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.     

Simulation and experimental tests on active mass damper control system based on Model Reference Adaptive Control algorithm

In the process of sudden natural disasters (such as earthquake or typhoon), the active mass damper (AMD) system can reduce the structural vibration response optimally, which serves as a frequently applied but less mature vibration-reducing technology in wind and earthquake resistance of high-rise buildings. As the core of this technology, the selection of control algorithm is extremely challenging due to the uncertainty of structural parameters and the randomness of external loads. It is not necessary for the Model Reference Adaptive Control (MRAC) based on the Minimal Controller Synthesis (MCS) algorithm to know in advance the structural parameters, which produces special advantages in conditions of real-time change of system parameters, uncertain external disturbance, and the nonlinear dynamic system. This paper studies the application of the MRAC into the AMD active control system. The principle of MRAC algorithm is recommended and the dynamic model and the motion differential equation of AMD system based on MRAC is established under seismic excitation. The simulation analysis for linear and nonlinear structures when the structural stiffness is degenerated is performed under AMD system controlled by MRAC algorithm. To verify the validity of the MRAC over the AMD system, experimental tests are carried out on a linear structure and a structure with variable stiffness with the AMD system under seismic excitation on the shake table, and the experimental results are compared with those of the traditional pole assignment control algorithm.     

The horizontal apparent mass of the standing human body

The driving-point dynamic responses of standing people (e.g. their mechanical impedance or apparent mass) influence their dynamic interactions with structures on which they are supported. The apparent mass of the standing body has been reported previously for vertical excitation but not for lateral or fore-and-aft excitation. Twelve standing male subjects were exposed to fore-and-aft and lateral random vibration over the frequency range 0.1-5.0 Hz for 180 s at four vibration magnitudes: 0.016, 0.0315, 0.063, and 0.125 m s⁻² rms. With lateral excitation at 0.063 m s⁻² rms, subjects also stood with three separations of the feet. The dynamic forces measured at the driving-point in each of the three translational axes (i.e. fore-and-aft, lateral and vertical) showed components not linearly related to the input vibration, and not seen in previous studies with standing subjects exposed to vertical vibration or seated subjects exposed to vertical or horizontal vibration. A principal peak in the lateral apparent mass around 0.5 Hz tended to decrease in both frequency and magnitude with increasing magnitude of vibration and increase with increasing separation of the feet. The fore-and-aft apparent mass appeared to peak at a frequency lower than the lowest frequency used in the study.     

Robust control of novel pendulum-type vibration isolation system

A novel pendulum-type vibration isolation system is proposed consisting of three active cables with embedded piezoelectric actuators and a passive elastomer layer. The dynamic response of the isolation module in the vertical and horizontal directions is modeled using the Lagrangian approach. The validity of the dynamic model is confirmed by comparing the simulation results for the frequency response in the vertical and horizontal directions with the experimental results. An approximate model is proposed to take into account system uncertainties such as payload changes and hysteresis effects. A robust quantitative feedback theory (QFT)-based active controller is then designed to ensure that the active control can achieve a high level of disturbance rejection in the low-frequency range even under variable loading conditions. It is shown that the controller achieves average disturbance rejection of ?14 dB in the 2–60 Hz bandwidth range and ?35 dB at the resonance frequency. The experimental results confirm that the proposed system achieves a robust vibration isolation performance under the payload in the range of 40–60 kg.     

Dynamic stability of a slender beam under horizontal–vertical excitations

The dynamic stability of a vertically standing cantilevered beam simultaneously excited in both horizontal and vertical directions at its base is studied theoretically. The beam is assumed to be an inextensible Euler–Bernoulli beam. The governing equation of motion is derived using Hamilton's principle and has a nonlinear elastic term and a nonlinear inertia term. A forced horizontal external term is added to the parametrically excited system. Applying Galerkin's method for the first bending mode, the forced Mathieu–Duffing equation is derived. The frequency response is obtained by the harmonic balance method, and its stability is investigated using the phase plane method. Excitation frequencies in the horizontal and vertical directions are taken as 1:2, from which we can investigate the influence of the forced response under horizontal excitation on the parametric instability region under vertical excitation. Three criteria for the instability boundary are proposed. The influences of nonlinearities and damping of the beam on the frequency response and parametric instability region are also investigated. The present analytical results for instability boundaries are compared with those of experiments carried out by one of the authors.     

Reduction of vibration and noise radiation of an underwater vehicle due to propeller forces using periodically layered isolators

Using periodic structure theory, the suppression of vibration and noise radiation from an underwater vehicle due to excitation from propeller forces is investigated. The underwater vehicle is modelled in two parts (the hull and the propeller/shafting system). A model of the propeller/shafting system is constructed using a modular approach and considers the propeller, shaft, thrust bearing, isolation structure and foundation. Different forms of isolator are considered – a simple spring-damper system, a continuous rod and a periodically layered structure. The dynamic properties of the underwater vehicle and the isolation performances of various isolators are compared and analysed. The stop band properties of the periodic isolator are used to enhance the passive control performance. Furthermore, an integrated isolation device is proposed that consists of the periodic isolator and a dynamic absorber, and its isolation performance is investigated. The effects of the absorber parameters on the performance of the integrated device are also analysed. Finally, the radiated sound pressure is calculated to verify the attenuation. The numerical results show that the vibration and noise radiation are greatly attenuated in the stop bands. By optimising the design of the periodic isolators and its integrated structures, the suppression of the vibration and noise radiation can be improved effectively.     

Analysis of a non-linear structure by considering two non-linear formulations

In recent years, modal synthesis methods have been extended for solving non-linear dynamic problems subjected to harmonic excitation. These methods are based on the notion of non-linear or linearized modes and exploited in the case of structures affected by localized non-linearity. Actually, the experimental tests executed on non-linear structures are time consuming, particularly when repeated experimental tests are needed. It is often preferable to consider new non-linear methods with a view to decrease significantly the number of attempts during prototype tests and improving the accuracy of the dynamic behaviour.This article describes two fundamental non-linear formulations based on two different strategies. The first formulation exploits the eigensolutions of the associated linear system and the dynamics characteristics of each localized non-linearity. The second formulation is based on the exploitation of the linearized eigensolutions obtained using an iterative process. This article contains a numerical and an experimental study which examines the non-linear behaviour of the structure affected by localized non-linearities. The study is intended to validate the numerical algorithm and to evaluate the problems arising from the introduction of non-linearities. The complex responses are evaluated using the iterative Newton-Raphson method and for a series of discrete frequencies. The theory has been applied to a bi-dimensional structure and consists of evaluating the harmonic responses obtained using the proposed formulations by comparing measured and calculated transfer functions.     

Combined primary–secondary system approach to the design of an equipment isolation system with High-Damping Rubber Bearings

Isolating acceleration-sensitive equipment from the motion of the supporting structure represents an effective protection from earthquake damage. In this paper, a passive equipment isolation system composed of High-Damping Rubber Bearings (HDRB) is designed by adopting a coupled approach in which the supporting structure and the isolated equipment are considered as parts of a combined primary–secondary system and analyzed together. This allows for taking into account their dynamic interaction when significant and non-negligible according to the mass ratio and to the frequency ratio. The design methodology is developed by resorting to a reduced-order 2-DOF model of the combined system, a linear visco-elastic constitutive model of the isolation system and to a modal damping constraint depending upon the damping properties of the HDRB and their rubber compound. A 1:5 scale experimental model, consisting of a two-storey steel frame and a heavy block-type mass isolated from the second floor, is subsequently used to exemplify the design methodology and to perform shaking table tests. The dynamic properties of the experimental model are identified and the seismic performance of the equipment isolation system is discussed under a wide selection of seismic inputs, both artificial and natural.     

Three dimensional vibration generators with a single rotational input

This paper presents a novel device capable of generating three-dimensional vibrations with a single-axis of rotation. The device resembles a vibration motor with an eccentric weight, but the weight is allowed to move up and down in parallel to the axis of rotations. While spinning of the eccentric weight causes lateral vibrations, vertical vibrations are excited by superposing a periodic torque on the rotary shaft. The frequency and magnitude of vertical oscillations can be independently regulated. Since the vertical natural frequency is sensitive to rotational speeds, maximum vertical oscillations can be achieved by properly adjusting the rotational speed according to the excitation frequency. Relations between the excitation torque and the vertical shaking force are examined using the frequency response for the linearized system. Numerical simulations on the original nonlinear system are conducted to verify the performance of vertical oscillations.     

Micromachined optical microphone structures with low thermal-mechanical noise levels

Micromachined microphones with diffraction-based optical displacement detection have been introduced previously [Hall et al., J. Acoust. Soc. Am. 118, 3000-3009 (2005)]. The approach has the advantage of providing high displacement detection resolution of the microphone diaphragm independent of device size and capacitance-creating an unconstrained design space for the mechanical structure itself. Micromachined microphone structures with 1.5-mm-diam polysilicon diaphragms and monolithically integrated diffraction grating electrodes are presented in this work with backplate architectures that deviate substantially from traditional perforated plate designs. These structures have been designed for broadband frequency response and low thermal mechanical noise levels. Rigorous experimental characterization indicates a diaphragm displacement detection resolution of 20 fm radicalHz and a thermal mechanical induced diaphragm displacement noise density of 60 fm radicalHz, corresponding to an A-weighted sound pressure level detection limit of 24 dB(A) for these structures. Measured thermal mechanical displacement noise spectra are in excellent agreement with simulations based on system parameters derived from dynamic frequency response characterization measurements, which show a diaphragm resonance limited bandwidth of approximately 20 kHz. These designs are substantial improvements over initial prototypes presented previously. The high performance-to-size ratio achievable with this technology is expected to have an impact on a variety of instrumentation and hearing applications.     

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.     

Experimental and numerical evidence for the existence of wide and deep phononic gaps induced by inertial amplification in two-dimensional solid structures

The aim of this paper is to show that a two-dimensional periodic solid structure with embedded inertial amplification mechanisms can possess a wide and deep phononic gap at low frequencies. The width and depth of the inertial amplification induced phononic gaps (stop bands) are determined both analytically using a distributed parameter model and numerically using one-dimensional (1D) and two-dimensional (2D) finite element models. The inertial amplification mechanisms are optimized to yield wide and deep gaps at low frequencies. These optimized mechanisms are used to form one- and two-dimensional periodic structures. Frequency responses of these periodic structures are obtained numerically using 1D and 2D finite element models. A deeper gap is generated with the two-dimensional periodic structure when compared with the one-dimensional periodic structure that has the same number of unit cells along the excitation direction. Then, the two-dimensional periodic structure is manufactured and its frequency response is determined via experimental modal analysis. The experimental and numerical frequency response results match quite well, which validate that the two-dimensional periodic solid structure has a wide and deep phononic gap.     

Suspended bridges subjected to moving loads and support motions due to earthquake

The paper deals with the vibration of suspended bridges subjected to the simultaneous action of moving loads and vertical support motions due to earthquake. The basic partial integro-differential equation is applied to the vertical vibration of a suspended beam. The dynamic actions of traffic loads are modelled as a row of equidistant moving forces, while the earthquake is considered by vertical motions of supports. The governing equation is solved first analytically to receive an ordinary differential equation and next numerically. Moreover, the designed world's largest suspended bridge—Messina Bridge—is investigated (central span of length 3.3 km). The paper studies the effect of various lags of the earthquake arrival because the earthquake may appear at any time when the train moves along a large-span bridge. The modified Kobe earthquake records have been applied to calculations. The results indicate that the interaction of both the moving and seismic forces may substantially amplify the response of long-span suspended bridges in the vicinity of the supports and increase with the rising speed of trains.     

Dynamics of a horizontal pendulum driven by high-frequency rocking

This paper investigates the dynamics of a horizontal pendulum subjected to high frequency rocking. The method of direct partition of motion is applied to the governing equation to separate the fast and slow dynamics. It is shown that two stable equilibria may coexist for certain parameter values. It is also shown that the high frequency excitation can stabilize an unstable equilibrium for a horizontal pendulum driven by a rocking motion. The aforementioned theoretical results show good agreement with numerical investigations. A series of experimental tests were also performed to corroborate the bifurcation threshold where forcing parameters can cause a change in stability.     

Dynamic impedances and free-field vibration analysis of pile groups in saturated ground

A three-dimensional (3D) numerical model basing on the thin layer element method and the flexible volume method was established for the computation of dynamic impedances and free-field vibrations of rigidly-capped pile groups embedded in saturated ground. The piles were considered as beams and the saturated ground was represented by Biot?s three-dimensional elastodynamic theory. By recourse to the thin layer element method, Green function of the three dimensional saturated ground was obtained and then verified. The dynamic interaction of the piles and the saturated ground was solved by using the flexible volume method, in which the piles were discretized into three dimensional Euler−Bernoulli beam elements and the dynamic stiffness matrix of saturated ground was formed at the pile−soil interaction nodes by using the Green function. Impedances of the 2×2 pile group and free-field displacement and pore pressure responses caused by harmonic vertical, lateral and rocking forces (moments) applied at the cap center were presented, respectively, for different soil permeability and excitation frequencies. It is found that the soil permeability and the excitation frequency have significant influence on the impedances and the free-field vibration responses.     

Perception,comfort and performance criteria for human beings exposed to whole body pure yaw vibration and vibration containing yaw and translational components

Human perception thresholds, in both the presence and the absence of visual cues, and equal sensation contours for low frequency whole body pure yaw vibration were investigated. The results from these and other laboratory tests were combined with field test data for the human response to predominantly yaw vibration, caused by rotational oscillations of civil structures about a vertical axis of the human subjects, to provide guidelines for probable human response to pure yaw vibration at different levels in a variety of circumstances. Relationships have also been derived to allow assessment of the probable responses of occupants of fixed structures to motion which exposes them to the more common case of simultaneous yaw and horizontal translational components of vibration.     

管间界面特性对周向超声导波传播特性的影响

采用界面弹簧模型对圆管结构的管间界面特性进行描述, 推导出含弱界面的圆管结构中声波沿周向传播时的位移场及应力场的数学表达式. 在此基础上采用导波的模式展开分析方法, 给出了与管间界面特性及激励源密切相关的周向超声导波模式展开系数的解析表达式. 数值分析了管间界面特性的变化对周向超声导波的频散和声场产生的影响. 理论与数值分析结果表明, 通过选择适当的驱动频率及周向导波模式, 可使周向超声导波的相速度及圆管外表面的位移场随管间界面特性的变化表现出非常敏感且单调的性质. 这一结果有助于采用周向超声导波方法准确定征圆管结构的管间界面特性.     

On the dynamic response at the wheel axle of a pneumatic tire

A method for calculating the steady state displacement response and force transmission at the wheel axle of a pneumatic tire-suspension system due to a steady state force or displacement excitation at the tire to ground contact point is developed. The method requires the frequency responses (or receptances)_of both tire-wheel and suspension units. The frequency response of the tire-wheel unit is obtained by using the modal expansion method. The natural frequencies and mode shapes of the tire-wheel unit are obtained by using a geometrically non-linear, ring type, thin shell finite element of laminate composite. The frequency response of the suspension unit is obtained analytically. These frequency responses are used to calculate the force-input and the displacement-input responses at the wheel axle. This method allows the freedom of designing a vehicle and its tires independently and still achieving optimum dynamic performance.     

The dynamic characteristics of a valve-less micropump

The aim of this paper is to investigate the dynamic characteristics of a valve-less micropump. A dynamic mathematical model of the micropump based on a hydraulic analogue system and a simulation method using AMESim software are developed. By using the finite-element analysis method, the static analysis of the diaphragm is carried out to obtain the maximum deflection and volumetric displacement. Dynamic characteristics of the valve-less micropump under different excitation voltages and frequencies are simulated and tested. Because of the discrepancy between simulation results and experimental data at frequencies other than the natural frequency, the revised model for the diaphragm maximum volumetric displacement is presented. Comparison between the simulation results based on the revised model and experimental data shows that the dynamic mathematical model based on the hydraulic analogue system is capable of predicting dynamic characteristics of the valve-less micropump at any excitation voltage and frequency.     

Harmonic pulsed excitation and motion detection of a vibrating reflective target

Elasticity imaging is an emerging medical imaging modality. Methods involving acoustic radiation force excitation and pulse-echo ultrasound motion detection have been investigated to assess the mechanical response of tissue. In this work new methods for dynamic radiation force excitation and motion detection are presented. The theory and model for harmonic motion detection of a vibrating reflective target are presented. The model incorporates processing of radio frequency data acquired using pulse-echo ultrasound to measure harmonic motion with amplitudes ranging from 100 to 10,000 nm. A numerical study was performed to assess the effects of different parameters on the accuracy and precision of displacement amplitude and phase estimation and showed how estimation errors could be minimized. Harmonic pulsed excitation is introduced as a multifrequency radiation force excitation method that utilizes ultrasound tonebursts repeated at a rate f(r). The radiation force, consisting of frequency components at multiples of f(r), is generated using 3.0 MHz ultrasound, and motion detection is performed simultaneously with 9.0 MHz pulse-echo ultrasound. A parameterized experimental analysis showed that displacement can be measured with small errors for motion with amplitudes as low as 100 nm. The parameterized numerical and experimental analyses provide insight into how to optimize acquisition parameters to minimize measurement errors.