应用浮动冲击平台考核舰载设备响应分析

为研究安装甲板模拟器的浮动冲击平台系统考核舰载设备的机理,对整个系统建立有限元模型进行数值模拟并建立力学模型进行了理论分析。根据船体甲板结构产生的垂向低通滤波特性,提出甲板模拟器具有减缓高频冲击并满足设备安装频率要求的作用。将被试设备的浮动冲击平台考核系统简化为有阻尼的三自由度系统强迫振动模型,通过拉普拉斯变换方法求解了不同冲击环境下被试设备的响应。数值模拟与理论计算结果比较吻合,被试设备响应迅速达到峰值后逐渐衰减,振动频率由高频向低频过渡,在分析浮动冲击平台舰载设备考核系统长时间响应时需考虑阻尼的影响。     

Dynamic behavior of bridge-erecting machine subjected to moving mass suspended by wire ropes

The dynamic behavior of a bridge-erecting machine, carrying a moving mass suspended by a wire rope, is investigated. The bridge-erecting machine is modelled by a simply supported uniform beam, and a massless equivalent “spring-damper” system with an effective spring constant and an effective damping coefficient is used to model the moving mass suspended by the wire rope. The suddenly applied load is represented by a unitary Dirac Delta function. With the expansion method, a simple closed-form solution for the equation of motion with the replaced spring-damper-mass system is formulated. The characters of the rope are included in the derivation of the differential equation of motion for the system. The numerical examples show that the effects of the damping coefficient and the spring constant of the rope on the deflection have significant variations with the loading frequency. The effects of the damping coefficient and the spring constant under different beam lengths are also examined. The obtained results validate the presented approach, and provide significant references in the design process of bridgeerecting machines.     

On the energy conservation and critical velocities for the propagation of a ＂steady-shock＂ wave in a bar made of cellular material

The propagation of shock waves in a cellular bar is systematically studied in the framework of continuum solids by adopting two idealized material models, viz. the dynamic rigid, perfectly plastic, locking （D-R-PP-L） model and the dynamic rigid, linear hardening plastic, locking （D-R-LHP-L） model, both considering the effects of strain-rate on the material properties. The shock wave speed relevant to these two models is derived. Consider the case of a bar made of one of such material with initial length L 0 and initial velocity v i impinging onto a rigid target. The variations of the stress, strain, particle velocity, specific internal energy across the shock wave and the cease distance of shock wave are all determined analytically. In particular the ＂energy conservation condition＂ and the ＂kinematic existence condition＂ as proposed by Tan et al. （2005） is re-examined, showing that the ＂energy conservation condition＂ and the consequent ＂critical velocity＂, i.e. the shock can only be generated and sustained in R-PP-L bars when the impact velocity is above this critical velocity, is incorrect. Instead, with elastic deformation, strain-hardening and strain-rate sensitivity of the cellular materials being considered, it is appropriate to redefine a first and a second critical impact velocity for the existence and propagation of shock waves in cellular solids. Starting from the basic relations for shock wave propagating in D-R-LHP-L cellular materials, a new method for inversely determining the dynamic stress-strain curve for cellular materials is proposed. By using e.g. a combination of Taylor bar and Hopkinson pressure bar impact experimental technique, the dynamic stress-strain curve of aluminum foam could bedetermined. Finally, it is demonstrated that this new formulation of shock theory in this one-dimensional stress state can be generalized to shocks in a one-dimensional strain state, i.e. for the case of plate impact on cellular materials, by simply making proper replacements of the elastic and plastic constants.     

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为了提高舰船及其设备的抗冲击能力,满足最新抗冲击标准的要求,同时提高传统冲击试验 机的最大测试能力,提出了一套全液压驱动的新型重载舰船设备抗冲击试验系统模型, 以解决系统高能量存储及瞬间释放和避免二次撞击的关键问题. 构建了系统非线性 动力学模型,并利用数值计算方法考察了在不同冲击速度测试条件下冲击机系统所能达到的 预期性能. 结果表明: 该系统可以产生与最新抗冲击标准BV043/85和MIL-S-901D相吻合的 冲击加速度波形,同时可根据不断提高的抗冲击标准以及测试能力要求进行相应的扩展.     

Stability analysis of the periodic solution of a piecewise-linear non-linear dynamic system

The stability of the periodic solution under harmonic excitation of a non-linear dynamic system with “linear hysteretic damping” is examined proceeding from first principles. The method can be extended to the case of multi-degree of freedom systems unlike regular perturbation procedure.     

Difference between the longitudinal Frenkel-Biot waves in water-and gas-saturated porous media

The problem of the propagation of longitudinal Biot waves in a porous medium saturated with a weakly compressible liquid (water) or a gas is considered theoretically. The frequency dependence of the phase velocities and damping coefficients is investigated numerically. It is shown that for a certain relationship between the parameters of the porous medium and the saturating fluid there is a “critical” frequency at which the properties of longitudinal waves of both kinds are identical. An analytical expression for this “critical” frequency is obtained. It is shown that for a gas-saturated porous medium, at a certain frequency, in both longitudinal waves the relative gas-matrix motion changes type. Assuming that the saturating-gas behavior corresponds to an adiabatic equation of state, an estimate is obtained for the threshold pore pressure necessary for the restructuring of the relative motion. The wave associated with matrix deformation is shown to have a high damping coefficient in a porous medium saturated with a weakly compressible liquid (water in the case considered) but to be only weakly damped in a gas-saturated porous medium.     

Bifurcation and chaos analysis of multistage planetary gear train

A nonlinear time-varying dynamic model for a multistage planetary gear train, considering time-varying meshing stiffness, nonlinear error excitation, and piece-wise backlash nonlinearities, is formulated. Varying dynamic motions are obtained by solving the dimensionless equations of motion in general coordinates by using the varying-step Gill numerical integration method. The influences of damping coefficient, excitation frequency, and backlash on bifurcation and chaos properties of the system are analyzed through dynamic bifurcation diagram, time history, phase trajectory, Poincaré map, and power spectrum. It shows that the multi-stage planetary gear train system has various inner nonlinear dynamic behaviors because of the coupling of gear backlash and time-varying meshing stiffness. As the damping coefficient increases, the dynamic behavior of the system transits to an increasingly stable periodic motion, which demonstrates that a higher damping coefficient can suppress a nonperiodic motion and thereby improve its dynamic response. The motion state of the system changes into chaos in different ways of period doubling bifurcation, and Hopf bifurcation.     

On the mechanism of unsteady shock oscillation in shock wave/turbulent boundary layer interactions

An experimental investigation into the mechanism of shock wave oscillation in compression ramp-generated shock wave/turbulent boundary layer interactions is presented. Particular emphasis is focused upon documenting the respective roles played by both burst-sweep events in the turbulent boundary layer immediately upstream of the interaction and the downstream separated shear layer upon unsteady shock front motion. Unlike the majority of compression ramp experiments which involve bulk separation and large-scale shock motion, consideration is given here to comparatively “weak” interactions in which the streamwise spatial excursion of the shock front is always less than one boundary layer thickness. In this manner any shock motion due to upstream burst-sweep events should be more apparent in relation to that oscillation associated with the separated region. A discrete Hilbert transform-based conditional sampling technique is used to obtain wall pressure measurements conditioned to burst-sweep events. The conditional sampling technique forms the basis by which the instantaneous shock motion is conditioned to the occurrence of upstream bursting. The relationship between the separation bubble and shock motion is also explored in detail. The results of the experiments indicate that the separation bubble represents a first-order effect on shock oscillation. Although it is demonstrated theoretically that the burst-sweep cycle can also give rise to unsteady shock motion of much lower amplitude, the experiments clearly demonstrate that there is no discernible statistical relationship between burst events and spanwise coherent shock front motion.     

On the interpretation and application of shock-test results in engineering designs

A theoretical study of the characteristics of a shock spectrum which is measured in a shock test of equipment is presented. For this purpose, the machine and the equipment are represented by two systems connected in series; an upper and a lower bound of the spectrum of the shock motion at the interface of the two systems are found using the Fourier transform and impedance method. The spectrum is shown to be affected by the characteristics of both systems. It is demonstrated that in a system containing negligible damping, hills would occur in the spectrum at the resonant frequencies of the combined system, whereas valleys (spectrum dips) would appear in the neighborhood of the fixed-base resonant frequencies of the equipment. The possible effects of damping and of the variation in the characteristics of the system on the phenomenon are also discussed. The results support, at least in the case of systems with low damping, the current design practice of the Navy in which an envelope of a group of the dips of measured spectra is used in creating a design spectra for similar equipment. The analysis developed here would also be useful in understanding the behavior of vibration absorber and other shock phenomena.     

一种冲击波作用下结构毁伤算法研究

针对爆炸冲击波与建筑物结构相互作用过程,分析了冲击波与结构碎块作用机理,发展了一种能够模拟建筑物结构破坏及冲击波传播过程的计算模型和方法。采用建筑物结构工程毁伤载荷作为判据,处理结构在冲击波作用下的破坏问题;利用流固耦合界面算法处理结构运动引起的泄压效应,利用“虚拟网格通气技术”处理结构碎块对冲击波的阻碍作用,模拟了冲击波作用下典型建筑物的毁伤过程及冲击波传播过程。结果表明,该模型在模拟冲击波与结构的作用过程中,压力计算结果与非结构动网格模拟结果符合较好;在典型建筑物毁伤过程的数值模拟中,计算得到的建筑物毁伤效果和冲击波超压分布与建筑物物理毁伤特点符合。     

Friction force model and rolling dynamics for a ball on a rough surface with presliding displacement taken into account

A model of sliding and spinning friction forces for a ball in the form of finite relations obtained by integrating the tangential stresses over the contact area whose parameters are determined by Hertz’s theory for the “ball-rough horizontal surface” tribological conjunction pair is supplemented with a model of rolling friction torques. The combined model is peculiar in that the presliding displacement effect in rolling and spinning friction torques is taken into account. It is shown that the ball motions in the presliding displacement zone are of quasilinear character and, under shock perturbations, have the form of damping vibrations in the three orientation angles. The numerical parameters of the rolling and spinning friction model are experimentally determined for the presliding displacement zones, while the sliding friction parameters and partly the spinning friction parameters are calculated. Mathematical modeling permits one to discover new properties of the ball, namely, its deceleration in rolling, the onset of damping vibrations at the beginning and end of motion, and the transient process parameters.     

FLOW-INDUCED VIBRATION OF A CIRCULAR CYLINDER AT LIMITING STRUCTURAL PARAMETERS

Transverse oscillation of a dynamically supported circular cylinder in a flow at Re=100 has been numerically simulated using a high-resolution viscous-vortex method, for a range of dynamical parameters. At the limiting case with zero values of mass, damping and elastic force, the cylinder oscillates sinusoidally at amplitudeA /D=0·47 and frequency fD/U_∞=0·156. For zero damping, the effects of mass and elasticity are combined into a new, “effective” dynamic parameter, which is different from the classic “reduced velocity”. Over a range of this parameter, the response exhibits oscillations at amplitudes up to 0·6 and frequencies between 0·15 and 0·2. From this response function, the classic response in terms of reduced velocity can be obtained for fixed values of the cylinder/fluid ratio m^*. It displays “lock-in” at very high values of m^*.     

Nonlinear analysis of a rub-impact rotor supported by turbulent couple stress fluid film journal bearings under quadratic damping

This work reports a numerical study undertaken to investigate the dynamic response of a rotor supported by two turbulent flow model journal bearings with nonlinear suspension and lubricated with couple stress fluid under quadratic damping. This may be the first time that analysis of rotor-bearing system considered the quadratic damping effect. The dynamic response of the rotor center and bearing center are studied. The analysis methods employed in this study are inclusive of the dynamic trajectories of the rotor center and bearing center, power spectra, Poincaré maps and bifurcation diagrams. The maximum Lyapunov exponent analysis is also used to identify the onset of chaotic motion. The modeling results provide some useful insights into the design and development of rotor-bearing system for rotating machinery that operates at highly rotational speed and highly nonlinear regimes.     

A Galerkin method for distributed systems with non-local damping

In this paper, a non-local damping model including time and spatial hysteresis effects is used for the dynamic analysis of structures consisting of Euler–Bernoulli beams and Kirchoff plates. Unlike ordinary local damping models, the damping force in a non-local model is obtained as a weighted average of the velocity field over the spatial domain, determined by a kernel function based on distance measures. The resulting equation of motion for the beam or plate structures is an integro-partial-differential equation, rather than the partial-differential equation obtained for a local damping model. Approximate solutions for the complex eigenvalues and modes with non-local damping are obtained using the Galerkin method. Numerical examples demonstrate the efficiency of the proposed method for beam and plate structures with simple boundary conditions, for non-local and non-viscous damping models, and different kernel functions.     

Stability analysis of the whirl motion of a breathing cracked rotor with asymmetric rotational damping

The stability of the whirl motion of a breathing cracked rotor with the distinction of stationary damping and the asymmetric rotational damping is studied. By Lagrange’s principal, the motion equations are formed in rotational frame such that the multi-asymmetric system, i.e., asymmetric rotational damping and asymmetric time-periodic varying stiffness, is simplified to be a system with anisotropic damping and anisotropic time-periodical varying stiffness in rotational operation. Based on the multiple scales solution of the simplified whirling equation in moving frame, root locus method for stability analysis is proposed. Different from the former stability estimation method, the corresponding Campbell diagram, decay rate plot, and root locus plot of the fifth-order approach are derived to prove the effects of both crack depth and damping effects. The numerical results of the instabilizing effects of the crack depth are well agreeing with the previous studies. In addition, the destabilizing influence of the rotational damping on the breathing cracked rotor is presented for the first time.     

船体与设备一体化抗冲击分析

从主从系统耦合振动理论出发,基于数值实验手段,分别以船用增压锅炉、齿轮箱为研究对象,设计多种冲击输入对非一体化与一体化抗冲击分析例证进行数值计算,并将计算结果进行对比。研究结果表明,非一体化抗冲击分析方法割裂了设备与船体结构之间的耦合效应,不能精确再现船用设备实船冲击环境,中远场水下爆炸时非一体化抗冲击分析得到的设备响应结果偏大,中近场时结果偏小。建议中近场水下爆炸时肋位跨度较大的船用大型设备抗冲击性能分析采用船体与设备一体化抗冲击分析方法,若条件所限尚无法进行一体化分析,则应对非一体化抗冲击分析结果进行修正。     

Elastic continua in high frequency excitation field

The response of an elastic continua to high frequency excitations is decomposed in two parts: “slow” motion which practically remains unchanged during the vanishingly small period of time τ, and “fast” motions whose mean value during this period is negligible, but the energy contribution is essential. After such a decomposition the “slow” and “fast” motions become nonlinearly coupled by the corresponding governing equations. This coupling leads to an additional “effective” potential energy which changes the “mean” stiffness characteristics. The results can be used for dynamical stiffening of flexible structural elements for a temporary increase of their stiffness in the course of occasional loads to prevent buckling or wrinkling.     

The damping in MEMS inertial sensors both at high and low pressure levels

Except for MEMS working in a ultra high vacuum, the main cause of damping is the air surrounding the system. When the working pressure is equal to the atmospheric one (from now on called “high pressure,” i.e., 10⁵ Pa), the mean free path of an air molecule is much smaller than typical MEMS dimensions. Thus, air can be considered as a viscous fluid and two phenomena occur: flow damping and squeeze film damping. These two phenomena can be evaluated through a simplified Navier–Stokes equation. In a medium vacuum (from now on called “low pressure”), i.e., the “packaging” pressure, the air cannot be considered as a viscous fluid any more since the mean free path of an air molecule is of the same order of magnitude of typical MEMS dimensions. Thus, the molecular fluid theory must be used to estimate the damping. To predict the damping of a MEMS device both at high and low pressure levels, a multiphysics code was used. The proposed approach was validated through comparison with experimental data.     

Dynamic analysis of nonlinear systems by modal synthesis techniques

Different kinds of modal synthesis method have been used widely in dynamic analysis of linear structure systems, but, in general, they are not suitable for nonlinear systems.In this paper, a kind of modal synthesis techniques is extended to dynamic analysis of nonlinear systems. The procedure is based upon the method suggested in [20],[21], which is applicable to vibration analysis for complex structure systems with coupling attachments but with simplified forms of linear springs and dampers. In fact, these attachments have nonlinear characteristics as those generally known to the cases of nonlinear elasticity and nonlinear damping, e.g., piecewise-linear springs, softening or hardening springs. Coulomb damping,elas-ioplastic hysteresis damping, etc. So long as the components of structure are still linear systems, we can get a set of independent free-interface normal mode information hut only keep the lower-order for each component. This can be done by computations or experiments or both. The global equations of linear vibration are set up by assembling of the component equations of motion with nonlinear coupling forces of attachments. Then the problem is reduced to less degrees of freedom for solving nonlinear equations. Thus considerable saving in computer storage and execution time can be expected. In the case of a very high-order system, if sufficient degrees of freedom are reduced, then it may be possible for the problem to be solved by the aid of a computer of ordinary grade.As the general nonlinear vibration of multiple degrees of freedom systems is quite involved, in general, the exact solution of a nonlinear system equations is not easy to find, so the numerical method can be adopted for solving the reduced nonlinear equations to obtain the transient response of system for arbitrary excitations.     

Nonlinear dynamics of an inclined beam subjected to a moving load

In this paper, the nonlinear dynamic response of an inclined pinned-pinned beam with a constant cross section, finite length subjected to a concentrated vertical force traveling with a constant velocity is investigated. The study is focused on the mode summation method and also on frequency analysis of the governing PDEs equations of motion. Furthermore, the steady-state response is studied by applying the multiple scales method. The nonlinear response of the beam is obtained by solving two coupled nonlinear PDEs governing equations of planar motion for both longitudinal and transverse oscillations of the beam. The dynamic magnification factor and normalized time histories of mid-pint of the beam are obtained for various load velocity ratios and the outcome results have been illustrated and compared to the results with those obtained from traditional linear solution. The appropriate parametric study considering the effects of the linear viscous damping, the velocity of the traveling load, beam inclination angle under zero or nonzero axial load are carried out to capture the influence of the effect of large deflections caused by stretching effects due to the beam’s immovable ends. It was seen that quadratic nonlinearity renders the softening effect on the dynamic response of the beam under the act of traveling load. Also in the case where the object leaves the inclined beam, its planar motion path is derived and the targeting accuracy is investigated and compared with those from the rigid solution assumption. Moreover, the stability analysis of steady-state response for the modes equations having quadratic nonlinearity was carried out and it was observed from the frequency response curves that for the considered parameters in the case of internal-external primary resonance, both saturation phenomenon and jump phenomenon can be predicted for the longitudinal excitation.