Effective suppression of pneumatic vibration isolators by using input-output linearization and time delay control

This paper presents a new state space representation of pneumatic vibration isolators (PVIs) and a design of a robust control, Time Delay Control (TDC), based on it. The new state space model, derived by using the input-output linearization method, is of the phase variable form with the air mass-flow as the control input. This model offers a framework that enables simultaneous suppression of both seismic vibration and direct disturbance (or payload disturbance) with an accelerometer only. Based on this model, TDC is designed and verified with experiments on a single chamber PVI with an accelerometer only. In the experiment, the PVI with TDC successfully suppresses seismic vibration and direct disturbance, both individually and simultaneously. Faced with seismic vibration, the transmissibility of the PVI with TDC has virtually no resonance peak at low frequency; under direct disturbance, the former achieves a 68 percent reduction in settling time of the latter. The final analysis of experimental result shows that TDC effectively estimates the modeling error along with other uncertainties and cancels them, while achieving desired closed-loop dynamics.     

Stiffness scaling laws and vibration isolators

The variation in dynamic stiffness due to a geometrical shift of a cylindrical vibration isolator is predicted by a scaling law and compared to the results of a waveguide solution. The simple scaling law fails to model satisfactorily the stiffness variation due to a single length or radius shift, while predicting successfully the results of an isolator shape invariant shift. The small deviations arise from a disregarded material property shift.     

Temperature field in rubber vibration isolators

The temperature field inside a vibrating rubber solid cylinder is investigated. The rubber cylinder, a specimen of a vibration isolator rubber (Neoprene GR), is subjected to a repeatedly cyclic compressive force by means of an electrodynamic shaker. In the experimental investigation the temperatures at 16 different locations inside the cylinder have been measured by means of copper-constantan thermocouples. After the estimation of the heat generated per unit volume per unit time with the help of the estimated damping and stiffness coefficients of rubber, one can attempt the solution of the heat conduction equation describing the temperature field inside the rubber specimen. The values of the temperature found from the analytical investigation compare fairly well with the experimental measurements.     

Active vibration control in Duffing mechanical systems using dynamic vibration absorbers

This paper deals with the multi-frequency harmonic vibration suppression problem in forced Duffing mechanical systems using passive and active linear mass–spring–damper dynamic vibration absorbers. An active vibration absorption scheme is proposed to extend the vibrating energy dissipation capability of a passive dynamic vibration absorber for multiple excitation frequencies and, simultaneously, to perform reference position trajectory tracking tasks planned for the nonlinear primary system. A differential flatness-based disturbance estimation scheme is also described to estimate the unknown multiple time-varying frequency disturbance signal affecting the differentially flat nonlinear vibrating mechanical system dynamics. Some numerical simulation results are provided to show the efficient performance of the proposed active vibration absorption scheme and the fast estimation of the vibration disturbance signal.     

Transient response of unidirectional vibration isolators with many degrees of freedom

Following a procedure developed by the authors for the investigation of the dynamic behaviour of an n-degree-of-freedom linear elastic system with damping, the corresponding transient response is dealt with. The procedure is based on a class of polynomials depending on the mechanical properties of the system and the Laplace transformation is applied. As an example, a four-degree-of-freedom is examined.     

A dynamic Lagrangian frequency-time method for the vibration of dry-friction-damped systems

A new frequency-time domain procedure, the dynamic Lagrangian mixed frequency-time method (DLFT), is proposed to calculate the non-linear steady state response to periodic excitation of structural systems subject to dry friction damping. In this formulation, the dynamic Lagrangians are defined as the non-linear contact forces obtained from the equations of motion in the frequency domain, with the adjunction of a penalization on the difference between the interface displacements calculate by the non-linear solver in the frequency domain and those calculated in the time domain from the non-linear contact forces, thus accounting for Coulomb friction and non-penetration conditions. The dynamic Lagrangians allow one to solve for the non-linear forces between two points in contact without using artifacts such as springs. The new DLFT method is thus particularly well suited to handling finite element models of structures in frictional contact, as it does not require a special model for the contact interface. Dynamic Lagrangians are also better suited to frequency-domain friction problems than the traditional time-domain method of augmented Lagrangians. Furthermore, a reduction of the non-linear system to relative interface displacements is introduced to decrease the computation time. The DLFT method is validated for a beam in contact with a flexible dry friction element connected to ground, for frictional constraints that feature two-dimensional relative motion. Results are also obtained for a large-scale structural system with a large number of one-dimensional dry-friction dampers. The DLFT method is shown to be accurate and fast, and it does not suffer from convergence problems, at least in the examples studied.     

Design of vibration isolators by exploiting the beneficial effects of stiffness and damping nonlinearities

The present study is concerned with the design of a new type of single degree of freedom (sdof) nonlinear vibration isolation system that can deal with harmonic excitations and take advantage of both spring and damping nonlinearities. For typical design requirements expressed in terms of a transmissibility envelope, the proposed design makes use of a recently developed method called the output frequency response function (OFRF) approach, which provides a direct relationship between the system output frequency response and parameters that define the system nonlinearity. Taking all output harmonics into account, a detailed step-by-step procedure is developed to systematically determine the nonlinear parameters from a small set of simulation or experimental data. Simulation studies are conducted to verify the results and demonstrate that the design can effectively achieve all the three requirements for a vibration isolation system of a low resonant peak, low high frequency transmissibility, and a large isolation range.     

Approximate expressions for the fundamental frequency of vibration of several dynamic systems

An approximate formula for the frequency of vibration of several dynamic systems is presented. This approximation is an extension of the existing approximate formulae for vibrating plates. The formula is applied to the problem of a vibrating membrane, and the free vibration of a shallow lake.     

Static and dynamic properties of XY systems with extended defects in cubic anisotropic crystallines

Static and dynamic critical behavior ofXY systems in cubic anisotropic crystallines, with extended defects (or quenched nonmagnetic impurities) strongly correlated along _d -dimensional space and randomly distributed ind – _d dimensions, were studied. These extended defects make the systems coordinate anisotropic, resulting in unique critical behavior due to competition between the cubic anisotropy and the coordinate anisotropy. The systems were analyzed by an ^1/2 (4 – d) type of expansion with double expansion parameters based on a renormalization-group (RG) approach. Critical exponents were calculated near the second-order phase transition point and the behavior of the first-order transition was evaluated near the tricritical point.     

Nonlinear fluctuation,frequency and stability analyses in free vibration of circular sector oscillation systems

In the present paper, the modified homotopy perturbation method (MHPM) is employed to investigate about both nonlinear swinging oscillation and the stability of circular sector oscillation systems. The sensitivity study performed for frequency analysis of the mentioned oscillatory circular sector body shows that frequency of nonlinear oscillation depends on some specific parameters and can be optimized. Furthermore onset of the instability is dependent to angle α and initial amplitude.Comparisons made among the results of the present closed-form analytical solution and the traditional numerical iterative time integration solution confirms the accuracy and efficiency of the presented analytical solution.In contrast to the available numerical methods, the present analytical method is free from the numerical damping and the time integration accumulated errors. Moreover, in comparison with the traditional multistep numerical iterative time integration methods, a much less computational time is required for the present analytical method. Responses of the dynamical systems to some extent are affected by the natural frequencies. Results reveal that for nonlinear systems, the natural frequency is remarkably affected by the initial conditions.     

Static and dynamic properties of pseudoscalar mesons

We report the results of form factors, charge radii and decay constants of both light and heavy flavoured pseudoscalar mesons in a QCD inspired quark model. We use the quantum mechanical perturbation theory and discuss its limitations in the present problem. Several predictions are also made for bottom and top flavours.     

The complex-mode vibration of ultrasonic vibration systems

The longitudinal-flexural and torsional-flexural vibrations are studied for the ultrasonic solid horn and the ultrasonic vibration system comprised of a sandwich transducer and a solid horn. The discussed solid horn is of arbitrary non-uniform cross-section. The analysis on flexural-mode vibration is based on Timoshenko theory. The theoretical results are verified by experiment.     

Unbalanced machinery vibration isolation with a semi-active pneumatic suspension

The problem of unbalanced machinery isolation is tackled in this paper. The proposed solution incorporates an air suspension that can be adapted depending on the turning frequency. The system is built with three main parts: an air spring, a reservoir and a connecting pipe. A model of the suspension excited by the unbalanced rotor is also shown in this paper. The properties of the system make it possible to use a configuration of the suspension (one pipe size) over a bandwidth range and another configuration (another pipe size) over the remaining bandwidth range. This idea is implemented with solenoid controlled valves and the results show significant improvements with respect to completely passive configurations.     

斜拉索风雨振的静态分岔研究

利用达朗伯原理建立了斜拉索风雨振连续体理论模型,实现了比截断模型能更好地体现连续体斜拉索完整的动力学特性.利用奇异性理论,对系统关于Z2对称的余维一分岔问题进行了分析,建立了分岔参数与物理参数的对应关系,得到了转迁集和分岔图,同时对平衡点附近的稳定性进行了讨论.从而有利于进一步开展斜拉索风雨振分岔行为的分析,为斜拉索桥的抗风雨振设计提供理论依据,便于拓展和应用到实际工程中.     

Modal properties and stability of centrifugal pendulum vibration absorber systems with equally spaced,identical absorbers

This work develops an analytical model of centrifugal pendulum vibration absorber systems with equally spaced, identical absorbers and uses it to investigate the structure of the modal vibration properties. The planar model admits two translational and one rotational degrees-of-freedom for the rotor and a single arclength degree-of-freedom for each absorber. The gyroscopic effects from rotor rotation are taken into account. Examination of the associated eigenvalue problem reveals well-defined structure of the vibration modes resulting from the cyclic symmetry of the absorbers. The vibration modes are classified into rotational, translational, and absorber modes. Characteristics of each mode type are analytically proved. The effects of the absorber tuning order on the modes are derived. The critical speeds and flutter instability of the system are studied numerically and analytically.