H-infinity optimization of a variant design of the dynamic vibration absorber—Revisited and new results

The H_∞ optimum parameters of a dynamic vibration absorber (DVA) with ground-support are derived to minimize the resonant vibration amplitude of a single degree-of-freedom (sdof) system under harmonic force excitation. The optimum parameters which are derived based on the classical fixed-points theory and reported in literature for this non-traditional DVA are shown to be not leading to the minimum resonant vibration amplitude of the controlled mass. A new procedure is proposed for the H_∞ optimization of such a dynamic vibration absorber. A new set of optimum tuning frequency and damping of the absorber is derived, thereby resulting in lower maximum amplitude responses than those reported in the literature. The proposed optimized variant DVA is also compared to a ground-hooked damper of the same damping capacity of the damper in the DVA. It is proved that the proposed optimized DVA has better suppression of the resonant vibration amplitude of the controlled system than both the traditional DVA and also the ground-hooked damper if the proposed design procedure of the variant DVA is followed.     

3D analysis of in-filled trench as passive barriers for ground vibration isolation

The three-dimensional (3D) problem of the ground vibration isolation by an in-filled trench as a passive barrier is studied theoretically. Integral equations governing Rayleigh wave scattering are derived based on the Green’s solution of Lamb problem. The integral equations are solved accurately and efficiently with an iteration technique. They are used to evaluate the complicated Rayleigh wave field generated by irregular scatterers embedded in an elastic half-space solid. The passive isolation effectiveness of ground vibration by the in-filled trench for screening Rayleigh wave is further studied in detail. Effects of relevant parameters on the effectiveness of vibration isolation are investigated and presented. The results show that a trench filled with stiff backfill material gets a better isolation effect than a soft one, and increasing the depth or width of the in-filled trench also improves its screening effectiveness. The effectiveness and the area of the screened zone are surging with the increase in the length of the in-filled trench. Supported by the National Natural Science Foundation of China (Grant Nos. 50678128 and 50538010) and the Research Fund for PhD Student of Chinese College (Grant No. 20050247030)     

Dynamic properties of the human head

Driving point mechanical impedance measurements were used to determine the dynamic response of the human head to sinusoidal vibration in the frequency range between 30 Hz and 5000 Hz at excitation levels of 0·98 m/s² and 3·4 m/s2. Because of the low excitation levels, the weight of the head was sufficient to couple the head to the vibration source.At 20 Hz the impedance magnitude was about 790 N-s/m but increased at approximately 6dB/octave to a peak near 3500 N-s/m at 70–90 Hz. Between 100 Hz and 2000 Hz impedance decreased by about two orders of magnitude while the apparent mass decreased by three orders of magnitude indicating good vibration isolation at higher frequencies. The impedance response contains the information for modelling the head as a dynamic system.The response of the head to vibration can be simulated by a two degree-of-freedom, mass-excited system consisting of a series connection of a small driving mass, a damper, a spring and damper in parallel and a large final mass. Parameter values, derived by computer techniques, suggest that the large mass represents the total head, the small mass the tissue in contact with the vibration input and the spring the skull stiffness.     

Shallow rectangular TLD for structural control implementation

A simple and practical model for the application of shallow rectangular tuned liquid damper (TLD) in structural vibration control is presented in this paper. The dynamic properties of shallow liquid in rectangular containers subjected to forced horizontal oscillation are analysed directly from the continuity and momentum equations of fluids. Following some practical assumptions, the nonlinear partial differential equations describing the wave movement of shallow liquid in rectangular containers are established and a numerical procedure for the solutions of these equations is proposed based on the finite element method. The formula for determining the control force provided by a shallow rectangular TLD is presented. The advantage of the proposed approach for the modeling of shallow rectangular TLD is that it simplifies a three-dimensional problem into a one-dimensional problem and therefore reduces the computation efforts significantly. The whole process forms a solid foundation and provides a simplified procedure for the design and analysis of shallow rectangular TLD.     

A comparison of two nonlinear damping mechanisms in a vibration isolator

The vibration transmissibility characteristics of a single-degree-of-freedom (SDOF) passive vibration isolation system with different nonlinear dampers are investigated in this paper. In one configuration, the damper is assumed to be linear and viscous, and is connected to the mass so that it is perpendicular to the spring (horizontal damper). The vibration is in the direction of the spring. The second configuration is one in which the damper is in parallel with the spring but the damping force is proportional to the cube of the relative velocity across the damper (cubic damping). Both configurations are studied for small amplitudes of excitation, when some analysis can be conducted based on analytical expressions, and for large amplitudes of excitation, where the analysis is based on numerical simulations. It is found that the two nonlinear systems can outperform the linear system when force transmissibility is considered. However, for displacement transmissibility, the system with the horizontal damper exhibits some desirable properties, but the system with cubic damping does not.     

Suppression of the primary resonance vibrations of a forced nonlinear system using a dynamic vibration absorber

In a single degree-of-freedom weakly nonlinear oscillator subjected to periodic external excitation, a small-amplitude excitation may produce a relatively large-amplitude response under primary resonance conditions. Jump and hysteresis phenomena that result from saddle-node bifurcations may occur in the steady-state response of the forced nonlinear oscillator. A simple mass-spring-damper vibration absorber is thus employed to suppress the nonlinear vibrations of the forced nonlinear oscillator for the primary resonance conditions. The values of the spring stiffness and mass of the vibration absorber are significantly lower than their counterpart of the forced nonlinear oscillator. Vibrational energy of the forced nonlinear oscillator is transferred to the attached light mass through linked spring and damper. As a result, the nonlinear vibrations of the forced oscillator are greatly reduced and the vibrations of the absorber are significant. The method of multiple scales is used to obtain the averaged equations that determine the amplitude and phases of the first-order approximate solutions to primary resonance vibrations of the forced nonlinear oscillator. Illustrative examples are given to show the effectiveness of the dynamic vibration absorber for suppressing primary resonance vibrations. The effects of the linked spring and damper and the attached mass on the reduction of nonlinear vibrations are studied with the help of frequency response curves, the attenuation ratio of response amplitude and the desensitisation ratio of the critical amplitude of excitation.     

Vibration suppression of a cantilever beam using magnetically tuned-mass-damper

Eddy currents are induced by the movement of a conductor through a stationary magnetic field or a time varying magnetic field through a stationary conductor. These currents circulate in the conductive material and are dissipated, causing a repulsive force between the magnet and the conductor. These electromagnetic forces can be used to suppress the vibrations of a flexible structure. A tuned mass damper is a device mounted in structures to reduce the amplitude of mechanical vibrations and is one of the effective vibration suppression methods. In the present study, an improved concept of this tuned mass damper for the vibration suppression of structures is introduced. This concept consists of the classical tuned mass damper and an eddy current damping. The important advantages of this magnetically tuned mass damper are that it is relatively simple to apply, it does not require any electronic devices and external power, and it is effective on the vibration suppression. The proposed concept is designed for a cantilever beam and the analytical studies on the eddy current damping and its effects on the vibration suppression. To show the effectiveness of the proposed concept and verify the eddy current damping model, experiments on a cantilever beam are performed. It is found that the proposed concept could significantly increase the damping effect of the tuned mass damper even if not adequately tuned.     

Semi-analytical analysis of the isolation to moving-load induced ground vibrations by trenches on a poroelastic half-space

A semi-analytical model is proposed to investigate the screening efficiency of trenches to moving-load induced ground vibrations. The ground is modeled as a fully saturated poroelastic half-space governed by Biot's dynamic poroelastic theory. The trenches are obtained by placing three rectangular elastic layers with appropriate width upon the poroelastic half-space. By Helmholtz decomposition, the displacement fields of the elastic layers are decomposed into three scalar potentials. Analytical solutions are obtained based on Fourier transform and Fourier series in the transformed domain. The time-domain results are obtained by the fast Fourier transform (FFT). The different performances of trenches on a saturated poroelastic half-space and a single-phase elastic half-space to the moving load-induced ground vibration are identified. It is found that the discrepancy of the screening efficiencies between the two models becomes significant when the load speed approaches the Rayleigh wave speed of the ground surface. Also, some parametric studies for the screening efficiency of the trench on the poroelastic half-space are presented.     

机载多框架光电吊舱两级隔振设计

在分析了目前常用的机载光电设备隔振系统的基础上,针对两轴四框架的结构特点,提出了一种基于多框架的两级隔振方案,克服了目前隔振系统体积、重量大,加工装配要求高的缺点。基于隔振模型的理论计算表明,根据系统给定的质量比和频率比,优化选择内外框架的刚度比,即选择合适的内外框隔振器可达到理想的隔振效果。通过某型光电吊舱的扫频实验...     

Experimental studies of the effects of buffered particle dampers attached to a multi-degree-of-freedom system under dynamic loads

This paper presents a systematic experimental investigation of the effects of buffered particle dampers attached to a multi-degree-of-freedom (mdof) system under different dynamic loads (free vibration, random excitation as well as real onsite earthquake excitations), and analytical/computational study of such a system. A series of shaking table tests of a three-storey steel frame with the buffered particle damper system are carried out to evaluate the performance and to verify the analysis method. It is shown that buffered particle dampers have good performance in reducing the response of structures under dynamic loads, especially under random excitation case. It can effectively control the fundamental mode of the mdof primary system; however, the control effect for higher modes is variable. It is also shown that, for a specific container geometry, a certain mass ratio leads to more efficient momentum transfer from the primary system to the particles with a better vibration attenuation effect, and that buffered particle dampers have better control effect than the conventional rigid ones. An analytical solution based on the discrete element method is also presented. Comparison between the experimental and computational results shows that reasonably accurate estimates of the response of a primary system can be obtained. Properly designed buffered particle dampers can effectively reduce the response of lightly damped mdof primary system with a small weight penalty, under different dynamic loads.     

On the detection of objects buried at a shallow depth using seismic wave reflections

This paper concerns the detection of shallow (of the order 1 m) buried objects using seismic excitation. Time-extended signals are used to generate a compressional wave using a shaker attached to the ground. The wave propagates through the ground, reflects off a buried object and is captured by an array of geophones on the surface. The envelopes of the cross-correlation functions between the measured ground velocities and the excitation signal are calculated and summed to generate a cross-sectional image of the ground. The wide cross-correlation peaks caused by high ground attenuation are partially compensated for by using the generalized cross-correlation function called the phase transform. Simple simulations are conducted to demonstrate the method, and some field experiments have been carried out aimed at the detection of a buried concrete pipe. In the experiments the pipe could be detected using the method proposed, with experimental and simulated data producing good agreement.     

A vibration isolation system in low frequency excitation region using negative stiffness structure for vehicle seat

This paper designs and fabricates a vibration isolation model for improving vibration isolation effectiveness of the vehicle seat under low excitation frequencies. The feature of the proposed system is to use two symmetric negative stiffness structures (NSS) in parallel to a positive stiffness structure. Here, theoretical analysis of the proposed system is clearly presented. Then, the design procedure is derived so that the resonance peak of frequency-response curve drifts to the left, the load support capacity of the system is maintained, the total size of the system is reduced for easy practical application and especially, the bending of the frequency-response curve is minimized. Next the dynamic equation of the proposed system is set up. Then, the harmonic balance (HB) method is employed to seek the characteristic of the motion transmissibility of the proposed system at the steady state for each of the excitation frequency. From this characteristic, the curves of the motion transmission are predicted according to the various values of the configurative parameters of the system. Then, the time responses to the sinusoidal, multi frequency and random excitations are also investigated by simulation and experiment. In addition, the isolation performance comparison between the system with NSS and system without NSS is realized. The simulation results reveal that the proposed system has larger frequency region of isolation than that of the system without NSS. The experimental results confirm also that with a random excitation mainly spreading from 0.1 to 10 Hz, the isolation performance of the system with NSS is greatly improved, where the RMS values of the mass displacement may be reduced to 67.2%, whereas the isolation performance of the system without NSS is bad. Besides, the stability of the steady-state response is also studied. Finally, some conclusions are given.     

Flexural vibration insulation with an elastic layer for a plate under nonuniform vibratory action

A method is proposed for calculating the vibration insulation of an elastic layer positioned between a finite-size plate with free edges and a vibrationally active base. The elastic layer consists of a discrete set of springs. In the case of an out-of-phase vibration of the base surface, the mean dynamic action on the plate decreases, which leads to an increase in vibration insulation. By contrast, the resonances of flexural plate vibrations reduce the vibration insulation at resonance frequencies. For different cases, the system parameters that correspond to a positive effect of vibration insulation are estimated. The simplest mass-spring system possessing a single degree of freedom is discussed.     

A comparison of a theoretical model for quasi-statically and dynamically induced environmental vibration from trains with measurements

This paper presents comparisons between a theoretical ground vibration model and measured data at three sites. The model, which is briefly outlined here, encompasses both the quasi-static and dynamic mechanisms of excitation. The vertical dynamics of a number of vehicles travelling at a constant speed on an infinite track are coupled to a semi-analytical model for a three-dimensional layered ground. This model is also used to demonstrate the roles of the two components of vibration at different frequencies and for train speeds below and above the lowest ground wave speed. It is found that, in most practical cases, the dynamic component gives rise to the higher level of vibration.     

EVALUATION OF VIBRATION AND SHOCK ATTENUATION PERFORMANCE OF A SUSPENSION SEAT WITH A SEMI-ACTIVE MAGNETORHEOLOGICAL FLUID DAMPER

The potential benefits of a semi-active magnetorheological (MR) damper in reducing the incidence and severity of end-stop impacts of a low natural frequency suspension seat are investigated. The MR damper considered is a commercially developed product, referred to as “Motion Master semi-active damping system” and manufactured by Lord Corporation. The end-stop impact and vibration attenuation performance of a seat equipped with such a damper are evaluated and compared with those of the same seat incorporating a conventional damper. The evaluation is performed on a servo-hydraulic vibration exciter by subjecting the seat-damper combinations to a transient excitation with dominant frequency close to that of the seat and continuous random excitation class EM1 applicable to earth-moving machinery, and a more severe excitation realized by amplifying the EM1 excitation by 150%. Tests are performed for medium and firm settings of the MR damper and for seat height positions corresponding to mid-ride and ±2·54 and ±5·08 cm relative to mid-ride. The results indicate that significantly higher levels of transient excitation are necessary to induce end-stop impacts for the seat equipped with the MR damper, particularly when set for firm damping, the difference with the conventional damper being more pronounced for seat positions closer to the end-stops. Under the EM1 excitation, the results indicate that under conditions which would otherwise favour the occurrence of end-stop impacts for a seat equipped with a conventional damper, the use of the MR damper can result in considerably less severe impacts and correspondingly lower vibration exposure levels, particularly when positioned closer to its compression or rebound limit stop.     

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.     

Identification of dynamic loading on a bending plate using the Virtual Fields Method

This paper aims at identifying local dynamic transverse forces and distributed pressures acting on the surface of a thin plate, from its measured vibration response. It is related to previous work by other authors on the so-called Force Analysis Technique but uses a different formulation. The paper first presents the theoretical developments based on the Virtual Fields Method and then, numerically simulated data are processed to validate the identification algorithm. Finally, experimental data are used. Both mechanical point load excitation, and distributed acoustic excitation of a bending panel are considered. The force reconstruction results are very satisfactory and the low computational times together with the simple implementation make the Virtual Fields technique attractive for this type of problem.     

一种光电载荷非线性隔振装置的研究

针对光电载荷对隔振性能的需求,提出一种采用菱形连杆机构作为负刚度组件,具有高静、低动刚度特点的非线性隔振器（简称菱形HSLDS隔振器）。采用静力学分析方法,建立了隔振器数学模型,研究了刚度参数设定以及非线性调节方法;利用谐波平衡法（HBM）求解动力学方程,分析了各参数对隔振性能的影响关系;采用动力学仿真软件ADAMS及实物样机对理论模型与结论进行了验证。测试结果表明:菱形HSLDS隔振器具有较方便的参数调整能力,零位刚度及刚度非线性可通过拉簧参数与连杆参数进行设定、优化,隔振的刚度非线性优化程度受主隔振器阻尼以及零位刚度参数影响。相比于传统线性隔振器,菱形HSLDS具有显著的非线性隔振优势,可较好地满足光电载荷隔振需求。     

Experimental and numerical study on long-span reticulate structure with multidimensional high-damping earthquake isolation devices

Multidimensional high-damping earthquake isolation device (MHEID) for long-span reticulate structure is an innovative passive vibration control device. In this paper, the results of horizontal and vertical property tests are presented first and then effects of excitation frequency, displacement on MHEID are studied. In order to consider the effects of excitation frequency, displacement amplitude and temperature on MHEID, a new mathematical model, i.e., fractional-derivative equivalent standard solid model, is put forward to describe the dynamic properties of MHEID precisely in both horizontal and vertical directions. Then, horizontal and vertical pseudo-dynamic tests on structures with and without MHEID are conducted. It can be seen from the experimental results that MHEID can obviously reduce the displacement responses, acceleration responses and input forces of the long-span reticulate structure. In order to analyze the earthquake isolation effect of MHEID on long-span reticulate structures, the dynamic responses are simulated by using a new dynamic response analysis method. The numerical results fit well with the experimental results and it is indicated that the proposed method can simulate the dynamic responses of the long-span reticulate structure.     

A modeling technique for active control design studies with application to spacecraft microvibrations

Microvibrations, at frequencies between 1 and 1000 Hz, generated by on board equipment, can propagate throughout a spacecraft structure and affect the performance of sensitive payloads. To investigate strategies to reduce these dynamic disturbances by means of active control systems, realistic yet simple structural models are necessary to represent the dynamics of the electromechanical system. In this paper a modeling technique which meets this requirement is presented, and the resulting mathematical model is used to develop some initial results on active control strategies. Attention is focused on a mass loaded panel subjected to point excitation sources, the objective being to minimize the displacement at an arbitrary output location. Piezoelectric patches acting as sensors and actuators are employed. The equations of motion are derived by using Lagrange's equation with vibration mode shapes as the Ritz functions. The number of sensors/actuators and their location is variable. The set of equations obtained is then transformed into state variables and some initial controller design studies are undertaken. These are based on standard linear systems optimal control theory where the resulting controller is implemented by a state observer. It is demonstrated that the proposed modeling technique is a feasible realistic basis for in-depth controller design/evaluation studies.