Imposing nodes for linear structures during harmonic excitations using SMURF method

Vibration absorbers are usually designed using the finite element (FE) model of structures. It is generally believed that the modal models are more accurate than FE models, because in modal testing the model is built by direct measurement of the test structure. In this paper, a method is proposed to design a translational vibration absorber using the measured frequency response functions of a primary structure. The designed vibration absorber imposes a node on the structure when it is excited by a harmonic force. The method is based on the structural modification using experimental frequency response functions technique and determines the required receptance of the absorber at the excitation frequency. Moreover, a procedure is developed to suppress the vibration amplitude of two arbitrary points on a linear structure subjected to harmonic excitations by attaching two sprung mass absorbers. A cantilever beam is considered for the numerical case study, and the sprung masses are designed to suppress the vibration amplitude of the beam at the selected arbitrary points. A U-shape plate was considered for the experimental validation of the method for imposing a node using one absorber. Also, a beam was tested to demonstrate the effectiveness of method for imposing two nodes on the structures. The experimental results show that the designed absorbers can considerably suppress the vibration amplitude at the selected points on the structure.     

Implementation of integral fixed-time sliding mode controller for speed regulation of PMSM servo system

The paper presents a new concept of absorbing car body vibrations, which consists in a modification of the construction of the classical mono-tube hydraulic shock absorber by the introduction of an additional inner cylinder with an auxiliary piston. By making an appropriate selection of the system parameters, one may obtain the damping force characteristics dependent on the excitation amplitude and frequency. In the case of driving on a good-quality road surface, the shock absorber displays the soft characteristics which are desired as far as the driving comfort is concerned. In the case of worse-quality roads or while overcoming large obstacles, the hard characteristics ensure a higher level of safety and protect the shock absorber from getting damaged. The developed nonlinear model makes it possible to effectively analyse the system responses to harmonic, impulse and random excitations. On the basis of the analysis of the impact of harmonic excitations on the driving comfort and safety indexes, one may estimate the optimal values of the shock absorber construction parameters. Impulse and random excitations are applied in order to finally verify the effectiveness of the operation of the proposed shock absorber.

     

Modeling wall effects in a micro-scale shock tube using hybrid MD–DSMC algorithm

Wall effects in a micro-scale shock tube are investigated using the Direct Simulation Monte Carlo method as well as a hybrid Molecular Dynamics–Direct Simulation Monte Carlo algorithm. In the Direct Simulation Monte Carlo simulations, the Cercignani–Lampis–Lord model of gas–surface interactions is employed to incorporate the wall effects, and it is shown that the shock attenuation is significantly affected by the choice of the values of tangential momentum accommodation coefficient. A loosely coupled Molecular Dynamics–Direct Simulation Monte Carlo approach is then employed to demonstrate incomplete accommodation in micro-scale shock tube flows. This approach uses fixed values of the accommodation coefficients in the gas–surface interaction model, with their values determined from a separate dynamically similar Molecular Dynamics simulation. Finally, a completely coupled Molecular Dynamics–Direct Simulation Monte Carlo algorithm is used, wherein the bulk of the flow is modeled using Direct Simulation Monte Carlo, while the interaction of gas molecules with the shock tube walls is modeled using Molecular Dynamics. The two regions are separate and coupled both ways using buffer zones and a bootstrap coupling algorithm that accounts for the mismatch of the number of molecules in both regions. It is shown that the hybrid method captures the effect of local properties that cannot be captured using a single value of accommodation coefficient for the entire domain.     

汽车模拟碰撞用液压缓冲器的动态仿真

汽车模拟碰撞(台车试验)用缓冲装置是汽车零部件安全试验中一个非常关键的设备。应用孔口节流理论，建立了汽车模拟碰撞用液压缓冲器的力学模型，同时对主要参数对模型的影响进行了具体的讨论。试验证明，进行参数优化后，计算曲线能够很好地模拟试验曲线。该仿真过程可以为类似液压缓冲器的理论建模和调试提供依据。     

Application of an Itô-based approximation method to random vibration of a pinching hysteretic system

In this paper, an extension of the Cumulant-Neglect closure scheme is utilized for the random vibration analysis of a single degree of freedom system with a general pinching hysteresis restoring force. The hysteresis element used in the system model can simulate commonly observed forms of stiffness, strength and pinching degradations. The second order statistics of the system response to a stationary Gaussian white noise input are derived using an Itô-based approximation technique. The validity of these response statistics are then verified by comparing them to Monte Carlo simulation results. The numerical studies performed for different combinations of degradation parameters and excitation levels show that the response estimates obtained by this solution method are in good agreement with Monte Carlo simulation. These studies also indicate the applicability of this technique for response analysis of complicated forms of non-linearities.     

Numerical solutions of the Boltzmann equation: comparison of different algorithms

In the paper we compare different algorithms for numerical solutions of the Boltzmann equation. For this comparison we have taken the standard problem of the shock wave structure in a mono-atomic rarefied gas. Different parameters characterizing the shock structure have been calculated by a Monte Carlo simulation (DSMC), a second order time-relaxed Monte Carlo method (TRMC2), a fully deterministic discrete velocity method (DV), a discrete velocity method with Monte Carlo calculations of collision integral (DVMC) and a molecular dynamics method (MD). Results of these calculations have been compared with the shock wave structure obtained in experiments in a shock tube. The results of the comparison are not conclusive. We have observed general agreement between numerical and experimental results but there is no single numerical method which fits best to the experimental measurements.     

Random excitation of coupled oscillators with single and simultaneous internal resonances

The primary objective of this paper is to examine the random response characteristics of coupled nonlinear oscillators in the presence of single and simultaneous internal resonances. A model of two coupled beams with nonlinear inertia interaction is considered. The primary beam is directly excited by a random support motion, while the coupled beam is indirectly excited through autoparametric coupling and parametric excitation. For a single one-to-two internal resonance, we used Gaussian and non-Gaussian closures, Monte Carlo simulation, and experimental testing to predict and measure response statistics and stochastic bifurcation in the mean square. The mean square stability boundaries of the coupled beam equilibrium position are obtained by a Gaussian closure scheme. The stochastic bifurcation of the coupled beam is predicted theoretically and experimentally. The stochastic bifurcation predicted by non-Gaussian closure is found to take place at a lower excitation level than the one predicted by Gaussian closure and Monte Carlo simulation. It is also found that above a certain excitation level, the solution obtained by non-Gaussian closure reveals numerical instability at much lower excitation levels than those obtained by Gaussian and Monte Carlo approaches. The experimental observations reveal that the coupled beam does not reach a stationary state, as reflected by the time evolution of the mean square response. For the case of simultaneous internal resonances, both Gaussian and non-Gaussian closures fail to predict useful results, and attention is focused on Monte Carlo simulation and experimental testing. The effects of nonlinear coupling parameters, internal detuning ratios, and excitation spectral density level are considered in both investigations. It is found that both studies reveal common nonlinear features such as bifurcations in the mean square responses of the coupled beam and modal interaction in the neighborhood of internal resonances. Furthermore, there is an upper limit for the excitation level above which the system experiences unbounded response in the neighborhood of simultaneous internal resonances.     

Monte Carlo method of radiative transfer applied to a turbulent flame modeling with LES

Radiative transfer plays an important role in the numerical simulation of turbulent combustion. However, for the reason that combustion and radiation are characterized by different time scales and different spatial and chemical treatments, the radiation effect is often neglected or roughly modelled. The coupling of a large eddy simulation combustion solver and a radiation solver through a dedicated language, CORBA, is investigated. Two formulations of Monte Carlo method (Forward Method and Emission Reciprocity Method) employed to resolve RTE have been compared in a one-dimensional flame test case using three-dimensional calculation grids with absorbing and emitting media in order to validate the Monte Carlo radiative solver and to choose the most efficient model for coupling. Then the results obtained using two different RTE solvers (Reciprocity Monte Carlo method and Discrete Ordinate Method) applied on a three-dimensional flame holder set-up with a correlated-k distribution model describing the real gas medium spectral radiative properties are compared not only in terms of the physical behavior of the flame, but also in computational performance (storage requirement, CPU time and parallelization efficiency). To cite this article: J. Zhang et al., C. R. Mecanique 337 (2009).     

Nonlinear oscillatory processes in wheeled vehicles

The free damped vibrations of a wheeled vehicle with independent suspension are analyzed with allowance for the nonlinear characteristics of the suspension springs and shock absorbers. The vibrations of a wheeled vehicle with a suspension with smooth nonlinear characteristics are studied for a model with seven degrees of freedoms. The skeleton curves and nonlinear normal modes are obtained. For a model with two degrees of freedoms (quarter-car) that corresponds to axisymmetric vibrations, the nonlinear normal modes are found in the case of a shock absorber with nonsmooth nonlinear characteristic     

Evaluation of coil absorber performance

A model was developed to determine the performance of the counter and parallel flow absorbers using water-lithium bromide solution. The simulation method of heat and mass transfer in the coil absorber is explained and a computer program was generated and applied. The effects of the main parameters on the absorber performance were determined and the results were presented in graphical form. It has been proved that the model explained in this study is capable of predicting an estimated wetted area and can approximate heat transfer coefficients and so can predict the absorber performance.     

随机激励下滞迟系统的稳态响应闭合解

滞迟系统属于一类典型的强非线性系统,滞迟力不仅取决于系统的瞬时变形,还与变形历程有关.虽然滞迟系统的随机振动问题已被广泛研究,但至今尚未得到滞迟系统随机响应概率密度函数的精确闭合解.本文运用迭代加权残值法获得了高斯白噪声激励下Bouc-Wen滞迟系统稳态响应概率密度函数的近似闭合解.首先,运用等效线性化法求出系统的稳态高斯概率密度函数;然后以此构造权函数,应用加权残值法求得了系统指数多项式形式的非高斯概率密度函数;最后引入迭代的过程,逐步优化权函数,提高计算所得结果的精度.以随机地震激励下钢纤维陶粒混凝土结构的稳态响应作为算例,其中Bouc-Wen模型的参数是基于拟静力学试验数据,并应用最小二乘法辨识获得.与Monte Carlo模拟结果相比,等效线性化法得到的结果精度较差;由加权残值法得到的结果能够表现出非线性特征,但其精度依然无法令人满意;采用迭代加权残值法得到的近似闭合解与Monte Carlo模拟的结果吻合非常好;对于较强随机激励情形,采用渐进迭代加权残值法具有较高的求解效率,所获得的理论解析解具有较高的精度.结果表明,所获得的近似闭合解不仅对于土木工程领域具有重要的实际应用价值,而且还可作为检验其他非线性系统随机响应预测方法的精度的标准.     

Nonlinear dynamic responses of twin-tube hydraulic shock absorber

Basically on the multi-body system dynamics, the virtual prototype of the hydraulic shock absorber for the bench test is developed in the ADAMS environment. Dynamic behaviors of the absorber are studied by both computer simulation and real test. Numerical predictions of dynamic responses are produced by the established virtual prototype of the absorber and compared with experimental results. It has been shown from the comparison that the vibration behaviors of the prototype with hysteretic damping characteristics are considered to be more identical with the bench test results than those of the same prototype with piecewise linear damping properties are. The current virtual prototype of the shock absorber is correct and can be a developing terrace for the optimizing design of the absorber and matching capability of the whole car.     

OPTIMAL DAMPING MATCHING Of SHOCK ABSORBER FOR A LIGHT TRUCK SUSPENSION SYSTEM

阻尼匹配是制约车辆悬架系统减振器设计的关键问题.以某轻型卡车为研究对象,利用MATLAB软件建立了悬架阻尼优化设计的半车模型.采用车体垂向加速度、俯仰角加速度和车轮动载均方根值作为评价指标,利用线性加权和法建立了悬架阻尼优化设计的目标函数.在随机路面激励下,对悬架系统阻尼进行了优化匹配和分析,并通过实车实验验证了优化效果.研究结果表明,悬架阻尼的匹配优化可有效提高车辆的行驶平顺性,从而为车辆悬架的动态设计提供有益参考.     

非高斯随机激励下滞迟系统响应与首次穿越失效

针对由有界噪声、泊松白噪声和高斯白噪声共同构成的非高斯随机激励,通过Monte Carlo数值模拟方法研究了此激励作用下双线性滞迟系统和Bouc-Wen滞迟系统这两类经典滞迟系统的稳态响应与首次穿越失效时间。一方面,分析了有界噪声和泊松白噪声这两种分别具有连续样本函数和非连续样本函数的非高斯随机激励,在不同激励参数条件下对双线性滞迟系统和Bouc-Wen滞迟系统的稳态响应概率密度、首次穿越失效时间概率密度及其均值的不同影响;另一方面,揭示了在这类非高斯随机激励荷载作用下,双线性滞迟系统的首次穿越失效时间概率密度将出现与Bouc-Wen滞迟系统的单峰首次穿越失效时间概率密度截然不同的双峰形式。     

Vibration absorbers for a rotating flexible structure with cyclic symmetry: nonlinear path design

This paper analytically investigates the nonlinear dynamics of order-tuned vibration absorbers applied to cyclic rotating flexible structures under traveling wave (TW) engine-order excitation. The primary cyclic structure is assumed to be governed by linear vibrations and the nonlinear absorber response arises from large amplitude kinematic effects. These dynamics are captured by a lumped-parameter model that consists of N blades with one blade mode and one absorber per blade, which are arranged with cyclic symmetry on a rotating disk. The governing equations of motion are formulated for arbitrary absorber paths to allow investigation of the absorber path design for nonlinear response. This paper extends previous work by the authors, which considered the linearized blade and absorber dynamics of a similar system. Several intriguing features of the dynamics were uncovered, most notably the existence of an absorber tuning range that avoids resonance at any rotation speed. Of particular interest is the existence and stability of the steady-state TW response to TW excitation, as experienced in turbomachinery, and how these are affected by selection of the absorber paths, which fix the linear and nonlinear tuning characteristics. It is shown that the TW response, which is unique for the linearized system, also exists for the weakly nonlinear model and can be captured by an equivalent two degree of freedom model obtained using the symmetry of the excitation and system response. The forced response exhibits the usual characteristics of a weakly nonlinear system, specifically, bistability and the attendant hysteresis near resonance. More significantly, it does not experience any additional instabilities associated with the symmetry. That is, the desired TW response is robust to nonlinear effects in the absorber, which allows use of the simple equivalent model for selection of absorber tuning parameters. For good performance and robustness, the linear absorber tuning should be in the “no-resonance zone” described by the linear theory and the absorber paths should have a slightly softening nonlinear characteristic.     

The effects of Coulomb friction on the performance of centrifugal pendulum vibration absorbers

We investigate analytically and experimentally the effects of Coulomb friction on the performance of centrifugal pendulum vibration absorbers (CPVAs), which are used to reduce torsional vibrations in rotating machinery. The analysis is based on perturbation methods applied to the nonlinear equations of motion for a rotor subjected to an engine order applied torque and equipped with a circular path CPVA with viscous and Coulomb damping. The experimental work is based on quantifying parameters for the damping model using free vibration measurements with a viscous and Coulomb damping identification scheme that is enhanced to better handle measurement noise, and running tests for steady-state operation under a range of loading conditions. The level of Coulomb damping is varied by adjusting the friction of the absorber connection bearing. Good agreement is found between the analytical predictions and the experimental data. It is shown that the absorber sticks up to a level of excitation that allows it to release, after which the Coulomb damping acts in the expected manner, resulting in lowered response amplitudes. The results obtained are of general use in assessing absorber performance when dry friction is present in absorber suspensions.     

Nonlinear Random Response of Ocean Structures Using First- and Second-Order Stochastic Averaging

This paper deals with the dynamic response of nonlinear elastic structure subjected to random hydrodynamic forces and parametric excitation using a first- and second-order stochastic averaging method. The governing equation of motion is derived by using Hamilton's principle, taking into account inertia and curvature nonlinearities and work done due to hydrodynamic forces. Within the framework of first-order stochastic averaging, the system response statistics and stability boundaries are obtained. Unfortunately, the effects of nonlinear inertia and curvature are not reflected in the final results, since the contribution of these nonlinearities is lost during the averaging process. In the absence of hydrodynamic forces, the method fails to give bounded response statistics, and the analysis yields stability conditions. It is the second-order stochastic averaging which can capture the influence of stiffness and inertia nonlinearities that were lost in the first-order averaging process. The results of the second-order averaging are compared with those predicted by Gaussian and non-Gaussian closures and by Monte Carlo simulation. In the absence of parametric excitation, the non-Gaussian closure solutions are in good agreement with Monte Carlo simulation. On the other hand, in the absence of hydrodynamic forces, second-order averaging gives more reliable results in the neighborhood of stochastic bifurcation. However, under pure parametric random excitation, the stochastic averaging and Monte Carlo simulation predict the on-off intermittency phenomenon near bifurcation point, in addition to stochastic bifurcation in probability.     

Stabilization of a 1/3-order subharmonic resonance using nonlinear dynamic vibration absorber

The paper proposes a stabilization method for a 1/3-order subharmonic resonance with a new type of nonlinear vibration absorber using nonlinear coupling between a main system and the absorber. The main system with nonlinear restoring force and harmonic excitation, i.e., subjected to a sinusoidally changed magnetic force, is introduced as a model which produces a 1/3-order subharmonic resonance. A damped pendulum, whose natural frequency is tuned to be in the neighborhood of twice that of the main system, is connected through a link to the main system as a nonlinear vibration absorber. Theoretical results using the method of multiple scales show that only a stable nontrivial steady state is changed into an unstable one due to the effect of absorber. In addition, we numerically confirm the validity of the proposed absorber using Runge–Kutta method.     

Multiple Internal Resonance in Suspended Cables under Random In-Plane Loading

The random excitation of a suspended cable with simultaneous internal resonances is considered. The internal resonances can take place among the first in-plane and the first two out-of-plane modes. The external loading is represented by a wide-band random process. The response statistics are estimated using the Fokker-Planck-Kolmogorov (FPK) equation, together with Gaussian and non-Gaussian closures. Monte Carlo simulation is also used for numerical verification. The unimodal in-plane motion exists in regions away from the internal resonance condition. The mixed mode interaction is manifested within a limited range of internal detuning parameters, depending on the excitation power spectrum density and damping ratios. The Gaussian closure scheme failed to predict bounded solutions of mixed mode interaction. The non-Gaussian closure results are in good agreement with the Monte Carlo simulation. The on-off intermittency of the autoparametrically excited modes is observed in the Monte Carlo simulation over a small range of excitation levels. The influence of the cable parameters, such as damping ratios, sag-to-span ratio, internal detuning parameters, and excitation level on the autoparametric interaction, is studied. It is found that the internal detuning and excitation level are the two main parameters which affect the autoparametric interaction among the three modes. Due to the system's nonlinearity, the response of the three modes is strongly non-Gaussian and the coupled modes experience irregular modulation.     

Nonlinear equivalent model and its identification for a delayed absorber with magnetic action using distorted measurement

For an absorber with the magnetic action and the delayed feedback, the equivalent strongly nonlinear model of the magnet force is proposed. We develop an identification algorithm with correcting distorted output measurement to identify and estimate the relevant parameters of the equivalently nonlinear model and the time delay in the feedback loop. The detailed steps of the algorithm are given analytically. We configure an experimental device of a delayed electromechanical absorber with action of the nonlinear magnetic force. The new algorithm is employed to identify the relative parameters of the device, such as time delay, damping and nonlinear stiffness, based on data of the output measurement with distortion. The results show that it is reasonable that the magnet action may be equivalent to the cubic nonlinear force. One may also see that the new algorithm may treat the experimental distorting measurement and correct it as long as the measurement still keeps periodicity. As an important result, values of the identified parameters with the correcting distortion are closer to those of the original measurement than those without the no correcting distortion for some excitation frequencies. It means that the algorithm may correct the polluted measurement, so that the quality of the identification is greatly improved. The new algorithm may be useful for design of nonlinear electromechanical absorber with time-delayed feedback.