结构振动的非线性控制及其试验研究

本文分析了结构振动控制系统的特点，提出了一种结构振动的非线性离散控制方案，该方案仅利用受控结构的输出信号，实现容易，对结构参数变化具有一定的鲁棒性，本文还建立了一套具有浮点运算功能的结构振动计算机控制装置，并就某受控结进行了试验，试验表明，该非线性控制方案是可行的，理论结果与试验结果具有良好的一致性。     

结构振动的滑模变结构半主动控制

研究应用磁流变阻尼器(MRD)对结构振动半主动控制的算法和原理。研制并对磁流变阻尼器进行了阻尼特性实验，采用非线性滞回双粘性模型描述磁流变阻尼器的阻尼特性，模型结果与实验结果非常一致。采用滑模控制算法和趋近律方法设计了半主动控制器。利用滑模控制方法所建立的控制器，本文给出了地震激励下结构振动半主动控制算例。计算分析表明，半主动滑模控制具有控制效果明显、鲁棒性好等优点，是一种非常有发展前途的控制方法。     

结构非线性振动智能控制试验与分析

在结构动力学与控制领域中,试验验证对于理论与数值研究是非常重要的. 但是,目前的模型试验大部分都只考虑结构的线性行为,所以考虑结构非线性振动的试验模型成为一个研究热点. 采用磁流变旋转阻尼器来模拟结构中的塑性铰,并通过调整输入到此旋转阻尼器中的电压来实现不同的非线性行为,然后在不同的非线性行为下验证了动态神经网络观测器和自适应模糊滑模控制算法的有效性. 试验结果表明建立的结构非线性试验模型可以在试验完成后不需要任何代价而恢复到初始状态,并且能够实现不同的非线性行为,同时采用的智能控制算法对结构非线性振动也有较好的控制作用.      

冰激结构振动的非线性分析

冰对结构的作用表现为冰的变形和破碎两个阶段，具有间隙非线性特征本文根据试验结果，将非线性分析方法应用到冰激结构振动方程中，从理论上阐明，冰激柔性结果的振动是一种多频干扰自激和强迫振动系统，并研究了试验中观察到的锁频现象的机理。计算结果与试验结果是一致的。本文得到的冰力计算公式可用于海洋工程结构的设计计算。     

地震作用下高层建筑重叠分散控制子结构划分机理研究

针对地震作用下高层建筑振动分散控制问题,引入信息共享的重叠分散策略,研究高层建筑振动重叠分散控制子结构划分机理。基于线型二次型(LQR)最优控制的最优权矩阵和H∞鲁棒控制的最优输出评价矩阵,分析评价高层建筑重叠分散控制子结构不同划分策略时的控制效果。对某20层Benchmark结构模型进行数值模拟与分析,结果表明,本文提出的两种重叠分散控制方法的性能评价方法,可指导任意层数高层建筑振动重叠分散控制子结构的合理划分,既保证控制系统良好的控制效果,又保证控制力在合理的范围内。     

回滞非线性结构的瞬态最优控制

本文对一种国滞非线性基础隔振的主从结构模型用瞬态最优控制法进行振动控制研究。利用四阶Ｒｕｎｇｅ－Ｋｕｔｔａ积分格式统一处理最优控制方程，可直接逐步积分求出系统在瞬态最优控制下的最优控制力与系统响应。分别对主从结构无主动控制及有主动控制时的两种情况（包含或不包含ｖｂ反馈）进行计算。结果表明瞬态最优控制可有效地抑制振动。     

复杂结构系统非线性振动分析的自由度压缩技术

本文系统地总结了对复杂结构系统进行非线性振动分析时基于混合坐标法和模态综合法的自由度压缩技术,提出了局部非线性系统振动分析的具体接子结构的模态综合法,并给出了处例。最的指了利用非线性动力系统进行二次降低来研究超高自由度非线性系统复杂动力学行之一思路。     

随机风场下高层结构振动隔震与TMD混合控制研究

针对风荷载作用下高层建筑结构振动控制问题,基于建筑隔震和调谐质量阻尼器振动控制原理,利用ANSYS软件分别建立高层结构带隔震层和带调谐质量阻尼器(TMD)的单一控制策略以及两者相结合的混合振动控制策略.根据Davenport脉动风速谱,采用自回归模型(Auto-Regressive,AR)法,考虑竖向相关性、平稳的多变...     

折叠式柔性结构振动主动控制的研究

建立了具有刚性运动基的折叠式柔性结构振动主动控制实验系统，采用带实时预测误差修正的预测控制算法进行了这类结构振动主动控制的实验研究。实验结果表明，在实验建模的基础上设计预测控制器对折叠式柔性结构进行振动主动控制，能够有效地抑制柔性结构的振动和提高刚性基姿态定向精度。     

多维地震作用下高层结构振动混合控制研究

针对水平和竖向地震作用下高层建筑结构的混合振动控制问题,研究调谐质量阻尼器(tuned mass damper, TMD)体系、隔震结构体系、隔震与TMD混合控制体系3种策略对水平与竖向地震共同作用下结构振动响应的减振效果。选取典型的20层钢结构Benchmark结构模型,利用ANSYS软件建立带有TMD和隔震层结构的有限元模型,比较了结构在水平地震单独作用下与水平和竖向地震共同作用下的振动响应。结果表明,水平方向上的振动响应无明显变化;竖直方向上,有控状态下的减振指标相对于无控状态出现了增大现象,尤其是层间隔震结构增大较为明显。研究成果可为高烈度区高层隔震结构设计提供参考。     

Trapping vibratory energy of main linear structures by coupling light systems with geometrical and material non-linearities

Cubic potential and hysteresis behavior (Bouc–Wen type) of a non-linear energy sink are used to localize the vibratory energy of a linear structure. A general methodology is presented to deal with time evolutionary energy exchanges between two oscillators. Invariant manifold of the system and its stability borders are detected at fast time scale while traced equilibrium and singular points at slow time scale let us predict possible behaviors of the system during its pseudo-stationary regime(s). The paper is followed by an example that considers the Dahl model for representing the hysteresis behavior of the non-linear energy sink. All analytical developments and results are compared with those obtained by direct integration of system equations. Obtained analytical developments can be endowed for designing non-linear energy sink devices with hysteresis behavior to localize vibratory energy of main structures for the aim of passive control, energy harvesting and/or both of them.     

Convection in a Porous Medium with Variable Gravity Field and Magnetic Field Effects

The problem of convection in a variable gravity field with magnetic field effect is studied using methods of linear instability theory and non-linear energy theory. Then, the accuracies of both the linear instability and global non-linear energy stability thresholds are tested using a three-dimensional simulation. The strong stabilizing effect of gravity field and magnetic field is shown. Moreover, the results support the assertion that the linear theory is very accurate in predicting the onset of convective motion, and thus regions of stability.     

The effect of non-linear interaction between gas and particle velocities on the hydrodynamic stability in the Blasius boundary layer

A weakly non-linear stability analysis of two phase flow in the Blasius boundary layer has been carried out. Two mathematical models have been established based on the perturbation shape preserved assumption and linear stability model of two phase flow proposed by Stuart [On the non-linear mechanics of hydrodynamic stability, J. Fluid Mech. 4 (1958) 1-21] and Saffman [On the stability of laminar flow of dusty gas, J. Fluid Mech. 13 (1962) 120-128], respectively. The perturbation model and the perturbation energy balance equation are solved numerically with Chebyshev spectral method and artificial boundary condition. The numerical program adopted in the present study is verified by comparison with former works. The results show that the non-linear interaction between mean flow and perturbation reduces the growth rate of perturbation, while the non-linear interaction between particle phase and gas phase increases the growth rate of perturbation amplitude. The distortion of the mean flow caused by the Reynolds stress modifies the rate of transfer of energy from the mean flow to disturbance. The existence of particle alleviates the distortedness. The result also indicates that the weakly non-linear stability theory is consistent to linear stability theory, and the addition of fine and coarse particles reduces and increases the critical Reynolds number.     

Elastic solids with different moduli in tension and compression

A new approach is given to the theory of non-linear elastic materials which have different behaviour in tension and compression. Two applications are made to incompressible non-linear materials using general forms for the strain energy functions. The linear form of the theory is shown to be equivalent to that used by previous writers.     

Exceedance probability criterion based stochastic optimal polynomial control of Duffing oscillators

An optimal polynomial control strategy is developed in the context of the physical stochastic optimal control scheme of structures that is well-adapted to randomly-driven non-linear dynamical systems. A class of Duffing oscillators with polynomial active tendons subjected to random ground motions is investigated for illustrative purposes. Numerical studies reveal that using an exceedance probability criterion with the minimum of the failure probability of system quantities in energy trade-off sense, a linear control with the 1st-order controller suffices even for strongly non-linear systems. This bypasses the need to utilize non-linear controls with the higher-order controller which may be associated with dynamical instabilities due to time delay and computational dynamics. The statistical variability, meanwhile, of system responses gains an obvious reduction, and the system performance is significantly improved. The 1st-order controller, however, does not have the same control effect to the higher-order controller when control criteria currently in used are employed, e.g. system second-order statistics evaluation and Lyapunov asymptotic stability condition, as indicated in the comparative studies of the exceedance probability criterion against the two control criteria. Besides, the proposed optimal polynomial control is insensitive to the non-linearity strength of the class of base-excited non-linear oscillators whereby a robust control of systems can be implemented, while the LQG control in conjunction with the statistical linearization technique, using a band-limited white noise input, does not have this advantage.     

Thermoelastic stability of layered shallow shells

The phenomena associated with thermal snap-through and snap-buckling of symmetrically layered shallow shells of polygonal planform are studied by means of a two-degree-of-freedom model derived from a Ritz–Galerkin approximation. The composite structure is homogenized considering perfect bond and the kinematic assumptions of the first order shear deformation theory. The simply supported shell edges are assumed to be prevented from in-plane motions. The geometrically non-linear, quasi-static equilibrium conditions are derived according to the von Kármán–Tsien theory and simplified by the Berger-approximation. A unifying non-dimensional formulation of the elastic stability analysis is presented that turns out to be independent of the special polygonal planform of the simply supported shallow shell.     

On the coupling of non-linear normal modes

The phenomenon of internal resonance is known as the exchange of energy between the modes and the existence of coupled-mode response under a single-mode excitation. This phenomenon is observed whenever a non-linear normal mode loses its stability, called the modal coupling. The details of modal coupling are formulated in the free vibrations of two-degree-of-freedom systems, and compared with internal resonance. The theory is based on the structural change in Poincaré map due to the stability change of normal modes. It is shown that every change in stability of normal modes gives rise to a pitchfork or a period-doubling bifurcation. The functional form is derived to compute the coupled modes by the method of harmonic balance. Examples are given to describe the procedure of stability analysis of non-linear normal modes, to compute the coupled modes, and then to demonstrate that results of internal resonances can be derived by model coupling. Other examples are given to demonstrate that the results of some modal couplings cannot be obtained by internal resonances.     

Control of primary and subharmonic resonances of a Duffing oscillator via non-linear energy sink

The use of non-linear energy sink to passively control vibrations of a non-linear main structure under the effect of bi-frequency harmonic excitation is addressed here. The excitation is assumed to induce both 1:1 and 1:3 resonance, and the response of the system is studied after using the Multiple Scale/Harmonic Balance Method, applied to obtain amplitude modulation equations in the slow time scale. The efficiency of the non-linear energy sink to reduce or suppress vibrations of the main structure is finally discussed.     

Magnetic torque attitude control of a satellite using the state-dependent Riccati equation technique

A non-linear attitude control method for a satellite with magnetic torque rods using the state-dependent Riccati equation (SDRE) technique has been developed. The magnetic torque caused by the interaction with the Earth's magnetic field and the magnetic moment of torque rods plays a role of the control torque. The detailed equations of motion for this system are presented using angular velocity and quaternions. The SDRE controller is developed for the non-linear systems which can be formed in pseudo-linear representations using the state-dependent coefficient (SDC) method without linearization procedure. The aim of this control system is to achieve a stable attitude within 5°, and minimize the control effort. The stability regions for the SDRE controlled satellite system are estimated through the investigation of the stability conditions developed for pseudo-linear systems and the application of Lyapunov's theorem. For comparisons, the Linear Quadratic Regulator (LQR) method using the solution of the algebraic Riccati equation (ARE) is also applied to this non-linear system. The performance of the SDRE non-linear control system demonstrates more robustness and stability than the LQR control system when subjected to a wide range of initial conditions.     

A switching fractional calculus-based controller for normal non-linear dynamical systems

In this paper, a fractional calculus-based terminal sliding mode controller is introduced for finite-time control of non-autonomous non-linear dynamical systems in the canonical form. A fractional terminal switching manifold which is appropriate for canonical integer-order systems is firstly designed. Then some conditions are provided to avoid the inherent singularities of the conventional terminal sliding manifolds. A non-smooth Lyapunov function is adopted to prove the finite time stability and convergence of the sliding mode dynamics. Afterward, based on the sliding mode control theory, an equivalent control and a discontinuous control law are designed to guarantee the occurrence of the sliding motion in finite time. The proposed control scheme uses only one control input to stabilize the system. The proposed controller is also robust against system uncertainties and external disturbances. Two illustrative examples show the effectiveness and applicability of the proposed fractional finite-time control strategy. It is worth noting that the proposed sliding mode controller can be applied for control and stabilization of a large class of non-autonomous non-linear uncertain canonical systems.