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.     

THE SECOND ORDER PERTURBATION ANALYSIS OF FREQUENCY RESPONSE FUNCTION OF STRUCTURE WITH NON-PROPORTIONAL CHANGEABLE; DAMPING

A simplified procedure is presented for the determintion of rates of change of frequency response function matrix of system for the non-proportional changeable damping ,by means of the second order perturbation technique in conjunction with complex modal analysis. Consequently, when excitation information in frequency domain is known,the sensitivity of the response power spectra and the response time history can be obtained.     

Modal parameters identification for short data sequences based on stratified sampling and optimism complex Morlet wavelet

A novel modal parameter identification method based on stratified sampling and optimism complex Morlet wavelet is proposed for short data sequences. Stratified sampling is applied to divide the structure response signal into different layers which called sub samples with different thresholds, and then free decrement response signal of each layer is extracted by random decrement technique. The optimism complex Morlet wavelet transform is applied to identify modal parameter of each layer, and the weight of the layer is also determined based on the sample standard deviation. The modal parameter of the structure can be obtained by weighted calculation.The engineering application shows that the proposed method has the ability to identify modal parameter accurately, decouple low frequency intensive modal composition and restrain high frequency fake modal effectively.     

A TIME AND FREQUENCY DOMAIN METHOD FOR IDENTIFICATION OF PHYSICAL PARAMETERS

In this paper, a-method using the complex modal theory to identify physical parameters of system with viscous damping is discussed. A procedure is present to calculate the mass, clamping, and stiffness matrices from the measured data in time and frequency domains. The double least squares approach is used to identify modal parameters. In identification of physical parameters, the data of different measured point is used in calculation for more accurate results.     

Testing and modal analysis on multi stage planetarygearbox housing of shield tunnelling machine

The finite element model is developed for the multi stage planetary gearbox housing in shield tunnelling machine (STM), and the the eigenvalue problem is solved by using block Lanczos method, and then the low order natural frequencies and corresponding modes are extracted. Based on the theory of experimental modal analysis, the modal testing is made for the gearbox housing by pulse excitation method. The least squares complex frequency domain (LSCF) estimation method is used to analyze the modal data, and the natural characteristics of housing is obtained. According to the modal assurance criterion (MAC), the experimental modal parameters are validated. Modal analysis shows that the experimental data is coincided with analytical results, which indicates the accuracy of the theoretical model and testing method. The coupling sympathetic vibration is disappearing between the gears train and housing, the local vibration is large at the high speed side of gearbox housing, and the torsional mode is outstanding under operating condition. The research results provide theoretical basis and experimental support for the structural optimization of the gearbox of STM.     

THE METHOD OF IMPROVING THE SPEED AND ACCURACY OF FFT AND SPECTRUM ANALYSIS

FFT(Fast Fourier Transform)is the basis of spectrum analysis. This paper gives out a method which can improve the speed and accuracy of FFT. The spectrum analysis based on the proposed method is of a high level: the amplitude error of spectrum is less then 1 % , the time of completing 1024 compler points FFT and 32 segments spectrum analysis is less then 250ms and only 5 seconds respectively.     

Weighted fusion algorithm for frequency estimation of the short signal with the same frequency and length

For high precise frequency estimation of the short sinusoid signal at low signal-to-noise ratio (SNR), a weighted fusion algorithm for frequency estimation of the short signal with the same frequency and length (SFL-Signal) is proposed. The spectrum model of SFL-Signal and the phase compensation matrix with phase coherent and noise cancellation are constructed. Secondly, the SFL-signal spectrum is weight-fused with the phase compensation matrix to obtain the result almost the same as that of the spectrum of the phase-coherent sinusoid signal. Consequently, high frequency estimation precision is obtained with spectral peak searching of the weight-fusion spectrum. Algorithm analysis and simulation results show that, compared with the existing methods,the proposed algorithm works better in term of precision, calculation complexity, noise immunity, and fits for any type of SFL-Signal.     

Comparative study on the identification of structural modal parameter using different methods

Chongqing Chaotianmen Yangtze River Bridge is the world's longest-span arch bridge. The node connections on its main truss’s lower chords are to bear millions of large-amplitude stress cycles caused by automobile and light-rail train loads. However, there exists no referential designing and testing experience in such detailing on long-span steel bridges at home and abroad as yet. High-cycle fatigue behavior testing on a detailing model has been conducted to study the fatigue reliability of the bridge’s critical node connections. The testing cycling load on the model is determined according to conventional specifications and the expected traffic flow on the Bridge. The 1/2-scale detailing model is carefully fabricated to simulate the node prototype and undergo the 2 million-cycle testing with the design load. Through testing, fatigue reliability of Chaotianmen Yangtze River Bridge’s main-truss lower-chord node connections during the design service life is verified. In addition, static test data are compared with those calculated by finite element analysis to prove the validity of the node model. In the end, fatigue destruction test of the model was carried out to get the fatigue failure law of the node connection and provide necessary parameters and reference for designing and monitoring of this bridge in the future.     

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.     

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。     

Digital modulation mode recognition based on multi-classclassification of support vector machine

To solve the overfitting, underfitting and local minimum existing in neural networks, a digital modulation mode recognition method based on support vector machine (SVM) is proposed. Seven characteristic parameters are extracted from instantaneous amplitude, instantaneous phase, instantaneous frequency, frequency spectrum, and changes in characteristics of the envelope to train support vector machine. Compared with the existing algorithms, using binary tree theory to design multi-class classifier has the features of simple, high-speed, high-precision. The simulation results indicate that the scheme can achieve 97% recognition accuracy when the signal to noise ratio (SNR) is above 15 dB with the AWGN channel.     

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.     

A Numerical Method for Transmission Line Equations

Transient analysis of transmission line has recently been received more attention because operating speeds in high-speed digital electronics are increasing. Transmission line equations are hyperbolic partial differential equations, firstly this paper deduces how to change transmission line equations into quasilinear differential equations , thus the transmission line equation numerical result is gotten by computing the differential formation of quasilinear differential equations. The constraint of voltage and current is be considered and lumped equivalent circuit mode at boundary network collaborated at the same time in finding boundary conditions. Finally the paper computes transient response of transmission line with two typical boundary conditions. Numerical result shows that this approach is an effective way. It is explicit algorithm with less CPU consumption which can get time field response directly. The agree-upon effective way does be frequency field method, however it could not get time response unless the numerical inverse laplace transformation (NILT) be introduced. Thus this approach is more effective than FFT algorithm.     

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.     

Calculation of lumped parameter of two-port network forvolume conduction energy transfer

Skin electrode unit is a channel through which energy can be transferred to the implanted device by volume conduction. The unit can be equivalent to lumped circuit, but so far there are no appropriate calculation methods of these circuit parameters, so variable load method based on field-circuit coupled is proposed. A skin electrode unit field circuit coupled model is established to obtain the relationship of the network parameters between voltage and current at electrode port, and the amplitude and phase of the power signal is extracted by the use of all phase FFT spectrum analysis. On this basis, equivalent circuit impedance parameters of the skin electrode unit under various conditions are obtained by the application of variable load method and the validity of the method is verified. As a result, the equivalent circuit impedance parameters obtained in this way can be used for the circuit analysis and optimization of the volume conduction energy transfer system.     

Parameter Optimization Analysis of Viscous Dampers for Dissipation Structure

The design method of parameter optimization of nonlinear viscous dampers for dissipation structure was analyzed based on response surface methods. The method included experimental design, finite element analysis, fitting the response surface function and parameter optimization. Taking a reinforced concrete frame structure for an instance, the mathematical model of parameter optimization of viscous dampers for dissipation structure was established by taking the minimum all damping force as objective function and taking the interlayer maximum displacement less than limits as constraints, and then the damper parameters were optimized using the method of nonlinear programming optimization. The results show that the method of parameter optimization of viscous dampers based on response surface method can ensure the structural displacement is less than limit and the construction cost can be reduced.     

Parameter Modifiability Based Transformer Substation State Estimation

The accuracy of transformer substation state estimation is widely low,and one reason of that is inaccurate(parameter) of model.Recently,most of papers about state estimation(SE) focus on improving algorithm.Based on classic SE and parameter estimation(PE),this paper takes advantage of the methods that putting parameters into state vector and putting parameters both into state vector and measurement vector in discussing the influence of parameter on transformer substation SE via simulation.The result of simulation shows: First,the error of parameters will be too high if only putting them into state vector,although the result of SE will be much better.Second,putting parameters both into state vector and measurement vector and giving them appropriate coefficient will lead a better result that can be used by engineering.     

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.     

Quantitative analysis of damage extent of transmission tower by using strain energy method

In order to solve the structural damage identification problem of transmission tower, a two-step identification method based on change rate and dissipation rate of modal strain energy is proposed. The damage location is identified by the change rate of modal strain energy method. Then, the modal strain energy dissipation rate theory is analyzed further by using the element stiffness matrix after injury. As a result, a more accurate damage quantification equation method is introduced. This method requires only several modals of vibration. The numerical simulation results show that this two-step method can find the damage location and damage degree of transmission towers effectively.     

Error Analysis between Relative Motion Solving Method and Absolute Displacement Direct Solving Method

Under multi-support earthquake excitation, the damping is proportional to the relative velocity in relative motion method, While the damping is proportional to the absolute velocity in method of direct solving absolute displacement, and the damping assuming difference may cause the calculation errors on structural responses. The structural response errors of the dynamic component of power spectral density between the two solving methods are derived by random vibration theoretical analysis in Rayleigh damping model, which include damping ratio and the ratio between excitation frequency and fundamental frequency of the structures. Based on probability theory, the variation errors of dynamic component response between the two solving methods are also derived by theoretical analysis, and some numerical examples are provided to verify the error analysis. At last, it is pointed out that the calculation errors between the two solving methods decrease with damping ratio, and it is negligible when the damping ratio of structure is less than 5%.