On the concept of a transmission absorber to suppress internal resonance

Internal resonances within vibration isolators have been shown to increase force transmission and consequently radiated noise from supporting structures. Previous research has successfully used dynamic vibration absorbers to attenuate internal resonances. This paper introduces the term transmission absorber to describe a system that exerts both restoring and inertial forces proportional to relative motion. A novel uni-axial vibration isolator concept incorporating transmission absorbers to suppress internal resonance is proposed and theoretically compared with an isolator including dynamic vibration absorbers. The designs are optimised by using a combination of particle swarm and gradient-based optimisation algorithms. It is shown that the proposed isolator concept, incorporating transmission absorbers, has the potential to outperform previous designs, demonstrating force transmissibility levels approaching those of an ideal isolator.     

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.     

Formulation and validation of a Ritz-based analytical model of high-frequency periodically layered isolators in compression

Periodically layered isolators exhibit transmissibility “stop bands” or frequency ranges in which there is very low transmissibility. A two-dimensional axisymmetric model was developed to accurately predict the location of these stop bands for isolators in compression. A Ritz approximation method was used to model the axisymmetric elastic behavior of layered cylindrical isolators. A modal analysis was performed for a single elastomer and metal layer combination or cell. A modal synthesis approach was then used to obtain a model of an n-celled isolator, from which overall isolator modal properties are determined. This model of the dynamic behavior of layered isolators was validated with experiments. Analytical and experimental transmissibilities are compared for test specimens having identical elastomer components, but different geometries and different numbers of cells. In all cases, experimental and analytical transmissibilities are in close agreement at frequencies ranging from zero to those associated with the initial roll-off of the stop bands. For three and four cell cases, minimum stop band analytical transmissibilities lie below the minimum experimental measurements, although an experimental noise floor imposed a minimum transmissibility measurement of approximately 1.4×10⁻⁴. Experiment suggests a practical isolator design could limit the minimum number of cells to three or four to ensure a pronounced stop band attenuation effect. In addition, analytical and experimental transmissibilities are compared for geometrically similar test specimens with differing elastomeric damping properties. The analytical and experimental results show that stop band effectiveness is not appreciably affected by the addition of modest damping.     

Direct energy flow measurement in magneto-sensitive vibration isolator systems

The effectiveness of highly nonlinear, frequency, amplitude and magnetic field dependent magneto-sensitive natural rubber components applied in a vibration isolation system is experimentally investigated by measuring the energy flow into the foundation. The energy flow, including both force and velocity of the foundation, is a suitable measure of the effectiveness of a real vibration isolation system where the foundation is not perfectly rigid. The vibration isolation system in this study consists of a solid aluminium mass supported on four magneto-sensitive rubber components and is excited by an electro-dynamic shaker while applying various excitation signals, amplitudes and positions in the frequency range of 20–200 Hz and using magneto-sensitive components at zero-field and at magnetic saturation. The energy flow through the magneto-sensitive rubber isolators is directly measured by inserting a force transducer below each isolator and an accelerometer on the foundation close to each isolator. This investigation provides novel practical insights into the potential of using magneto-sensitive material isolators in noise and vibration control, including their advantages compared to traditional vibration isolators. Finally, nonlinear features of magneto-sensitive components are experimentally verified.     

Experimental Investigation of Nonlinear Vibration Isolator with Fluidic Actuators (NLVIFA)

This paper elaborates a nonlinear fluidic low frequency vibration isolator designed with the characteristics of quasi-zero stiffness (QZS). The existing model of QZS vibration isolator enhances amplitude of vibration and attenuating vibration frequencies. This concern with displacement plays a vital role in the performance and instability of oblique spring setup reduces the isolator performance in horizontal non-nominal loads, in this accordance; this paper associates double acting hydraulic cylinder (fluidic actuators in short) in oblique and helical coil spring. An approximate expression of unique analytical relationship between the stiffness of vertical spring and bulk modulus of the fluid is derived for Quasi – Zero Stiffness Non-Linear Vibration Isolator with Fluidic Actuators (NLVIFA in short) system and the force transmissibility is formulated and damping ratio are discussed for characteristic analysis. Modal analysis carried out and compared with analytical results and an experimental prototype is developed and investigated. The performance of the NLVIFA reduces the external embarrassment more at low frequencies and the series of experimental studies showing that the soft nonlinearity causes limitation in the resonant frequency thereupon the isolation will be enhanced and NLVIFA greatly outperform some other type of nonlinear isolators.     

Design and experiment of a compact quasi-zero-stiffness isolator capable of a wide range of loads

This paper proposes the design and experiment of a vibration isolator capable of isolating a wide range of loads. The isolator consists of two oblique springs and one vertical spring to achieve quasi-zero stiffness at the equilibrium position. The quasi-zero-stiffness characteristic makes the isolator attenuate external disturbance more at low frequencies, when compared with linear isolators. Unlike previous studies, this paper focuses on the analysis of the effect of different loads and the implementation of an adjustment mechanism to handle a wide range of loads. To ensure zero stiffness under imperfect stiffness matching, a lateral adjustment mechanism is also proposed. Instead of using coil springs, special planar springs are designed to realize the isolator in a compact space. Static and dynamic models are developed to evaluate the effect of key design parameters so that the isolator can have a wide isolation range without sacrificing its size. A prototype and its associated experiments are presented to validate the transmissibility curves under three different loads. The results clearly show the advantage of quasi-zero-stiffness isolators against linear isolators.     

A study of the effect of inertia blocks on the stability of the vibratory system and the performance of vibration isolation

Resilient vibration isolators and inertia blocks are commonly used by building services engineers to isolate vibratory machines in buildings. They are selected in practice according to the force transmissibility method and some crude methods or the experience of building services engineers. These methods, however, can produce inaccurate predictions, and a power transmissibility method has recently been proposed to assess the performance of vibration isolation. In this paper, normalized average vibration velocities and overall rotational velocities are proposed to study the stability of the vibratory system. The result shows that the use of an inertia block primarily does not improve the performance of vibration isolation, but does increase the stability of the vibratory system regardless of whether the machine is of even or uneven mass distribution and whether it is driven by the vibratory force or the rocking moment.     

A power transmissibility method for assessing the performance of vibration isolation of building services equipment

Force transmissibility is commonly adopted in building services engineering to assess the performance of vibration isolation. However, it neglects the effect of floor mobility on structure-borne sound power transmitted from a vibratory machine to the floor/roof and the interactions among several contact points between the vibratory machine and the floor/roof. The problem that motivated this study is the occasional occurrence of unsatisfactory performance of vibration isolators observed in building services engineering. This problem may be due to the over-simplification of the vibratory problem in the usual definition of the un-damped force transmissibility or isolation efficiency commonly used in engineering practice. In this paper, use of a “power transmissibility”, which includes the effect of floor mobility and the interaction of all dynamic forces transmitted to the floor through the vibration isolators, is proposed.     

Nonlinear vibration isolator with adjustable restoring force

This paper presents a vertical quasi-zero stiffness (QZS) vibration isolator with a mechanism for adjusting restoring force. QZS vibration isolators have high initial stiffness and QZS around the static equilibrium position. This way, excessive deformation due to self-weight can be avoided while having enough vibration reduction capability to dynamic excitations. One of the main issues left for QZS vibration isolators is the difficulty in keeping the vibration reduction capability when the vibration isolated object is replaced. In such a case, adjustment of its restoring force becomes necessary in accordance with the self-weight of the newly placed vibration isolated object. This paper attempts to address this issue by proposing a mechanism that enables quick and easy adjustment of the restoring force of a QZS vibration isolator. The proposed mechanism consists of cranks and a screw jack. With the present mechanism, the restoring force provided by horizontally placed springs can be converted into the vertical restoring force of the vibration isolator. In the conversion, the vertical resisting force can be adjusted simply by applying and removing torque to the screw jack to change and hold the angle of inclined bars placed in the cranks. In this study, a prototype of a class of QZS vibration isolator having the proposed mechanism is produced. Shaking table tests are performed to demonstrate the efficacy of the present mechanism, where the produced prototype is subjected to various sinusoidal and earthquake ground motions. It is demonstrated through the shaking table tests that the produced prototype can reduce the response acceleration within the same tolerance even when the mass of the vibration isolated object is changed.     

Comparison of moments and couple-generating forces near discontinuities in structural-acoustic systems

In modeling vibration isolators in structural-acoustic systems, the isolator's dynamic properties are often treated as acting only in the axial direction as moments are often neglected. Furthermore, the size, or scale, of the isolator is often neglected and the isolator is assumed to act at single points on the connected structures. Previous work has shown that concentrated moments can be particularly important when located near a fixed support or a structural discontinuity. This research extends that work to examine the importance of moment scale effects for a system containing a distributed structural discontinuity with its own scale. Moment scale effects are examined by determining the difference in radiated acoustic power for a simple system that is excited by a couple-generating distributed force and a concentrated moment. The distributed force produces a couple that is equivalent to the concentrated moment. As a result, only the scale is being examined. Particular interest occurs when the excitation is located near the structural discontinuity. Based on the cases studied here, moment scale is shown to be important at lower frequencies when the excitation is located near the edges of the discontinuity. At higher frequencies, any overlap of the excitation and discontinuity may warrant the need to consider moment scales.     

Experimental modal analysis of three small-scale vibration isolator models

This paper discusses the experimentally measured free–free dynamics of three small-scale vibration isolator models: two single-stage isolators and one two-stage isolator. The first comprises two steel plates and one rubber element, the second two steel plates and four rubber elements, and the third three steel plates and eight rubber elements. The natural frequencies, mode shapes and associated modal damping derived from curve-fitting procedures applied to the measured frequency-response functions (FRFs) are presented. The modal behaviour of the isolators is more complicated than might at first be assumed, a major feature being significant coupling between different degrees of freedom. The modal properties can be used to reconstruct a complete set of FRFs for the isolator, including FRFs which were not measured directly. Vibration isolators are often characterised through the use of four-pole parameters or various transmissibilities, and so methods for calculating these parameters from the reconstructed FRFs are also given.     

Octo-strut vibration isolation platform and its application to whole spacecraft vibration isolation

Stewart platform is widely used for vibration isolation and precise pointing. As it is a statically determinate structure, if any strut has fault, a disaster could be unavoidable. In the present paper, an octo-strut passive vibration isolation platform with redundancy is introduced and applied to whole-spacecraft vibration isolation. This platform is modeled with the Newton–Euler method. To avoid such possibility that the spacecraft may interact with the fairing, an approach of stiffness design is proposed to reinforce the rotation stiffness of the platform. With the mathematical model, design parameters of the isolator that will affect the nature frequencies of the isolator-spacecraft system are studied. The transmissibility of the isolator topped with rigid and flexible spacecraft is also studied. Results of analytical and numerical studies show that the octo-strut platform is a reliable and effective approach to improving the dynamic environment of a spacecraft.     

Static and dynamic stability of pneumatic vibration isolators and systems of isolators

Pneumatic vibration isolation is the most widespread effective method for creating vibration-free environments that are vital for precise experiments and manufacturing operations in optoelectronics, life sciences, microelectronics, nanotechnology and other areas. The modeling and design principles of a dual-chamber pneumatic vibration isolator, basically established a few decades ago, continue to attract attention of researchers. On the other hand, behavior of systems of such isolators was never explained in the literature in sufficient detail. This paper covers a range of questions essential for understanding the mechanics of pneumatic isolation systems from both design and application perspectives. The theory and a model of a single standalone isolator are presented in concise form necessary for subsequent analysis. Then the dynamics of a system of isolators supporting a payload is considered with main attention directed to two aspects of their behavior: first, the static stability of payloads with high positions of the center of gravity; second, dynamic stability of the feedback system formed by mechanical leveling valves. The direct method of calculating the maximum stable position of the center of gravity is presented and illustrated by three-dimensional stability domains; analytic formulas are given that delineate these domains. A numerical method for feedback stability analysis of self-leveling valve systems is given, and the results are compared with the analytical estimates for a single isolator. The relation between the static and dynamic phenomena is discussed.     

A new type of semi-active hydraulic engine mount using controllable area of inertia track

Automotive engine mounts function to constrain the engine shake motion resulting at low-frequencies, as well as to isolate noises and vibrations generated by the engine with unbalanced disturbances at the high frequencies. The property of the mount depends on vibration amplitude and excitation frequency. It means that the excitation amplitude is large in low excitation frequency range and small in high frequency range. In this paper, a new hydraulic engine mount with a controllable area of inertia track is proposed and investigated. Theoretical works with the mount model to isolate the engine-related vibrations were conducted by an optimal algorithm to control the area of the inertia track under shocks and multi-signal force excitations. This research clearly gives an analysis of the considerable changes in the mount dynamic properties according to the changes in the inertia track area. Consequently, when the inertia track area is tuned, the transmissibility of the mount is effectively reduced.     

Characteristics of distributed parameter isolators

The widely used traditional massless isolator model is only valid at relatively low frequencies. In this paper two classes of distributed parameter isolator, non-dispersive and dispersive, which are valid over a wide range of frequencies, are studied and compared. The important characteristics of such distributed parameter isolators in isolating a mass are given, as are the parameters which control the isolator performance at various frequencies. The theoretical findings for one distributed parameter isolator are validated experimentally using a helical spring, as an example of a non-dispersive isolator.     

Response of a mindlin plate with trunnion

The vibratory response of a circular plate with a central trunnion is considered. A harmonic force is allowed to act on the trunnion in a plane parallel to the surface of the plate. The model allows for arbitrary location of the center of mass of the trunnion and the line of action of the exciting force. The plate equations include the effects of transverse shear deformations and rotatory inertia, which makes the analysis useful for either thick or thin plates at acoustic frequencies. Application of the model in the control of noise and vibration of rotating machinery is illustrated.     

Analysis and experiment of a vibration isolator using a novel magnetic spring with negative stiffness

The vibration isolator using a novel magnetic spring with negative stiffness (MS-NS) is proposed in this paper. The proposed isolator which combines a positive stiffness spring with the MS-NS in parallel possesses the characteristic of high-static–low-dynamic stiffness. The MS-NS is composed of three cuboidal magnets configured in repulsive interaction. An analytical expression of the stiffness of the MS-NS is derived by using the magnetic charge model, and the approximation to the exact analytical expression is sought. Then, the nonlinearity of the stiffness is analyzed, and it is shown that the MS-NS is approximately linear for small oscillations. In order to validate the correctness and effectiveness of the MS-NS, the vibration transmissibility of the proposed isolator with and without the MS-NS is measured. The experimental results demonstrate that combining a vibration isolator with the MS-NS in parallel can lower the natural frequency of the isolator; and the analytical calculations and experimental results show a good consistency.     

Vibration isolation characteristics of a nonlinear isolator using Euler buckled beam as negative stiffness corrector: A theoretical and experimental study

This paper concerns the vibration isolation characteristics of a nonlinear isolator using Euler buckled beams as negative stiffness corrector. Both analytical and experimental studies are carried out. The Harmonic Balance Method (HBM) is used to determine the primary resonance response for the single degree of freedom (SDOF) nonlinear system composed by a loaded mass and the nonlinear isolator. The distuning of the loaded mass is taken into consideration, resulting in a Helmoholtz–Duffing equation. The performance of the nonlinear isolator is evaluated by the defined two kinds of transmissibility and compared with that of the linear isolator without the stiffness corrector. The study shows that the asymmetric SDOF nonlinear system can behave like a purely softening, a softening–hardening or a purely hardening system, depending on the magnitude of the excitation level. An experimental apparatus is set up to validate the analytical results. The transmissibility results of the SDOF nonlinear system under base excitation with both discrete sinusoidal frequencies and slowly forward and backward sweeps are given and discussed. The complex jump phenomena under different excitation levels are identified. By introducing the stiffness corrector, the starting frequency of isolation of the nonlinear isolator is found to be lower than that of the linear one with the same support capacity. The proposed nonlinear isolator performs well in applications where the excitation amplitude is not too large.     

Sensor fusion for active vibration isolation in precision equipment

Sensor fusion is a promising control strategy to improve the performance of active vibration isolation systems that are used in precision equipment. Normally, those vibration isolation systems are only capable of realizing a low transmissibility. Additional objectives are to increase the damping ratio of internal vibration modes and to provide a high support stiffness. It is shown that these three objectives cannot be realized simultaneously if only acceleration or force feedback is used. An active hard mount suspension with a feedback strategy based on sensor fusion is proposed that uses the acceleration signal at low frequencies and the force signal at high frequencies. Using sensor fusion, the three objectives can be achieved simultaneously. Experiments on a single-axis setup show that this feedback strategy provides an excellent performance.     

Effect of viscous damping on power transmissibility for the vibration isolation of building services equipment

Vibration isolation plays an important role in both the vibration and noise control of building services equipment. To evaluate vibration isolation performance, the force transmissibility method is commonly adopted. However, increasing the damping effect in the force transmissibility method reduces both the resonance peak value and the isolation performance in the “isolation region”. The limitation of the method is that the transmitted displacement of a floor structure and the interaction of mounting points are neglected. To include the floor displacement and the interaction of mounting points, Mak and Su recently proposed the power transmissibility method to assess the performance of vibration isolation. In this paper, the effect of viscous damping on power transmissibility is investigated. A practical procedure for experimentally determining the damping ratio is also given.