SOME PROBLEMS FOR LINEAR ELASTIC SYSTEMS WITH DAMPING

In the present paper we investigate linear elastic systems with damping in Hilbert spaces, where A and B ars unbounded positive definite linear operators. We have obtained the most fundamental results for the holomorphic property and exponential stability of the semigroups associated with these systems via inclusion relation of the domains of A and B.

ON INFLUENCE OF KINEMATICS TO EQUIVALENT LINEAR DAMPING OF HELICOPTER BLADE HYDRAULIC DAMPER

An analytical model of hydraulic damper was presented in forward flight accounting for pitch/flap/lag kinematic coupling and its nonlinear force-velocity curve. The fourth order Runge-Kutta was applied to calculate the damper axial velocity in time domain. Fourier series based moving block analysis was applied to calculate equivalent linear damping in terms of transient responses of damper axial velocity. Results indicate that equivalent linear damping will be significantly reduced if pitch/flap/lag kinematic coupling introduced for notional model and flight conditions.

Estimation of Nonlinear Roll Damping by Analytical Approximation of Experimental Free-Decay Amplitudes

Damping is critical for the roll motion response of a ship in waves. A common method for the assessment of damping in a ship’s rolling motion is to perform a free-decay experiment in calm water. In this paper, we propose an approach for estimating nonlinear damping that involves a linear exponential analytical approximation of the experimental roll free-decay amplitudes, fol- lowed by parametric identification based on the asymptotic method. The restoring moment can be strongly nonlinear. To validate this method, we first analyzed numerically simulated roll free-decay data using rolling equations with two alternative parametric forms: linear-plus-quadratic and linear-plus-cubic damping. By doing so, we obtained accurate estimates of nonlinear damping coefficients, even for large initial roll amplitudes. Then, we applied the proposed method to real free-decay data obtained from a scale model of a bulk barrier, and found the simulated results to be in good agreement with the experimental data. Using only free-decay peak data, the proposed method can be used to estimate nonlinear roll-damping coefficients for conditions with a strongly nonlinear restoring moment and large initial roll amplitudes.

Pullback attractor of 2D nonautonomous g-Navier-Stokes equations with linear dampness

The pullback attractors for the 2D nonautonomous g-Navier-Stokes equations with linear dampness axe investigated on some unbounded domains. The existence of the pullback attractors is proved by verifying the existence of pullback D-absorbing sets with cocycle and obtaining the pullback ：D-asymptotic compactness. Furthermore, the estimation of the fractal dimensions for the 2D g-Navier-Stokes equations is given.

ANALYTICAL SOLUTION FOR MODE Ⅲ DYNAMIC RUPTURE OF STANDARD LINEAR VISCOELASTIC SOLID WITH NONLINEAR DAMPING

Introducing the nonlinear Rayleigh damping into the governing equation of the Mode Ⅲ dynamic rupture for standard viscoelastic solid, this equation is a partial differential and integral equation. First, eliminating the integral term, a PDE of third_order is obtained. Then, applying the small parameter expansion method, linearized asymptotic governing equation for each order of the small parameter is obtained. Dividing the third_order PDE into an elastic part with known solution, the rest part pertains to viscous effect which is neither a Mathieu equation nor a Hill one. The WKBJ method is still adopted to solve it analytically.

ON THE CAUCHY PROBLEM FOR AW-RASCLE SYSTEM WITH LINEAR DAMPING

The existence of global BV solutions for the Aw-Rascle system with linear damping is considered.In order to get approximate solutions we consider the system in Lagrangian coordinates,then by using the wave front tracking method coupling with and suitable splitting algorithm and the ideas of[1]we get a sequence of approximate solutions.Finally we show the convergence of this approximate sequence to the weak entropic solution.

Global Attractors and Asymptotic Smoothing Effect for Navier-Stokes Equations with Linear Damping on R^2

This paper studies the long time behavior of solutions to the Navier-Stokes equations with linear damping on R^2. The authors prove the existence of L^2-global attractor and Hi-global attractor by showing that the corresponding semigroup is asymptotically compact. Thereafter, they establish that the two attractors are the same and thus reveal the asymptotic smoothing effect of the solutions.

Equivalent linear model for seismic damage evaluation of single-degree-of-freedom systems representing reinforced concrete structures considering cyclic degradation behavior

In this study,a novel equivalent damping ratio model that is suitable for reinforced concrete(RC)structures considering cyclic degradation behavior is developed,and a new equivalent linearization analysis method for implementing the proposed equivalent damping ratio model for use in seismic damage evaluation is presented.To this end,Ibarra’s peak-oriented model,which incorporates an energy-based degradation rule,is selected for representing hysteretic behavior of RC structure,and the optimized equivalent damping for predicting the maximum displacement response is presented by using the empirical method,in which the effect of cyclic degradation is considered.Moreover,the relationship between the hysteretic energy dissipation of the inelastic system and the elastic strain energy of the equivalent linear system is established so that the proposed equivalent linear system can be directly integrated with the Park-Ang seismic model to implement seismic damage evaluation.Due to the simplicity of the equivalent linearization method,the proposed method provides an efficient and reliable way of obtaining comprehensive insight into the seismic performance of RC structures.The verification demonstrates the validity of the proposed method.

STABLE NONLINEAR RELAXATIONS IN A MULTIPHASIC Al-Zn ALLOY

The experiments reveal the characteristics of stable damping in a multiphasic Al-Zn eutectoid alloy:（1）Thewhole damping(Q-1)has the same dependence on measured frequency（f）,i.e.Q-1ocf-n,where n is a parameterand is independent of temperature.（2）In a low-temperature（low-T）and low-strain-amplitude（low-A）region,Q-1=（B/）exp（-nH/kT）,where B is a parameter,H the atomic diffusion activation energy,k Boltzmann′sconstant,and T the absolute temperature.n,Ho（=nH）and H are all independent of A.The damping comesfrom an anelastic motion of the phase-interface.（3）In an intermediate region including a low-Tand a high-A,a middle-T and middle A and a high-T and low-A regions,the equation Q-1=（C/fn）exp（nH/kT）stillholds,but the damping has a normal amplitude effect C,n,and H all vary with A;the damping results from anonlinear relaxation of phase-interface.（4）In a high-T and high-A region,there is no longer a linear relationship between InQ-1 and T-1,whereas the relation Q-1f-n is still satisfied,where n increases as A increases,andthe damping has a normal amplitude effect but one which is weaker than that in the case（3）.The damping maybe attributed to another kind of nonlinear relaxation between phase-interfaces.

四分点集中阻尼弦系统本征解的性质

带有集中阻尼的张紧弦系统在力学模型上属于混杂动力学系统,通常采用近似方法求解本征值以满足工程应用需求,为进一步明确该类系统的振动特性,有必要从解析角度探讨其本征问题。针对四分点集中阻尼弦系统,推导并化简其频率方程的代数形式,求得代数方程的解,经过换元逆过程,获得原频率方程的所有闭合解。发现闭合解共存在3组,其中两组互为共轭,根据代数基本定理讨论闭合解的结构。结果表明:系统存在两种相同的运动特征,其单位时间对数衰减率相同,频率互为相反数;系统中3个解支对应的单位时间对数衰减率和频率,总是随着阶次的增加而呈周期循环的;在同一解支下的各单值分支也呈周期性循环,即随着阶次的增加,其对应频率增加4π的整数倍,而单位时间对数衰减率保持不变。综上可知,集中阻尼弦系统的运动特性总是随着阶次的增加而重复变化,且变化周期与阻尼安装位置相关。

具阻尼项的二阶非线性中立型微分方程的振动准则

建立了二阶非线性中立型阻尼微分方程[a(t)|z′(t)|^(α-1 )z′(t)]′+b(t)|z′(t)|^(α-1) z′(t)+q(t)|x(σ(t))|^(β-1) x(σ(t))=0的若干振动准则,其中z(t)=x(t)+p(t)x(τ(t))。改进、推广和统一了已有文献的相关结果,并通过实例说明了所得准则的广泛应用效果。

考虑并网变流器调节能力的广域阻尼控制策略研究

针对含并网变流器电力系统,提出了一种利用并网变流器来提升系统小干扰功角稳定的广域阻尼控制策略及其设计方案。基于含并网变流器电力系统的小干扰稳定模型,该方案以模态线性二次型调节器为依据设计了状态反馈控制策略,可以实现不同功角振荡模式的解耦控制。考虑到不同并网变流器具有不同的调节能力,进一步构建了以模态线性二次型调节器权重矩阵为待优化变量,以关键振荡模式的阻尼比和并网变流器调节能力作为约束的阻尼控制分配模型,并利用遗传算法进行求解。在PSAT中搭建IEEE 68节点系统模型,对所提控制方案进行验证,结果表明该控制方案能够有效利用各个并网变流器向系统提供足够的阻尼支持。

Enhancing microseismic/acoustic emission source localization accuracy with an outlier-robust kernel density estimation approach

Monitoring sensors in complex engineering environments often record abnormal data,leading to significant positioning errors.To reduce the influence of abnormal arrival times,we introduce an innovative,outlier-robust localization method that integrates kernel density estimation(KDE)with damping linear correction to enhance the precision of microseismic/acoustic emission(MS/AE)source positioning.Our approach systematically addresses abnormal arrival times through a three-step process:initial location by 4-arrival combinations,elimination of outliers based on three-dimensional KDE,and refinement using a linear correction with an adaptive damping factor.We validate our method through lead-breaking experiments,demonstrating over a 23%improvement in positioning accuracy with a maximum error of 9.12 mm(relative error of 15.80%)—outperforming 4 existing methods.Simulations under various system errors,outlier scales,and ratios substantiate our method’s superior performance.Field blasting experiments also confirm the practical applicability,with an average positioning error of 11.71 m(relative error of 7.59%),compared to 23.56,66.09,16.95,and 28.52 m for other methods.This research is significant as it enhances the robustness of MS/AE source localization when confronted with data anomalies.It also provides a practical solution for real-world engineering and safety monitoring applications.

滑橇式直升机地面共振非线性时域仿真

为研究非线性因素对滑橇式直升机地面共振的影响,针对滑橇式起落架弹性结构及机体阻尼器连接方式的特点,建立了简洁有效的直升机地面共振当量平面模型。该模型不仅计入了桨叶减摆器以及机体阻尼器的非线性,还考虑了机体阻尼器非比例阻尼对机体固有特性的影响。通过激振法激出机体模态稳态响应,并采用模态阻尼识别法对瞬态响应进行模态阻尼识别。分析可知,机体阻尼器提供的非比例非线性阻尼使得机体模态阻尼在时域上呈现较复杂的变化,系统稳定时,激出的阻尼器稳态响应速度幅值越大,其变化就越滞后。

OSCILLATION OF A SECOND-ORDER HALF-LINEAR NEUTRAL DAMPED DIFFERENTIAL EQUATION WITH TIME-DELAY

In this paper,the oscillation for a class of second-order half-linear neutral damped differential equation with time-delay is studied.By means of Yang-inequality,the generalized Riccati transformation and a certain function,some new sufficient conditions for the oscillation are given for all solutions to the equation.

煤矿直线振动筛减振弹簧失效性能研究

为深入探究煤矿直线振动筛中减振弹簧的失效问题,研究人员基于有限元分析的方法,对减振弹簧在日常筛分情况下的运行状态进行仿真分析研究,初步确定了引起减振弹簧失效的主要原因,并通过实际对比确定了仿真结果的可靠性,以期为今后的减振弹簧优化设计工作提供依据参考。

基于变步长精细积分法的电磁暂态仿真计算方法

随着大规模新能源的并网以及新型电力电子器件的应用,电力系统数字仿真的复杂性不断提高,电磁暂态特性也变得日趋复杂。电力电子系统在进行电磁暂态仿真时,会遇到很多不连续现象和状态突变现象。在计算时,变步长精细积分多步法可以通过对步长的调节,使每一段步长达到要求的计算精度。为克服在不连续情况下由状态变量突变引起的数值波动,进一步优化电磁瞬态模拟,拟利用基于Adams线性多步法的精细积分法,并通过误差估计实现对非均匀项的自适应逼近。在MATLAB/Simulink仿真平台利用理论分析法进行数值模拟,结果表明,所提算法可以有效地提高电磁暂态计算效率和计算精度。该方法弥补了实际应用中传统的临界阻尼调整算法“忽略”不连续问题这一漏洞。

颗粒阻尼的动态特性研究

颗粒阻尼技术已经成功的应用于多个领域抑制振动。然而,由于颗粒阻尼复杂的碰撞和摩擦减振机理,很难预测其减振特性。本文建立了颗粒阻尼的粉体力学模型,并用于研究颗粒阻尼容器的截面形状及尺寸关系对其减振特性的影响。通过试验研究,揭示了颗粒阻尼的非线性阻尼特性,并应用等效阻尼的原理提出了合理的颗粒阻尼的等效数学模型。

冻融循环中低应力水平加卸载作用下砂岩动力特性研究

采用不会造成较大附加损伤的近似无损低应力水平加、卸载的方法,开展了考虑时间效应的冻融循环作用试验。在试验成本受限的情况下大幅度地降低了试验所需的岩样数。较常规试验方法,在试验岩样数不变的前提下,无需因岩样的离散性而进行主观地筛选数据,从而使得有效数据增多。随着冻融循环周期数增加,岩样表面孔隙及微裂隙不断扩大并出现软化层,裂纹加深,颗粒脱落程度加剧,发生片落、剥蚀,水分向岩石内部迁移,冻融损伤程度由内向外逐渐加深,并研发滴定技术定量标定了这种层进式损伤。进一步分析不同冻融循环周期数下岩样在不同上限应力循环作用下的动力响应变化规律。研究显示,阻尼比、阻尼系数及动泊松比均与冻融循环周期数呈线性递增的关系,动弹性模量与冻融循环周期数呈线性递减的关系;阻尼比、动泊松比均与幅值应力呈线性递减的关系,动弹性模量与幅值应力呈线性递增的关系。给出了阻尼比、动泊松比、阻尼系数、动弹性模量相互之间的定量关系,可通过一种参数的变化规律,预测另一种参数的变化趋势。在有限的试验条件、试验次数下,可有效地精简试验所需检测的参数。幅值应力越大,加、卸载转换时岩样弹性变形响应越迅速,不可逆变形越小,在同一幅值应力的情况下所吸收的能量减少。随着冻融循环周期数的增加,循环加、卸载前岩样的斜坡加载段逐渐变长,应力-应变曲线斜率逐渐变小;循环加、卸载后,不同加、卸载幅值应力下的每个周期中首次达到应力上限时岩样的轴向应变与冻融周期数呈线性关系,说明在冻融循环作用下,岩样孔隙率逐渐变大,密实程度降低,岩样有逐步软化的趋势。当幅值应力较大时,岩样的塑性累积量与冻融周期数呈指数型关系加速递增;当幅值应力较小时,岩样的塑性累积量与冻融周期数呈线性关系匀速递增;说明幅值应力会带来显著的加速劣化效果。

刚度和阻尼频率相关的等效线性化方法

在实际工程中发现,在强地震动作用下等效线性化方法低估了地表地震动的峰值加速度反应。通过与场地效应竖向台阵观测记录的对比分析证实了这一现象,其主要原因是等效剪应变水平的取值高于高频段实际剪应变水平,从而抑制了土层地震反应中的高频成份。若干分析表明,动力反应过程中土体的剪应变是随频率而变化的,且试验表明土体的刚度和阻尼是与剪应变相关的,据此假设土体刚度和阻尼是与频率相关的。基于这一假设,对传统等效剪应变的选取如何使得土层对基底地震动输入中的高频成分产生滤波效应的原理进行探讨,且通过频率相关的等效线性化方法对该原理进行证明。将该方法应用于PortIsland场地效应竖向台阵的分析,并与实际地震动记录进行了对比,结果表明,较之传统等效线性化方法,能更加合理地考虑地震动输入中的高频成分。