Numerical Study of the Vibrations of Beams with Variable Stiffness under Impulsive or Harmonic Loading

The behavior of beams with variable stiffness subjected to the action of variable loadings (impulse or harmonic) is analyzed in this paper using the successive approximation method. This successive approximation method is a technique for numerical integration of partial differential equations involving both the space and time, with well-known initial conditions on time and boundary conditions on the space. This technique, although having been applied to beams with constant stiffness, is new for the case of beams with variable stiffness, and it aims to use a quadratic parabola (in time) to approximate the solutions of the differential equations of dynamics. The spatial part is studied using the successive approximation method of the partial differential equations obtained, in order to transform them into a system of time-dependent ordinary differential equations. Thus, the integration algorithm using this technique is established and applied to examples of beams with variable stiffness, under variable loading, and with the different cases of supports chosen in the literature. We have thus calculated the cases of beams with constant or variable rigidity with articulated or embedded supports, subjected to the action of an instantaneous impulse and harmonic loads distributed over its entire length. In order to justify the robustness of the successive approximation method considered in this work, an example of an articulated beam with constant stiffness subjected to a distributed harmonic load was calculated analytically, and the results obtained compared to those found numerically for various steps (spatial h and temporal τ ¯ ) of calculus, and the difference between the values obtained by the two methods was small. For example for ( h=1/8 , τ ¯ =1/ 64 ), the difference between these values is 17%.

An explicit time domain solution for ground stratum response to harmonic moving load

Based on the thin layer method originally proposed in frequency domain, an explicit time domain semi-analytical solution has been developed for simulating three-dimensional layered ground responses to harmonic moving loads. The Fourier-Laplace transforms were applied to derive the transformed solution that satisfied the boundary conditions of horizontal infinities. The eigenvalue decomposition was performed with respect to Laplace parameter to express the ground motion corresponding to the eigenmodes. The formulation for each eigenmode incorporating the moving load expression was transformed back into time domain analytically, and the global system responses were given by means of the general mode superposition method. The proposed explicit time domain solution is suitable for studying various types of moving load acting on or inside the ground. In this paper a moving harmonic load with rectangular distribution was adopted to demonstrate the ground response simulation. Two illustrative examples for moving load with speeds below or above the ground Rayleigh wave velocity were presented to test the computational accuracy and efficiency of the proposed approach. A parametric study was also performed to investigate the influences of soil properties on the ground responses.

Nonlinear vibration of embedded single-walled carbon nanotube with geometrical imperfection under harmonic load based on nonlocal Timoshenko beam theory

Based on the nonlocal continuum theory, the nonlinear vibration of an embedded single-walled carbon nanotube （SWCNT） subjected to a harmonic load is in- vestigated. In the present study, the SWCNT is assumed to be a curved beam, which is unlike previous similar work. Firstly, the governing equations of motion are derived by the Hamilton principle, meanwhile, the Galerkin approach is carried out to convert the nonlinear integral-differential equation into a second-order nonlinear ordinary differ- ential equation. Then, the precise integration method based on the local linearzation is appropriately designed for solving the above dynamic equations. Besides, the numerical example is presented, the effects of the nonlocal parameters, the elastic medium constants, the waviness ratios, and the material lengths on the dynamic response are analyzed. The results show that the above mentioned effects have influences on the dynamic behavior of the SWCNT.

A closed-form solution for a double infinite Euler-Bernoulli beam on a viscoelastic foundation subjected to harmonic line load

The dynamic response of a double infinite beam system connected by a viscoelastic foundation under the harmonic line load is studied. The double infinite beam system consists of two identical and parallel beams, and the two beams are infinite elastic homogeneous and isotropic. A viscoelastic layer connects the two beams continuously. To decouple the two coupled equations governing the response of the double infinite beam system, a variable substitution method is introduced. The frequency domain solutions of the decoupled equations are obtained by using Fourier transforms as well as Laplace transforms successively. The time domain solution in the generalized integral form are then obtained by employing the corresponding inverse transforms, i.e. Fourier transform and inverse Laplace transform. The solution is verified by numerical examples, and the effects of parameters on the response are also investigated.

Research on Harmonic Characteristics of Nonlinear Loads in PEMFC Generator

Hydrogen as a clean energy source is made full use, this paper researches the electrical model of PEMFC generator, analyzes the harmonic trend and its hazards when the generator operates with linear load and nonlinear load running synchronously, comparatively analyzes the commonly used harmonic suppression technology. Simulate and analyze the filter performance when APF is used. The results illustrate that as a filter device, APF can absorb the harmonic properly in PEMFC power system.

HALF-SPACE GREENS'S FUNCTION DUE TO A SPATIALLY HARMONIC LINE LOAD AND SCATTERED FIELDS IN THE FAR FIELD REGION

Half-space Green's function due to a spatially harmonic line load has been expressed as a sum of the full-space Green's functions and a 2-D integral representation of the reflected waves by the free surface of the half-space.By using the obtained half-space Green's function,an integral rep- resentation of the scattered waves by a cylindrical obstacle is then derived.Finally,by analyzing the far-zone behavior of the integrands of the integral representation.the far-field pattern of the scattered waves in a half-space obtained.

Power System Harmonics Study for Unbalanced Microgrid System with PV Sources and Nonlinear Loads

Harmonics distortion is a crucial problem in microgrid. Harmonic sources can be categorized as two main factors: renewable energy integration and nonlinear loads. Both factors are investigated in this paper. For renewbale energy, photovoltaic (PV) power is one of the most effective solutions for energy crisis and it is showing great potential for serving customers in microgrid. A three- phase PV source model is establised and integrated at different locations in order to observe the impact of harmonics on a microgrid and power quality (PQ). A composite load is modeled using Crossed Frequency Admittance Matrix theory. A practicdal microgrid loacated at GA, USA is used as a study system. The microgrid, PV model and nonlinear load model are simulated in MATLAB/ Simulink environment. The results show the impact of installing PV sources at two types of locations considering linear and composite nonlinear loads. In addition, three PQ indices are discussed to show the numerical impacts with various perspectives.

Load Static Models for Conservation Voltage Reduction in the Presence of Harmonics

The Conservation Voltage Reduction (CVR) is a technique that aims to achieve the decrease of power consumption as a result of voltage reduction. The customer is supplied with the lowest possible voltage level compatible with the stipulated level by the regulatory agency. International Standards ANSI C84.1-2006 and IEEE std 1250-1995 specify the range of supply voltage to electronics equipment from 0.9 to 1.05 pu of nominal voltage. To analyse the CVR effect in distribution systems with different load characteristics (residential, commercial, industrial or a combination of these), mathematical load models are used. Typically, these equipment/load models are used to analyse load aggregation without any consideration of its nonlinearity characteristics. Aiming to analyse the nonlinear characteristics and its consequences, this paper presents a discussion of the neglected variables as well as the results of a set of measurements of nonlinear loads. Different mathematical models are applied to obtain them for each load. Using these models the load aggregation is evaluated. It is presented that although the models show adequate results for individual loads, the same does not occur for aggregated models if the harmonic contribution is not considered. Consequently, to apply the load model in CVR it is necessary to consider the harmonics presence and the model has to be done using only the fundamental frequency data. The discussion about the causes is done and the models are compared with the measurements.

The research of load spectrum between flexible gear and wave generator of harmonic drive

The harmonic drive is a kind of gear transmission that uses wave generator to produce controllable soft round elastic deformation and engages with rigid gear to transmit motion and power. The load distribution on the surface of the flexible gear and wave generator is an important parameter of studying the deformation of flexible gear and flexible bearing outside the wave generator and is also a necessary condition for studying the fatigue damage of flexible gear under alternating load. In this paper, a 3D model of 32-type 80：1 harmonic drive is build. Based on the generalized Hooke law, a hypothesis of load distribution which is proved to be validity by using finite element simulation is proposed on the interface of flexible gear and wave generator. On this base, the mathematic model and the quantitative calculation formula of the load distribution on the surface of the flexible gear and wave generator are proposed which provide a basis for the dynamic analysis and the fatigue damage of harmonic gear drive.

Harmonic Contributions of Utility and Customer Based on Load Model Using Field Measurements

In recent years, sinusoidal waveform of the current and voltage disturbs in the electrical distribution system because of the due to the increasing number of non-linear loads. Many standards of IEC and IEEE standards have been published in order to limit the voltage and current waveform distortion. The operators of the electricity distribution network widely use the power quality monitoring systems at the point of common connection (PCC). It has been identified that there are substantial number of harmonic currents excess of the standards transferred to the grid according to the data obtained from power quality monitoring systems. In case of exceeding the limits specified in the standards, there is a need to determine the network and customer responsibilities for the implementation of required sanctions. In this study, using recorded data at the PCC of a medium voltage electrical distribution system, voltage and current harmonic distortion responsibilities of the network and customer are determined by the improved harmonic current vector method. Up-to-date load model based on field measurement which provides more accurate results has been used instead of the constant load impedance in the proposed method.

Equivalent Impedance Parameter Calculation of Three-phase Symmetrical Loads for Harmonic Source Location

The equivalent impedance parameters of loads have been widely used to identify and locate the harmonic sources.However,the existing calculation methods suffer from outliers caused by the zero-crossing of the denominator.These outliers can result in inaccuracy and unreliability of harmonic source location.To address this issue,this paper proposes an innovative method of equivalent impedance parameter calculation of three-phase symmetrical loads that avoid outliers.The correctness and effectiveness of the proposed method are verified by simulations on Simulink using actual monitoring data.The results show that the proposed method is not only simple and easy to implement but also highly accurate.

Harmonic Analyses of Hydrodynamic Characteristics for Gap Resonance Between Fixed Box and Vertical Wall

Two marine structures arranged side by side with a narrow gap may suffer from violent free-surface resonance,which would cause green water on deck,dramatically raise hydrodynamic loads on structures and seriously threaten the operation safety.The CFD-based open-sourced software,OpenFOAM?,is employed to simulate the twodimensional fluid resonance inside a narrow gap between a fixed box and a vertical wall induced by regular waves with different wave heights.The topographies with various plane slopes are placed in front of the wall.The focus of this article is on the influences of the incident wave height and the topographic slope on the nonlinear characteristics of various hydrodynamic parameters(including the wave height in the gap,the vertical wave force,and the horizontal wave force on the box)during gap resonance.The ratios of their high-order to the corresponding 1 st-order components under different sets of the incident wave height and the topographic slope are analyzed.It is found that the relative importance of all the high-order components increases gradually with the incident wave height for all the three parameters.The topographic influence on them closely depends on the type of the parameters and the incident wave height.In addition,the occurrence of the 2 nd-order gap resonance phenomenon can cause the 2 nd-order wave height and horizontal force to be significantly larger than the corresponding 1 st-order components.

Coordinated Control for Harmonic Mitigation of Parallel Voltage-source Inverters

The increasing use of power electronic devices can deteriorate the power quality by introducing voltage and current harmonics.In islanded microgrids,the presence of nonlinear loads can distort the point of common coupling(PCC)voltage,while the dead-time effect can also bring additional circulating current harmonics among parallel inverters.To simultaneously attenuate the PCC voltage harmonics and suppress the dead-time induced circulating current harmonics,this paper proposes a coordinated control strategy for harmonic mitigation of parallel inverters.The proposed control strategy allows inverter impedances to be properly reshaped at selective harmonic frequencies.As a consequence,the PCC voltage harmonics are filtered by the inverter operating in the harmonic compensation mode(HCM),whereas the dead-time induced circulating current harmonics are suppressed by the inverter operating in the harmonic rejection mode(HRM).Experimental results from an islanded microgrid prototype with two parallel inverters are provided to validate the effectiveness of the proposed control strategy.

Effects of Harmonics on Power Loss in XLPE Cables

Harmonics in power systems is increasingly at high level. Also, there has been an incredible growth in the use of cross linked polyethylene (XLPE) cables in distribution systems. Harmonics cause additional power loss/temperature rise;causing premature failure of cables. Catastrophic failure of power cables leads to great inconvenience to consumers and loss of system reliability and money. To avoid the overheating of power cables;the additional power loss due to harmonics should be accurately calculated and properly accommodated by derating the cable. The present method of calculating the power loss in cables in harmonics rich environment is very arduous. The aim of this paper is to present the reasonably accurate method for evaluating effects of harmonics on the power loss in XLPE cables. Computational model is developed in MATLAB for power loss calculation using conventional method. Using this model, calculations are performed for aluminium and copper conductor XLPE cables of different size and type;for three different types of harmonics spectrums having total harmonics distortion (THD) of 30.68%, including all odd harmonics components up to 49th order. Using these results;a mathematical model in the form of simple empirical formula is developed by curve fitting technique. The results obtained by various models are presented and compared with error justification.

考虑风电谐波影响与出力随机性的电力系统无功优化方法

电容器组等无功补偿装置的优化调整不仅可以减小电力系统网损,还会对电力系统的谐波潮流与谐波网损产生影响.风电不仅存在出力不确定性,而且会产生谐波污染,影响谐波潮流与谐波网损.然而,传统无功优化方法没有同时考虑风电的谐波特性与出力不确定性对谐波潮流和谐波网损的影响,可能导致谐波超标问题,不利于电力系统降低网损.因此,本文首先构建计及风电谐波影响的电力系统无功随机优化模型.该模型通过场景法对风电出力随机性进行建模,目标函数同时考虑基波和谐波网损,约束条件包括基波和谐波潮流约束、电压谐波总畸变率约束等.然后,针对该谐波约束的无功随机优化模型,本文提出了融合驱动力可调粒子群算法和全连接型深度神经网络的高效求解方法 .最后,通过三个修改后的IEEE测试系统对所提模型与方法的有效性进行了验证.

Pasternak地基中H(t)-V受荷桩水平响应有限杆单元法分析

为探讨桩顶水平动荷载H(t)与竖向荷载V联合作用下桩基的水平响应,基于Pasternak地基和Euler梁理论,建立了桩-土相互作用水平振动分析模型,采用改进的有限杆单元方法求解考虑P-Δ效应、土体剪切效应影响的综合刚度矩阵方程,结合桩土连续边界条件得到桩身内力与位移解答.通过与已有解析解、有限元解和模型试验的结果比较,验证了计算方法的合理性.最后,对影响桩身内力与位移的主要因素进行分析.结果表明:1)传统Win⁃kler地基相较于Pasternak地基模型,忽略了地基土体的剪切效应,将夸大桩体结构的实际受力,使得计算得到的桩身水平位移和弯矩均大于Pasternak地基所得结果,且随着桩土弹模比Ep/Es的降低,两种地基模型计算的桩身最大水平位移和弯矩的差异性呈现出增强趋势;2)随着桩顶竖向荷载的增加,桩身水平位移和弯矩受P-Δ效应的影响显著.当桩顶竖向荷载特征参数λ由0增至2时,桩身最大水平位移和弯矩分别提高40.85%和78.57%;3)相较无限长桩(L>20d_(p)),有限长桩的水平位移和弯矩的动力响应受桩身长径比L/d_(p)影响更大;桩身最大水平位移和弯矩随着水平简谐荷载幅值H_(0)的增加而增大,随着无量纲频率a_(0)的增大而减小.

车用SLM成形DP780钢的疲劳损伤非线性电磁超声换能检测

为了提高对车用选区激光熔化(SLM)成形DP780钢的疲劳损伤检测精度,提出了一种基于非线性电磁超声换能的疲劳加载信号分析方法,通过高次谐波检测技术测定合金的损伤情况。研究结果表明:时域信号波形相对较为稳定,基波幅值在频率为5 MPa时出现,在5000次疲劳测试后,与初始试件相比,试样中产生信号的幅值更显著。非线性电磁超声换能检测很容易影响二次谐波的产生。二次谐波具有更高的幅值,大量疲劳裂纹存在于基体内部。本研究可满足精准检测疲劳损伤条件。在对疲劳损伤程度确定时,参考疲劳寿命和循环加载周次,超声非线性系数在周边测试点处增长幅度相对较小,中心测试点较大,主要原因是内部结构变形情况更明显。

基于盲源分离的工业谐波源负荷分类识别方法

针对传统谐波源辨识方法无法实现工业用户谐波源具体类型的非侵入式识别的问题,该文提出一种基于盲源分离的工业谐波源负荷分类识别方法。该方法仅依据工业用户进线处电压、电流数据即可实现谐波源负荷具体类型的非侵入式识别。首先,从负荷等值阻抗模型入手,建立工业用户多负荷等值阻抗并联电路模型;其次,采用集合经验模态分解与奇异值分解相结合的方法确定构成用户进线处监测点综合等值阻抗信号的源阻抗信号数目;然后,采用快速独立分量分析实现将谐波源负荷等值阻抗信号从综合负荷等值阻抗信号中分离;最后,将分离出谐波源负荷等值阻抗信号频率特征与典型谐波源负荷进行匹配,进而实现分类识别。仿真与实测实验结果均表明,所提方法能够准确识别工业用户所含多种谐波源负荷的具体类型,具有较好的可行性和实用性。

复杂电能信号谐波时频域特征分析及其对电能计量影响

为准确分析复杂电能信号谐波时频域特性对电能计量的影响,提出了一种零值搜索-短时傅里叶变换时频域电压、电流信号幅度和相位分析算法,利用信号波形过零特征,自适应调整短窗傅里叶变换的时域窗宽,解决了电网频率波动导致的相位累积效应对相位分析的影响,算法的幅值分析误差为10-3、相位分析误差小于1°;建立了复杂电能信号时频域数据表征模型和4类时频域全局化特征矩阵提取算法,解决了时频域特性表征与提取的问题;以典型非线性动态负荷中频炉为分析案例,分析给出了其4类时频域全局化特征,并建立了畸变波形动态电能测试信号特征模型,通过辅助实验验证了4个时频域全局化特征对电能表动态超差的影响,提出了对国际和国内标准修改的建议。

简谐荷载作用下井字梁楼盖动力特性试验研究

以某工业厂房井字梁楼盖在大型动力设备运行时存在的异常振动问题为例,提出了增加井字梁高度、增大楼板厚度2种减振加固方案,通过缩尺模型试验研究了简谐荷载作用下不同加固方案对井字梁楼盖结构的减振效果,并通过有限元分析软件ABAQUS的数值模拟对缩尺模型试验结果进行了验证。结果表明,2种加固方案均能降低楼盖结构的竖向振动,其中增加井字梁高度比增大楼板厚度的减振效果更加显著。