Floating Raft Isolation System Research Articles

Design of a floating raft system by exploiting the nonlinear damping

In the present study, the optimization design of the cubic nonlinear damping is conducted for a floating raft isolation system, which can be simplified as a multiple degree-of-freedom system with double parallel freedom inputs. The direct relationship between the power transmissibility and cubic nonlinear damping parameters is derived by taking advantage of the output frequency response function (OFRF) approach. The design requirements are proposed in order to achieve low resonant peak values, low power transmissibility over the high frequency range. The detailed step-by-step design process of the floating raft isolation system applied in a practical vessel is provided. A polynomial function, in terms of the required frequency range, is developed and validated from the simulation data. The case application indicates that the design method determined by the OFRF approach can effectively realize the design requirements of a floating raft isolation system, which can deal with the relationship of the power transmissibility and nonlinear damping parameters.

Vibration control of a marine centrifugal pump using floating raft isolation system

In order to study the influence of floating raft isolation system (FRIS) on the vibration characteristics of marine pump, a marine centrifugal pump with/without FRIS under the same operation condition, which specific speed is 66.7, was experimentally measured. The maximum efficiency of the pump is 75.8%, which is under 1.2 Qd. Results show that the characteristic frequencies in the vibration spectrums of the pump with/without FRIS are APF (axial passing frequency), the BPF (blade passing frequency) and its high-order harmonic frequency. After installing FRIS, under 0.8 Qd, 1.0 Qd and 1.2 Qd, the vibration intensity of the pump at inlet flange is slighter than that at pump base and larger than that at pump bracket. The vibration intensity at outlet flange is slighter than that at the pump bracket and larger than that at pump body, and the vibration intensity at connecting plate is the lowest. The vibration velocity level of pump base decreases with the increase of flow rate, the maximum vibration intensity at M1–M4 is reduced by 88% than that without FRIS, and the maximum vibration velocity of the APF at M1–M4 is reduced by 83.3% than that without FRIS.

Dynamic condensation of non-classically damped structures using the method of Maclaurin expansion of the frequency response function in Laplace domain

As the number of degrees of freedom (DOFs) in structural dynamic problems becomes larger, the analyzing complexity and CPU usage of computers increase drastically. Condensation (or reduction) method is an efficient technique to reduce the size of the full model or the dimension of the structural matrices by eliminating the unimportant DOFs. After the first presentation of condensation method by Guyan in 1965 for undamped structures, which ignores the dynamic effects of the mass term, various forms of dynamic condensation methods were presented to overcome this issue. Moreover, researchers have tried to expand the dynamic condensation method to non-classically damped structures. Dynamic reduction of such systems is far more complicated than undamped systems. The proposed non-iterative method in this paper is introduced as 'Maclaurin Expansion of the frequency response function in Laplace Domain' (MELD) applied for dynamic reduction of non-classically damped structures. The present approach is implemented in four numerical examples of 2D bending-shear-axial frames with various numbers of stories and spans and also a floating raft isolation system. The results of natural frequencies and dynamic responses of models are compared with each other before and after the dynamic reduction. It is shown that the result accuracy has acceptable convergence in both cases. In addition, it is indicated that the result of the proposed method is more accurate than the results of some other existing condensation methods.

Vibration transmission analysis of nonlinear floating raft isolation system with magneto-rheological damper

The vibration transmission characteristics of a three-degree of freedom nonlinear floating raft isolation system are studied in order to analyze the influence of magneto-rheological damper on primary resonance attenuation. A revised Bingham model verified by experiment is adopted to describe the nonlinear magneto-rheological damping force, and the dissipated energy based on the model is given which is more than general viscous damper. Then, the approximately analytic solution for primary resonance of floating raft isolation system is obtained by means of averaging method, and it is compared with numerical integration solution. Force transmissibility is proposed to evaluate the effectiveness of magneto-rheological damper. The influences of magneto-rheological damper parameters on force transmissibility are also investigated. The results show that force transmissibility decreases as the increase of viscous damping coefficient of magneto-rheological damper and zero-force velocity. The influence of control force is the same with in the first and third resonance frequency but has opposite effect in the second one. The results obtained from this work are benefit to control vibration transmission of rotating machine.

A novel composite vibration control method using double-decked floating raft isolation system and particle damper

This paper presents a composite vibration control method that uses a double-decked floating raft isolation system and particle dampers to control the severe vibration of a heavy compressor set. In view of the structural characteristics of the compressor set, a mechanical impedance method is employed to investigate the acceleration transfer ratios of the double-decked floating raft isolation system, and to design three isolating schemes. Numerical results indicate that the particle damping technology does not disturb the isolating performance of the double-decked floating raft isolation system while reducing only its acceleration amplitude. To improve the damping performance of particle dampers, an anti-resonance method and a co-simulation technique are used to optimize the installation location of the particle dampers, as the damping effect is related to the vibrating velocity at the damper’s position. Furthermore, two types of particle damper—cylindrical and cuboid—are designed, based on conclusions drawn from experiments using the anti-resonance method. The damping effectiveness of the particle damper scheme is also examined using the co-simulation technique; results indicate that the proposed installation scheme can effectively suppress the vibration of the compressor rack. In addition, the presented schemes using the composite vibration control method are verified and compared in on-site experiments, and results demonstrate that the third isolating scheme presented, combined with particle damping technology, is best in controlling vibration of the compressor set.

H∞ active control of frequency-varying disturbances in a main engine on the floating raft vibration isolation system

Reducing the vibration of marine power machinery can improve warships' capabilities of concealment and reconnaissance. Being one of the most effective means to reduce mechanical vibrations, the active vibration control technology can overcome the poor effect in low frequency of traditional passive vibration isolation. As the vibrations arising from operation of marine power machinery are actually the frequency-varying disturbances, the H∞ control method is adopted to suppress frequency-varying disturbances. The H∞ control method can solve the stability problems caused by the uncertainty of the model and reshape the frequency response function of the closed loop system. Two-input two-output continuous transfer function models were identified by using the system identification method and are validated in frequency domain of which all values of best fit exceeds 89%. The method of selecting the weighting functions on the mixed sensitivity problem is studied. Besides, the H∞ controller is designed for a multiple input multiple output (MIMO) system to suppress the single-frequency-varying disturbance. The numerical simulation results show that the magnitudes of the error signals are reduced by more than 50%, and the amplitudes of the dominant frequencies are attenuated by more than 10 dB. Finally, the single excitation source dual-channel control experiments are conducted on the floating raft isolation system. The experiment results reveal that the root mean square values of the error signals under control have fallen by more 74% than that without control, and the amplitudes of the error signals in the dominant frequencies are attenuated above 13 dB. The experiment results and the numerical simulation results are basically in line, indicating a good vibration isolation effect.

Accurate method for harmonic responses of non-classically damped systems in the middle frequency range

This paper is aimed at eliminating the influence of the problem of the harmonic response analysis of non-classically damped systems with lower-higher-modal truncation. Based on the Neumann expansion theorem and the frequency shifting technique, the relationships satisfied by eigensolutions and system matrices are established and an explicit expression on the lower-higher-modal truncation error of harmonic responses can be expressed as a sum of available modes and system matrices. A correction method, which only involves the available modes and system matrices, is then presented to calculate the harmonic responses. The method maintains original-space without having to involve the state-space equation of motion such that it is efficient in computational effort and storage capacity. The method is convergent if and only if all the modes whose resonant frequencies lie within the range of excitation frequencies are available. Finally, a two-stage floating raft isolation system and a sandwich plate are used to to validate the effectiveness of the presented method.

Fuzzy Logic Controlled Semi-Active Floating Raft Vibration Isolation System

A warship may be detected in hostile waters because of its unique acoustic signature. A typical two-stage passive vibration isolation system used on ships and submarines to isolate onboard machinery is the floating raft isolation system. The passive isolation system, though robust, may result in substantially high transmission of forces to the foundation at certain excitation frequencies, adversely affecting the ship's stealth. This paper highlights the results of a simulation study aimed at the design of a semi-active floating raft vibration isolation system with the objective of mitigating the acoustic signature of a warship by minimising the transmission of forces, resulting from operation of onboard machinery, to the foundation. A semi-active control scheme with variable damping has been proposed for the floating raft, the variable damping being achieved by means of an electrorheological (ER) damper. A fuzzy logic controller has been designed to achieve the best isolation effect by analysing the characteristics of the frequencies in the excitation signal. The designed semi-active control system is subjected to a time-varying signal, each time-segment corresponding to a different optimal damping ratio. The MATLAB simulation results indicate that the proposed fuzzy logic control method is more effective in vibration isolation than the passive method thereby indicating the potential of the designed semi-active control system in reducing a ship's acoustic signature.

A hybrid expansion method for frequency response functions of non-proportionally damped systems

This study is aimed at eliminating the influence of the higher-order modes on the frequency response functions (FRFs) of non-proportionally viscously damped systems. Based on the Neumann expansion theorem, two power-series expansions in terms of eigenpairs and system matrices are derived to obtain the FRF matrix. The relationships satisfied by eigensolutions and system matrices are established by combining the two power-series expansions. By using the relationships, an explicit expression on the contribution of the higher-order modes to FRF matrix can be obtained by expressing it as a sum of the lower-order modes and system matrices. A hybrid expansion method (HEM) is then presented by expressing FRFs as the explicit expression of the contribution of the higher-order modes and the modal superposition of the lower-order modes. The HEM maintains original-space without having to use the state-space equation of motion such that it is efficient in computational effort and storage capacity. Finally, a two-stage floating raft isolation system is used to illustrate the effectiveness of the derived results.

The Vibration Isolation Effect Research of the Floating Raft Isolation System Based on the Adjustable Flexibility of Foundation

The floating raft isolation system is widely used in the field of marine engineering for its vibration isolation effect. Along with the application of light thinning structure of the ship, the flexibility of foundation of floating raft isolation system makes the vibration isolation effect vary widely between the practical floating raft isolation system and its theoretical results. In order to research the vibration isolation effect of the floating raft isolation system on different flexibility of foundation, the floating raft isolation system with flexible foundation is designed in this paper, and the adjustable flexibility of foundation is achieved by using elastic beams. With simulation and analysis of test system in ADAMS, the results of the relationship between flexibility and vibration isolation effect are obtained.

Suppression of vibration and noise radiation in a flexible floating raft system using periodic structures

This paper investigates the suppression of vibration and noise radiation in a flexible raft system through the use of periodic structure theory. A floating raft isolation system is constructed. The transfer matrix method, the finite element method and periodic structure theory are combined to calculate the dynamic response of the system and the dispersion relations of the periodic structure. The effects of substructure resonances on vibration and noise radiation are analyzed. Next, the periodic isolation structure is used to suppress the vibration and noise radiation in the floating raft system. The isolation performance of the combination of periodic structures and continuous isolators are investigated. Additionally, the influences of the parameters of the floating raft system on vibration and noise are discussed. The numerical results demonstrate that vibration and noise are significantly suppressed in stop bands and are not worsened in pass bands.

Eigensensitivity analysis of damped systems with distinct and repeated eigenvalues

This paper considers the computation of eigensolution sensitivity of viscously damped eigensystems with distinct and repeated eigenvalues. To simplify the computation, a combined normalization, which combines two traditional normalizations, is presented. Based on the combined normalization, a method for sensitivity analysis of eigenvalues and eigenvectors is studied. In the case of distinct eigenvalues, the proposed method can determine the eigenvector derivatives directly and is robust since the components of coefficient matrices are all of the same order of magnitude. The computational cost of the second-order sensitivities of eigenvectors can be reduced remarkably since the matrix decomposition of the coefficient matrix is available from the computation process of the first-order eigensensitivities. In the case of repeated eigenvalues, an algorithm is presented for computing the eigensolution sensitivities. The algorithm maintains N-space without using state-space equations such that the computational cost is reduced. The method is accurate, compact, numerically stable and easy to be implemented. Finally, three numerical examples have demonstrated the validity of the proposed method. The capacity of predicting the changes of eigensolutions with respect to the changes of design parameters in terms of the first- and second-order eigensensitivities is studied with application to the analysis of a two-stage floating raft isolation system.

Design and experiment of a cradle truss type floating raft system

In this paper, a new design concept of an isolated cradle trusslike structure to support vibrating machinery is proposed. The acoustic and vibratory energy transmission in this isolation system is investigated to improve the vibration isolation performance of conventional floating raft system. The finite element method and experimental measurements are used to understand the dynamic behavior of this cradle truss. In conjunction with experiments, a vectorial four pole parameter numerical model is used to identify power flow of the floating raft isolation system. The proposed floating raft design achieved a vibration reduction of 30–40dB in the frequency range of 20–600Hz. It is also shown that the loss factors of the cradle truss configured floating raft are up to 4dB than conventional floating flat raft.

Parameters Performance to the Vibration Isolation in Three-Dimensional Elastic Floating Raft Isolation System

Based on the three-dimensional elastic floating raft isolation system model, this paper using the finite element method to calculate vibration response of the system, and then analyze the performance of floating raft under different mass and stiffness, providing useful conclusions for vibration isolation designing.

Study on Floating Raft Vibration Isolation System for Pumping Unit

In this paper, based on the theory of double layered vibration isolation, the finite element dynamic model of floating raft vibration isolation system has been established for the project of vibration and noise control in a heat exchange station. The dynamic model of single pump is simplified an elastic cylinder based on the principle of equivalent parameters, and the elastic raft frame is used of steel structure. The dynamic characteristics of the system is analyzed by used of ANSYS with SOLID45 unit and COMBIN14 spring-damper unit, which provide an important basis for the engineering design of floating raft isolation system with pumping units.

Dynamic investigation on floating raft with elastic limiters

In this paper, we consider a floating raft isolation system with elastic limiters. The limiters might be “contact” or “no contact”, thus forming a unilateral system generating possible contacts. In order to avoid the large displacement of the floating raft under shock, limiters might be adopted but good limiters design requires the values of the gaps. Based on the contact dynamics, the multi-degree-freedom dynamic model of floating raft isolation system with elastic limiters is established. The artificial neural network has been developed to dingtinguish the contact state of elastic limiters at each step. The example analysis shows that the algorithm of neural network for contact can shorten the time of caclaution. From the example analysis, we get some interesting results that may be useful to the ship engineering.

A Two-stage Floating Raft Isolation System Featuring Electrorheological Damper with Semi-active Static Output Feedback Variable Structure Control

In this study, a semi-active static output feedback variable structure control (VSC) strategy is presented to control a two-stage electrorheological (ER) floating raft isolation system. A continuous semi-active static output feedback VSC controller is designed and a bypass ER damper is applied to achieve the best control effect more rapidly and accurately. The sliding surface parameters are determined in terms of the Routh—Hurwitz stability criterion. The optimal vibration attenuation of the intermediate mass is guaranteed due to the control rule that damping force only dissipates the vibration energy of the intermediate mass. The robustness of the control method with respect to parameter variations and the effectiveness of vibration isolation are demonstrated by numerical simulation results. It shows that the designed semi-active static output feedback VSC strategy realized by the ER damper can achieve better performance than that of optimally passive damping even if system parameter uncertainties exist. In addition, the experiment was carried out to demonstrate the practical effectiveness of the presented control scheme in this study. The experimental results are satisfied.

A Two-stage Floating Raft Isolation System Featuring Electrorheological Damper with Semi-Active Fuzzy Sliding Mode Control

In this article, a semi-active fuzzy sliding mode control (FSMC) strategy for the vibration attenuation is presented based on the fact that for two-stage electrorheological (ER) damper floating raft isolation system, the upper bounds for uncertainty external disturbance and the parameters perturbation are hard to estimate in advance, and the damping force of ER damper is controlled continuously. The parameters of sliding surface are selected based on Hurwitz stable judgement of sliding mode motion equation. Fuzzy controller is designed in terms of the sliding mode reaching condition and the maximal damping force of ER damper. The optimal vibration attenuation of the intermediate mass is guaranteed due to the control rule that damping force only dissipates the vibration energy of the main object. The robustness of the proposed semi-active FSMC method with respect to parameter variations and the effectiveness of the controller designed in this study are demonstrated by numerical simulation. It showed that the proposed semi-active FSMC strategy realized by the ER damper can achieve better performance than those of optimally passive damping and maximum damping variety even if system parameter variations exist. In addition, the experiment was carried out to demonstrate the practical effectiveness of the presented control scheme in this study. The experimental results are satisfied.

Semi-active fuzzy sliding mode control for floating raft isolation system

A semi-active static output feedback fuzzy sliding mode controller is designed for floating raft isolation system with electro-rheological (ER) damper. Sliding surface matrix is selected in accordance with Hurwitz stable judgement of sliding mode motion equation. Force transmissibility, input force and output force response of floating raft isolation system, respectively, under chirp exciting signal and dual-frequency exciting signal are simulated. The simulation results indicate that the performance of floating raft isolation system designed with semi-active static output feedback fuzzy sliding mode control method is remarkably better than those of optimally passive damping.

Model Order Reduction of Viscously Damped Vibration Systems Using Accelerated Iterative Dynamic Condensation

An accelerated iterative dynamic condensation method for the model order reduction of vibration systems with viscous damping is proposed. A group of governing equations for dynamic condensation matrix are derived from the eigenvalue equations defined in the state space. Two iterative schemes for solving these governing equations are provided. Based on different state space formulations, two more groups of governing equations are developed. A comparison of the present method with three iterative approaches proposed recently is provided. The present approach is implemented into two practical vibration systems, a tall building with one tuned mass damper and a floating raft isolation system. The results show that the proposed method has much higher accuracy than the other three approaches while the computational effort is almost the same.