Finite element model of coupled systems for vibration reduction plates with smart constrained layer damping

Considering the relationships of coupling movement and compatible displacement among bonding layer, piezoelectric layer, damping layer, and base structure, a finite element dynamic model of coupled systems for vibration reduction plates is established. The model combined with piezoelectric theory, finite element theory and ADF model of viscoelastic damping material can be suitable for vibration model of complex SCLD structure. The dynamics parameters for clamped-clamped steel plate with partially treated smart constrained layer damping are obtained by theoretical calculation, ANSYS modal analysis and modal experiment. The results show that theoretical values are closer to the test results and ANSYS analysis, and the methods proposed is more accurate and effective.     

Dynamic Responses of the High Slender Structure Under Non-Gaussian Model of Wind Load

With reference to the effect of the quadratic component of turbulent-wind fluctuation, the statistical moments of wind load up to the 4~(th) order are derived and the spectrum densities are given based on the Fourier transformation. By means of the Gram-Charlier series, the first-order probability densities of the structure responses are then constituted with the former 4~(th) order central moments of responses. Under the independent hypothesis of the structural displacement and its derivative, whose applicability is verified by the correlation between the two signals, the joint probability density function is developed and a numerical scheme for the analysis of the dynamic behaviors of the high-slender structure under wind excitation is obtained. Parametric analysis on dynamic responses and reliability under both Gaussian and non-Gaussian models of wind load are then investigated.     

Method for Calculating Steady Vibration Response of Shafting with Local Nonlinearity

A method which is used for calculating steady vibration response of shipping propulsion shafting connecting with a coupling with nonlinear hysteresis characteristics are studied. On condition that the nonlinear dynamic stiffness and hysteresis damping of the coupling be considered, on the basis of GLM(Galerki Levenberg Marquard) method, a method called SSGILM(Separate System Galerkin and Improved Levenberg-Marquardt)to be used for calculating steady vibration response of propulsion shafting with local nonlinear dynamic stiffness and hysteresis damping, is proposed. A simple example is given out and the analyses show that it is effective to calculate steady vibration response of the shafting with local nonlinear dynamic stiffness and hysteresis damping by SSGILM method. From initial response values given arbitrarily, the automatic search algorithm in SSGILM method can converge the given initial response values to the response values accorded with required accuracy quickly; nonlinear dynamic stiffness and hysteresis damping of the coupling have different effect on vibration response of the shafting at different range of frequency. At the area of close nature frequency of the shafting ,displacement amplitude of the shafting is bigger. Beyond the range, the characteristics of the coupling have restraint effect on vibration of the shafting.     

Combination Forecasting Models Using Regression Analysis Method

Using regression analysis method,the methods for solving the weights of combination forecasting model(CFM) are proposed. At first, the linear regress CFM are presented based on the least absolute criteria and least square criteria. Then the weights can be evaluated using the least square princinple. Because the objective function of CFM based on least absolute criteria is non differential, the traditional programming methods can not solve it. So the least square method with the modified weights is proposed to solve this problem. At the same time, methods for solving CFM is given with the aim of minimizing sum of percentage error absolutes. From many cases, the results show that the forecasting precision of CFM is very high and the effect of regression is remarkable.     

Topology optimization for constrained layerdamping material in structures using ESO method

Topology optimization for constrained damping material in structures is investigated in order to suppress structural vibration through the optimal placement of constrained damping material in structure. A mathematical model to describe the topology optimization problem is established. In the topology optimization approach, structural modal damping ratio is designed as objection function, while constrained damping material consumption is considered as constraint condition. The sensitivity of modal damping ratio to the place is analyzed. An evolutionary criterion for placement of constrained damping material in a structure is presented. The formula of sensitivity is derived and used to determine the optimized placement of constrained damping material in structure. The topology optimization problem is further solved by evolutionary structural optimization (ESO) method. The numerical examples are given. The results show that a stable and dramatic increase of the modal damping ratio during the course of iterations can be observed. Therefore, an optimal layout of constrained damping material in structure is obtained. The comparison of amplitude frequency characteristics with the optimal and fully covered layout validates the effectiveness of proposed topology optimized approach.     

Response Spectrum Method for Seismic Response Calculation of Pipeline System Multiply Supported on Structures

In order to ensure the function of building in the earthquake, reduce economic losses and facilitate post-disaster relief, it is necessary to accurately evaluate the seismic performance of pipeline system on the structure under seismic excitation. Considering this practical need, seismic response calculation methods of piping systems on structures were systematically studied. Firstly, theoretical derivation was performed based on the pseudo-excitation method for seismic response of pipeline system. It is found that the formula in previous studies has obvious defect: the accurate relative displacement values of degree of freedom near the supports can not be obtained in the formula. Thereby, the theoretical basis for derivation was mended to correct the defect, and the uniform combination expressions available for pipeline's seismic response calculation which is in the form of ground response spectrum or floor response spectrum were presented. Moreover, the simplified formulas and calculation method of correlation coefficients in the obtained expressions were put forward according to the assumption of white noise earthquake excitation. Finally, case studies were adopted to verify the proposed method's effectiveness and applicability in the seismic response calculation of pipeline system.     

Junction stiffness analysis and vibration noise prediction of wind power speed-increase gearbox

In order to study the vibration characteristics and radiation noise of wind power speed-increase gearbox, a torsional vibration model of wind power speed-increase gearbox is established based on the analysis of supporting stiffness of bearing and contact stiffness of gear pairs. By solving the vibration differential equation with the help of Matlab, the frequency and corresponding vibration mode are obtained. With taking stiffness excitation, error exaction and meshing impact exaction into account, the dynamic finite element model of speed-increase gearbox is set up, and the dynamic response simulation is carried out. Regarding vibration displacement of the nodes on gearbox surface as boundary condition, an acoustic boundary element model of speed-increase gearbox is built. The surface acoustic pressure of gearbox and the radiation noise of field points are solved by the direct boundary element method. The results show that there is a great difference between torsion frequency and excitation frequency of wind power speed-increase gearbox, and so the resonance doesn't occur. The maximum structural noise and radiation noise mainly appear near the double octave of the gears meshing frequency of high-speed grade.     

Perturbation Analysis of Complex Modes for Vibration System with Viscous Damping and Its Application

The sensitivity characteristics of the undamped natural frequencies and complex mode shapes of vibration system with the non-proportional viscous damping with respect to structural mass, stiffness and damping modifications are analyzed in this paper using the matrix perturbation of complex modes. The general principles for the selectivity of the design and the most sensitive positions of the structural perturbation modifications are shown thereby. This is of importance to a great computational savings in the dynamic characteristic improvement of large or complex structures. By the dynamic characteristic sensitivity analysis of a test device type RDT-1,the optimal structural design for its especial requirement of dynamic characteristics is obtained easily and the principles presented in this paper are confirmed by the numerical results of perturbation analysis.     

Blade kinematic theory for rotary vane compressor

The advantage of blade-offset rotary vane compressor is analyzed, and its kinematic model is established through simplifying the vane motion to the circle center movement of the main vane arc by using equidistant curve envelope principle. Then, the relationship between the displacement, velocity, acceleration of blade and the angle of rotor is obtained. Finally, based on the theory obtained, the simulation is also carried out. Results show this method can avoid complex process for finding the contact point, which meanwhile has good solving accuracy. Because of the differences on kinematic characteristics, the blade kinematic analysis for blade-cardiac cannot be simply used for the blade-offset one, and the kinematic and dynamic characteristics of cylinder profile cannot be shown by the simplified analysis. However, the scientific theory calculation method for the kinematic analysis of blade-offset rotary vane compressor put forward provides a reliable theoretical basis for the innovation of multi-stage combination cylinder profile with high volumetric efficiency and compression ratio, and also broadens the design theory of the rotary vane compressor.     

Longitudinal Vibrations of a Single Pile in Saturated Viscoelastic Soil

Based on Biot's theory, the longitudinal vibrations of a single pile in saturated viscoelastic soil are investigated in the frequency domain subject to the harmonic load. By the Novak plane strain model, the control equations for the saturated viscoelastic soil are derived. Regarding the pile as the one-dimensional rod model, the vibration equation of the pile is established. Based on the continuity conditions of the pile and soil, the dynamic stiffness and dynamic damping of the pile top are obtained. It is compared with the solution for Novak, and the influence of different physical parameters of the pile and soil on the longitudinal vibrations of the soil and pile system is examined. It is shown that the dynamic characteristics of the pile in the dry soil as well as the saturated soil have some differences; the resonance effect of dynamic stiffness factor and equivalent damping is obvious weakening with the increase of the ratio of the length to radius of the pile. The resonance effect and natural frequency are increasing when the modulus ratio of the pile to soil increases; the interaction coefficient of the flow-solid and the damping ratio of soil skeleton have few influences on the responses.     

Experimental Analysis of Vibration Behavior for Large-span Underground Structure

In this paper, a shaking table test for large-span underground structure is introduced. Based on the test, the frequency of inherent vibration, damping ratio and the dynamic response of the structure are studied. The response of the underground structure for vertical seismic excitation is studied as a key point. With the different imbedding depth, the influence of interaction of soil and structure on the earthquake-resistant capacity of the underground structure is discussed.     

Neumann Series Solution of Newmark Method and Its Convergence for Solving Dynamic Equations

The convergence of Newmark Neumann series method for solving dynamic equations is discussed.Conditions of convergence and the estimating expressions of approximate solution and error for the series solution are also given.     

Multi-objective dynamic optimization design of high-power wind turbine gearbox

A dynamic model of NGW helical planetary gear transmission for high-power wind turbine gearbox is established by considering these factors as errors of gears and time-varying mesh stiffness by using mass centralized method. Moreover, the random wind velocity is simulated as external seismic excitation making the results more conform to practical condition. And on this basis, this system is optimized for minimum gearbox volume and minimum component torsional acceleration with the restriction of reliability and strength restrain. The result indicates that the optimized parameters make gear transmission lightweight and the dynamic property improved so as to reduing vibration and noised.     

Least-square-based Optimization of Frequency Response Function Estimation in Modal Parameters Identification

The accuracy of modal parameters identification has the influence on the quality of dynamic characteristics analysis of mechanical structure directly. And the precision of the frequency response function estimation has the great influence on the accuracy of modal parameters identification. In the engineering the frequency response function can be estimated by the average power spectrum and cross-power spectrum with the hel Pof FFT. As the result of limited frequency resolution in the course of FFT and the noise, the accuracy of modal parameters identification is influenced by the frequency response function estimation. This paper has put forward a least-square-based optimization of frequency response function estimation in modal parameters identification. According to the optimized frequency response function, the peak value can be searched to identify the damped natural frequencies and damping ratio directly. An experiment has been made to validate the proposed method. The result indicates that the damped natural frequencies and damping ratio identified by the optimized frequency response function are closer to the true results than which without the optimized frequency response function. So the accuracy of modal parameters identification can be improved by adopting the proposed method.     

Numerical Prediction of Frequency of Delaminated Advanced Grid Stiffened plate

The paper aims to investigate natural frequency of delaminated advanced grid stiffened composite plates by hump resonance method.The composite laminated plate element and the rib element are adapted to simulate the laminated plate and the ribs.Based on the composite laminated plate and beam element model considering first-order shear effect,a damping model on the basis of Rayleigh damping model in conjunction with Adams' strain energy method(MSE) and a Hertz nonlinear dynamic contact model to avoid the overlap and penetration phenomenon between the upper and lower sub-laminates at the delaminated region.A numerical analysis method of dynamic response for the delaminated composite plates is carried out by precise time-integration method,and then the natural frequencies are achieved when the dynamic deflections reach the hump peak.For the frequency-domain analysis provided in the former research papers,it is a difficult problem to avoid the embedded phenomenon in the mode shapes at the delamination zone,while in the current time-domain analysis,the embedded phenomenon can be successfully overcome by using nonlinear contact model.By vibration excitation test,the specimens were excited by different excited frequency and the amplitude frequency response characteristics obtained are used to extract the frequency.The extracted frequencies of the narrow delaminated composite plates measured,which agrees well with the predicted natural frequencies.     

Vibration control of active constrained layer damping structure

A finite element dynamic model for plates with active constrained layer damping (ACLD) treatments is derived based on the constitutive equations of elastic, viscoelastic and piezoelectric materials by application of Hamilton principle. The closed loop control system considering displacement and velocity feedback of self sensing voltage from sensor layer is developed. The dynamic behaviors of active constrained layer damping (ACLD) plates including nature frequencies, loss factors and responses in frequency domain are investigated. The influence of control gains on vibration suppression is discussed. Numerical examples demonstrate the validity of the finite element model and the control strategy approach. The proposed control strategy can be widely used to structure vibration control with ACLD patches due to its simple scheme and easy implementation.     

基于行人动力学模型的人桥竖向动力相互作用

基于行人动力学模型,研究了人桥竖向动力相互作用。行人动力学模型采用以行人步频和体重表示的刚度质量阻尼（SMD）模型,人行桥假定为Euler-Bernoulli梁模型,建立人桥竖向动力相互作用控制方程。采用状态空间法进行非比例阻尼系统瞬时模态的求解,得到系统的时变频率和阻尼比;利用变步长四阶五级Runge-Kutta-Felhberg算法求解时变控制方程,对比分析考虑人桥竖向动力相互作用和只在人行荷载作用下人行桥的动力响应。结果表明：考虑人桥动力相互作用,人行桥自振频率略有降低,阻尼有显著增大;当行人以人行桥的频率行走时,考虑人桥竖向动力相互作用结构的动力响应比不考虑人桥相互作用显著降低。     

Deduction and Analysis of All Well Posed Convergence Linear 2-steps Methods Formula

By means of symbol operation of Matlab and the convergent condition of the linear muhistp method formula, the authors attained the well posed convergent formulas directly for all linear 2-step methods. Some convergent formulas are gotten after screening and the fraction coefficients, errors coefficients, orders and intervals of absolute stability are calculated. Then figure of region of absolute stability of the absolute stability formula is drawn by means of root locus method. The performance of those formulas simply is analyzed. One new A - stable formula of linear 2-step methods of order 2 is derived and proved.     

Solving Method for Soil Spring Stiffness of Shallow Shield Tunneling

Based on complex variable theory in plane elasticity, the equivalent spring stiffness is derived from the analytical solution by means of simplifying shallow shield tunneling to semi-infinite plane with hole, which is applied to response displacement method. The performances of the analytical solution are evaluated and compared with that of the deep shield tunneling through a series of selected various tunnel depths and soil Poisson's ratios. The relation of compression and shear spring stiffness is discussed. Meanwhile, two factors affected soil spring stiffness, tunnel depth and soil Poisson's ratio, are also analyzed. It is shown that soil spring stiffness of shallow shield tunneling is different from that of deep shield tunneling, and the ratio of compression and shear spring stiffness varies along shallow shield tunneling. It is also found that the value and distribution law of soil spring stiffness of shallow shield tunneling greatly depend on tunnel depth and soil Poisson's ratio.     

Application of Meshless Method in Dynamic Mechanics

As a new type of meshless method which has appeared in recent years, the Reproducing Kernel Particle Method has such meshless features as the need for nodes only without classified units, and is advantageous in the process of calculation. The present study introduces the Reproducing Kernel Particle Method and applies it to the research of nonlinear dynamic mechanics. The dynamic process involves different kinds of nonlinearity. The study assumes that deformation of dynamic analysis belongs to small one and that the material nonlinearity has been taken into account. When under small strain, the increment constitutive law and the total Lagrangian model of calculation are adopted to deduce the dynamic control equation by the Reproducing Kernel Particle Method. The instances of calculation demonstrate that this method is effective in the analysis of dynamic problems.