H2 optimization of a non-traditional dynamic vibration absorber for vibration control of structures under random force excitation

The H₂ optimum parameters of a dynamic vibration absorber of non-traditional form are derived to minimize the total vibration energy or the mean square motion of a single degree-of-freedom (sdof) system under random force excitations. The reduction of the mean square motion of the primary structure using the traditional vibration absorber is compared with the proposed dynamic absorber. Under optimum tuning condition, it is shown that the proposed absorber when compared with the traditional absorber, provides a larger suppression of the mean square vibrational motion of the primary system.     

Suppression of random vibration in flexible structures using a hybrid vibration absorber

A design method is proposed to suppress stationary random vibration in flexible structures using a hybrid vibration absorber (HVA). While the traditional vibration absorber can damp down the vibration mainly at the pre-tuned mode of the primary structure, active damping is generated by the proposed HVA to damp down all resonant modes of interest of the vibrating structure and the spatial average mean square motion of the vibrating structure can be minimized. Only one absorber and one feedback signal are required to achieve global vibration suppression of a flexible structure under stationary random excitation. A special pole-placement controller is designed such that all vibration modes of the flexible structures become critically damped. It is proved analytically that the proposed HVA damps the vibration of the entire structure instead of just the attachment point of the absorber. The proposed optimized HVA is tested on a beam structure and it shows a superior performance on global suppression of broadband vibration in comparison to other published designs of passive and hybrid vibration absorbers.     

Design optimization of a damped hybrid vibration absorber

In this article, the H_∞ optimization design of a hybrid vibration absorber (HVA), including both passive and active elements, for the minimization of the resonant vibration amplitude of a single degree-of-freedom (sdof) vibrating structure is derived by using the fixed-points theory. The optimum tuning parameters are the feedback gain, the tuning frequency, damping and mass ratios of the absorber. The effects of these parameters on the vibration reduction of the primary structure are revealed based on the analytical model. Design parameters of both passive and active elements of the HVA are optimized for the minimization of the resonant vibration amplitude of the primary system. One of the inherent limitations of the traditional passive vibration absorber is that its vibration absorption is low if the mass ratio between the absorber mass and the mass of the primary structure is low. The proposed HVA overcomes this limitation and provides very good vibration reduction performance even at a low mass ratio. The proposed optimized HVA is compared to a recently published HVA designed for similar propose and it shows that the present design requires less energy for the active element of the HVA than the compared design.     

Active control effort of hybrid piezoelectric absorber for structural control

This paper aims at addressing the active control effort of the active-shunted hybrid piezoelectric absorber for structural vibration suppression. Both active control efforts of the integrated and separated hybrid piezoelectric absorbers are analyzed by using a simple cantilevered beam example. It is recognized that a new hybrid piezoelectric absorber based on a switching operation is capable of reducing the active control effort. A switching type of the hybrid piezoelectric absorber can be developed by the simple combination of integrated and separated hybrid piezoelectric absorbers. It is demonstrated that the switching type of the absorber has the capability of the trade-off between the active control effort and the damping performance.     

Material damping under random excitation

The damping capacity of three materials subjected to narrow-band strain fluctuations is investigated, the material effectively undergoing sinusoidal strain with randomly varying amplitude. For this case, a theoretical relationship is established between the expected value of the energy dissipated per unit volume of the material per period of the narrow-band process and the r.m.s. value of the strain history. This is expressed in terms of material damping constants obtained from harmonic damping measurements. The theoretical relationship is checked against experimental results from narrow-band random experiments on three different materials over low and intermediate stress ranges. Good agreement is found.     

Elastic-plastic oscillators under random excitation

Simulation studies reveal that the elastic-plastic oscillator cannot be successfully treated by any linearization procedure. In order to compute the main response quantities, such as the yielding increment, the permanent set, the dissipated energy and the crossing rates, a so-called two-state approach is suggested. With the separation between the elastic and plastic parts of the response kept as originally proposed by Karnopp and Scharton, one linear equation is obtained for each state. The fundamental step then is to set up a conditional probability density for the plastic state variable under Gaussian stationary or non-stationary white noise excitation. The yielding duration is found to be half-normal distributed. Numerical results demonstrate the approach and the range of parameters where it can be successfully applied.     

The effective damping approach to design a dynamic vibration absorber using Coriolis force

In this paper, the vibration reduction of a pendulum structure with dynamic vibration absorber (DVA) using Coriolis force is investigated. When the pendulum structure is subjected to a single harmonic excitation, the effective damping of Coriolis force is used with the second-order approximations to obtain the closed forms of optimal parameters of the DVA. The closed forms obtained show that the natural frequency of the absorber should be tuned to twice that of the pendulum. The closed forms of optimal parameters are verified by numerical optimization. The modified forms of optimal parameters are proposed to be used in case of general excitation. Base on this modified form, the design procedure is demonstrated by the numerical calculation of the free vibration and wind-induced vibration of a ropeway gondola.     

First-passage failure of a business cycle model under time-delayed feedback control and wide-band random excitation

First-passage failure of a classical business cycle model subject to time-delayed feedback control and wide-band random excitation is investigated in this paper. First, we get the averaged equation by using a stochastic averaging method, and then a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. The conditional reliability function, the conditional probability density and moments of first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations analytically and numerically with suitable initial and boundary conditions. The results show that time delay in the feedback control forces may remarkably reduce the conditional reliability and the mean first-passage time of the controlled economics system.     

Stochastic stability of a gyropendulum under random vertical support excitation

The mean square stability of a gyropendulum under random vertical support excitation is considered. The intensity and the correlation time of the stochastic excitations are assumed to be small in order to obtain approximate analytical results. The stochastic averaging procedure of Stratonovich and Khasminskii is used to establish the drift and diffusion coefficients in the corresponding Itô equation. Explicit results are obtained for stochastic stability boundaries.     

Response statistics of discretized structures to non-stationary random excitation

Closed-form time-dependent response statistics such as (i) the variance of displacement response and variance of velocity response, (ii) the covariance of displacement and velocity responses, and (iii) covariances of displacement responses and velocity responses of structures, discretized by the finite element method, subjected to a wide class of non-stationary random excitations are presented. The response statistics include the contribution due to the evolutionary coincident and quadrature spectral density functions. Application of the expressions obtained has been made to a quarter-scale physical model of a class of mast antenna structures excited at the base. Computed results indicate that the contribution due to the evolutionary quadrature spectral density function is insignificant.     

Semi-active friction tendons for vibration control of space structures

Semi-active vibration control systems are becoming popular because they offer both the reliability of passive systems and the versatility of active control without high power demands. In this work, a new semi-active control system is proposed and studied numerically. The system consists of variable-friction dampers linked to the structure through cables. Auxiliary soft springs in parallel with these friction dampers allow them to return to their initial pre-tensioned state. Using cables makes the system suitable for deployable, flexible and lightweight structures, such as space structures (spacecraft). A control system with three control laws applied to a single-degree-of-freedom structure is studied. Two of these laws are derived by using Lyapunov theory, whereas the third one is developed heuristically. In order to assess the performance of the control system, a parametric study is carried out through numerical simulations. An application of the proposed method to multi-degree-of-freedom structures is also presented and demonstrated through a numerical example. The system in semi-active mode is more effective than in passive mode and its effectiveness is less sensitive to loss of pre-tension.     

Analyses for random flow-induced vibration of cylindrical structures subjected to turbulent axial flow

In this paper, stochastic analytical equations for obtaining the vibratory response of bundles of cylinders in turbulent axial flow, with various degrees of computational efficiency, are presented. Lateral components of the turbulent fluid force-per-unit-length cross-spectral densities in a bundle of cylinders are obtained by the integration of differential wall-pressure fluctuations around the circumferences of the cylinders. These quantities are used as excitation in the calculation of random vibration response spectral densities of the cylindrical structures. Properties of symmetry applicable to lateral forces in bundles of symmetrically arranged cylinders are also discussed.     

Temporal properties of random lasers under ultrashort pulse excitation

Temporal properties of random lasing under ultrashort pulse excitation are investigated in a two-dimensional disordered medium. The pumping light is described individually and coupled into the rate equations. The Maxwell equations and rate equations are numerically solved by using the finite-difference time domain method. The time evolution of the emission pulse is studied with the variation of the surface-filling fraction, refractive index,and scatterer radius. Results show that the behavior of random lasing depends strongly on the sample parameters. Our work enriches the knowledge about random lasers in the ultrashort pulse pumping regime and offers some guidance for relevant experiments.     

Optimum vibration absorber (tuned mass damper) design for linear damped systems subjected to random loads

Optimum design of dynamic vibration absorbers (DVAs) installed on linear damped systems that are subjected to random loads is studied and closed-form design formulas are provided. Three cases are considered in the optimization process: Minimizing the variance of the displacement, velocity and acceleration of the main mass. Exact optimum design parameters for the velocity case, which to the best knowledge of the author do not exist in the literature, are derived for the first time. Exact solutions are found to be directly applicable for practical use with no simplification needed. For displacement and acceleration cases, a solution for the optimum absorber frequency ratio is obtained as a function of optimum absorber damping ratio. Numerical simulations indicate that optimum absorber damping ratio is not significantly related to the structural damping, especially when the displacement variance is minimized. Therefore, optimum damping ratio derived for undamped systems is proposed for damped systems for the displacement case. When acceleration variance is minimized, however, the optimum damping ratio derived for undamped systems is found not as accurate for damped systems. Therefore, a more accurate approximate expression is derived. Numerical comparisons with published approximate expressions at the same level of complexity indicated that proposed design formula yield more accurate estimates. Another important finding of the paper is that for specific applications where all of the response parameters are desired to be minimized simultaneously, DVAs designed per velocity criteria provide the best overall performance with the least complexity in the design equations.     

Band/wheel system vibration under impulsive boundary excitation

Measurements of band vibration undertaken here show that passage of the butt weld connecting the ends of continuous band over wheels excites vibration in the band/wheel system. A displacement impulse occurs each time the weld initially contacts and separates from the wheels. The excitation is periodic, and it can excite instability. The vibration and stability of the coupled band/wheel system under impulsive boundary displacements are analyzed in this paper. The theoretical and experimental findings show that resonance occurs in the system when the weld passage (impulse) period is an integer multiple of any system natural period.