the pressure of the blank holder are investigated. Based on the simulation results, the reasons and control methods of wrinkling are pointed out. Moreover, the experiment on the multi-point die forming of the shallow rectangle cup by the MPF machine is done to validate the efficiency of the numerical simulation, and the result proves that the application of an elastic cushion in the forming can restrain wrinkling efficiently.

Double Symplectic Eigenfunction Expansion Method of Free Vibration of Rectangular Thin Plates

The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonian. Moreover, the existence and completeness of normed symplectic orthogonal eigenfunction systems of these two block operators are demonstrated. Based on the completeness, the general solution of the free vibration of rectangular thin plates is given by double symplectie eigenfunction expansion method.

Stochastic Bifurcation of Rectangular Thin Plate Vibration System Subjected to Axial Inplane Gaussian White Noise Excitation

A stochastic nonlinear dynamical model is proposed to describe the vibration of rectangular thin plate under axial inplane excitation considering the influence of random environment factors. Firstly, the model is simplified by applying the stochastic averaging method of quasi-nonintegrable Hamilton system. Secondly, the methods of Lyapunov exponent and boundary classification associated with diffusion process are utilized to analyze the stochastic stability of the trivial solution of the system. Thirdly, the stochastic Hopf bifurcation of the vibration model is explored according to the qualitative changes in stationary probability density of system response, showing that the stochastic Hopf bifurcation occurs at two critical parametric values. Finally, some explanations are given in a simple way on the potential applications of stochastic stability and bifurcation analysis.

Stochastic Optimal Control of First-Passage Failure for Rectangular Thin Plate Vibration Model under Gaussian White-Noise Excitations

A rectangular thin plate vibration model subjected to inplane stochastic excitation is simplified to a quasinonintegrable Hamiltonian system with two degrees of freedom. Subsequently a one-dimensional Ito stochastic differential equation for the system is obtained by applying the stochastic averaging method for quasi-nonintegrable Hamiltonian systems. The conditional reliability function and conditional probability density are both gained by solving the backward Kolmogorov equation numerically. Finally, a stochastic optimal control model is proposed and solved. The numerical results show the effectiveness of this method.

Analytical Approaches of Composite Rectangular Thin Plates

The purpose of the present study was to explore and subsequently establish a technique for determination of analytical solutions for the differential equation for composite thin plates. The considered reasons for the solutions were to exactly satisfy the boundary conditions and to verify as close as possible the differential equation of the plate. There are studied two solutions for orthotropic plate with clamped edges, and made comparisons with the solutions presented by Reddy [1] and with the exact solution by Timoshenko and Woinowsky. The models are based on the CLPT （classical laminated plate theory）. The Ritz method, in conjunction with the weighted residue method for the coefficients calculation, is used to analytically determine the bending solutions of orthotropic laminated plates subjected to uniform pressure on the bottom laminate. The purposed solutions were critically analysed considering a FEM （finite element method） solution for comparison. Finally, it is presented the experimental device and the experimental test results, as well. Fabrics have been incorporated into two composite plates were required scalps on one direction, thus ensuring different elasticity modules on both directions. Thorough comparison between analytical solutions, numerical results and experimental data is performed and a good agreement is obtained.

An extended high-dimensional Melnikov analysis for global and chaotic dynamics of a non-autonomous rectangular buckled thin plate

By using an extended Melnikov method on multi-degree-of-freedom Hamiltonian systems with perturbations,the global bifurcations and chaotic dynamics are investigated for a parametrically excited,simply supported rectangular buckled thin plate.The formulas of the rectangular buckled thin plate are derived by using the von Karman type equation.The two cases of the buckling for the rectangular thin plate are considered.With the aid of Galerkin's approach,a two-degree-of-freedom nonautonomous nonlinear system is obtained for the non-autonomous rectangular buckled thin plate.The high-dimensional Melnikov method developed by Yagasaki is directly employed to the non-autonomous ordinary differential equation of motion to analyze the global bifurcations and chaotic dynamics of the rectangular buckled thin plate.Numerical method is used to find the chaotic responses of the non-autonomous rectangular buckled thin plate.The results obtained here indicate that the chaotic motions can occur in the parametrically excited,simply supported rectangular buckled thin plate.