Torsional Natural Frequencies Research Articles

An inspection of the metal-foam beam considering torsional dynamic responses

Metal foam is a multifunctional material with a lower specific weight, high stiffness and compressive strength, and high energy absorption. These remarkable properties make metal foams a promising candidate for conventional materials in different industrial fields. Despite numerous researches on mechanical behavior either static or dynamic of structures made of metal foams, torsional vibration analysis of metal foam structures is still uninvestigated. In this investigation, the influence of various imperfection distribution patterns on the torsional dynamic response of metal foam beams is examined within the framework of Timoshenko-Gere's theory. Two common materials i.e. SUS304 and Aluminum foams are considered the constructive materials of structure. Moreover, three imperfection distribution patterns are taken into account. The virtual work's principle has been employed to derive the torsional governing equation of metal foam beams. Then, the derived governing equation has been solved via an analytical method. The accuracy of the employed methodology has been compared with the findings of former research in the literature. Finally, the influences of different notable parameters on the variation of natural torsional frequency have been examined and demonstrated in a group of tables and diagrams.

Static response of wind turbine blades: Comparison of low- and high-fidelity numerical models

As wind turbine blades become longer and more flexible, the structural models employed in current aeroelastic simulation tools, usually based on beam formulations, are challenged. Effects previously considered negligible in the response of these beam-like structures might now become significant to obtain accurate predictions of their behaviour. To assess this, a test matrix covering key geometric and material characteristics of wind turbine blades is defined and three test cases are analysed as an initial stage of this study. For each case, the static deflection of the beam model from the aeroelastic tool HAWC2 is compared against higher-fidelity shell/solid finite element models. Three structures are studied: an isotropic box beam, a composite box beam and a 12.6 m wind turbine blade from DTU. A good match is observed for the box beam test cases, which study the effects of out-of-plane and distortion warping and bend-twist coupling. Important aspects of high-fidelity models (such as end effects) are highlighted. The study of the DTU 12.6 m blade shows a significant difference (15%) in the torsion natural frequencies of the beam model, though a good agreement in twist angle under torsional loading. More pronounced differences in twist angle are observed when a load distribution based on the steady state response is applied, likely resulting from challenges in modelling complex structural features and three-dimensional effects.

Research on modified lumped parameter method in torsional vibration analysis of reciprocating compressor shaft

Abnormal vibrations often occur during the operation of reciprocating compressors under different load conditions. To efficiently and accurately calculate the torsional vibration response of the shafting under various working conditions, a modified lumped parameter method (MLPM) based on finite element mode modification is proposed. MLPM is derived from the lumped parameter method (LPM) and incorporates corrections to the stiffness matrix based on the multi-degree-of-freedom modal calculation using a finite element model. This allows MLPM to combine the high accuracy of finite element method (FEM) with the fast computing speed of LPM. To demonstrate the effectiveness of MLPM, an abnormal vibration compressor equipped with a stepless capacity control system is considered. MLPM is utilized to calculate the torsional natural frequency (TNF) and torsional torque response of the compressor’s shafting. The computed 1st-order TNF error between MLPM and FEM is only 0.20%. In the time domain, the torque response error of MLPM is less than 3.07%, while in the frequency domain, it is less than 0.57%. Moreover, MLPM exhibits a significantly increased calculation speed of more than 95% compared to FEM. By comparing MLPM results with torsional vibration test data, the 1st-order TNF error is found to be less than 0.50%, and the frequency-domain torque response error is no more than 8.91%. Furthermore, MLPM is effectively applied to solve the abnormal vibration problem of the compressor. It proposes a modification plan for the shafting, which successfully avoids torsional resonance and reduces the peak value of the torque response by 54.77%. These results demonstrate that MLPM is highly suitable for practical engineering applications due to its combination of high accuracy and fast computing speed.

Torsional Vibration Analysis Using Rotational Laser Vibrometers.

Torsional vibration is a critical phenomenon in rotor dynamics. It consists of an oscillating movement of the shaft and causes failures in multiple oscillating fields of application. This type of vibration is more difficult to measure than lateral vibration. Torsional vibrometers are generally invasive and require a complicated setup, as well as being inconvenient for field measurements. One of the most reliable, non-invasive, and transportable measuring techniques involves the laser torsional vibrometer. For this research, two laser heads with different measurement capabilities were utilized. An experimental test rig was used to perform a relative calibration of the two laser vibrometers. The frequency of the acting force and the rotation speed of the shaft vary in the same range, which is commonly found in rotating machines. Finally, experimental measurements of torsional vibrations using laser vibrometers were compared with numerical results from a 1D finite element model of the same test rig. The main outcome of this paper is the definition of a reliable measuring procedure to exploit two laser vibrometers for detecting torsional mode-shapes and natural frequencies on real machines. The relative calibration of two different measuring heads is described in detail, and the procedure was fundamental to properly correlate measuring signals in two machine sections. A good correspondence between the numerical and experimental results was found.

Chaotic vortex-induced rotation of an elliptical cylinder.

Non-linear oscillations of an elliptical cylinder, which can rotate about an axis that passes through its symmetry axle due to a torsional spring and hydrodynamic torque produced by the flow of a Newtonian fluid, were analyzed in terms of a single parameter that compares vortex shedding frequency with the torsional spring's natural frequency. The governing equations for the flow coupled with a rigid body with one degree of freedom were solved numerically using the lattice-Boltzmann method. The Reynolds number used was Re=200, which, in the absence of torsional spring, produces chaotic oscillations of the elliptical cylinder. When the torsional spring is included, we identified three branches separated by transition regions when stiffness of the restorative torque changes, as in the case of vortex-induced vibrations. However, in this case, several regions presenting chaotic dynamics were identified. Two regions with stable limit cycles were found when both torques synchronized and when stiffness of the torsional spring is big enough so that the ellipse's oscillation is small.

Autodrillers, Rig-Control Systems, Driller Procedures Reduce BHA Failures

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 214997, “The Role of Autodrillers, Rig-Control Systems, and Driller Procedures in Reduction of Bottomhole Assembly Failures,” by Pablo E. Barajas, SPE, Paul Pastusek, SPE, and Aaron Lacey, ExxonMobil, et al. The paper has not been peer reviewed. _ Reducing bottomhole-assembly (BHA) failures has been this operator’s focus in US land intermediate and lateral sections to reduce cost per foot. BHA failures can be mitigated with better autodriller processes, improved rig-control-system technology, and drilling-mechanics-based procedures. The operator, rig contractor, and BHA service providers engaged in an intensive continuous improvement process for 18 months to help two rigs in Oklahoma reduce the number of BHAs used per well. The goal was to determine how to best tune the autodriller and standardize set-point practices. Introduction The operator has found that rig-control systems, particularly the autodriller, can be unstable in many drilling situations. The operator and contractor laid out the framework to measure autodriller dysfunction suspected to affect rate-of-penetration (ROP) and BHA integrity. The team engaged in a structured and intensive continuous improvement process with the following objectives: - Understand if end-user tuning and set-point practices from the contractor were being applied consistently at the rig floor level - Evaluate if the tuning practices were appropriate or effective in mitigating dysfunction in different formations - Increase subject-matter experts’ support and involvement in proactively identifying when rig-control systems were not behaving as designed to reduce impact on ROP and the BHA - Evaluate whether the operator’s drilling roadmaps and BHA safety-limit protections were being properly integrated into autodriller control loops - Use downhole sensors to understand how surface controls induced dysfunctions and confirm when they were mitigated - Propagate learnings across all rigs and crews in the basin to reduce the number of BHAs required to drill each well Observations Autodriller Dysfunction Identification. Standardizing the identification of dysfunction patterns to be avoided was a step based on physics of the system, bit-run performance and dulls (Fig. 1), directional tool damage, high-frequency (1,024 samples per second) downhole data, and high-frequency (six samples per second) surface data. Currently, the focus is to quickly identify and mitigate autodriller dysfunction by the rig teams, including the types of dysfunction described in this section. Stick/Slip. The operator developed a test to run the autodriller in different control loops to determine when stick/slip was initiated or intensified by the autodriller. Restarting drilling in ROP mode with the rig’s torsional dampening system active eliminated the autodriller as the source of stick/slip. It was determined that excessive weight on bit (WOB) used to pass the tool joint through the rotating head in the managed-pressure-drilling’s rotating control device (RCD), combined with low rotational speed, were key factors in initiating stick/slip. WOB Dysfunction. Any significant WOB variation can drive enough torque variation to drive stick/slip. This is particularly true if the WOB variation has a frequency close to the natural torsional frequency of the system.

Dynamic modeling and nonlinear analysis for lateral–torsional coupling vibration in an unbalanced rotor system

Imbalance is a common problem in rotating machinery. In addition to the unbalanced force, lateral–torsional coupling vibration can also be induced by the mass imbalance. However, the related nonlinear behaviors and coupling mechanism are still not well understood, especially when lateral-angular motion is incorporated in a model. In this paper, a model for coupling lateral and torsional vibrations of an unbalanced rotor is developed by Lagrangian dynamics, in which the coupling of lateral-angular and torsional motions is first considered. Based on the model, the lateral responses, torsional responses, coupling excitation characteristics and coupling mechanisms are investigated in detail. The results show that mass imbalance can lead to nonlinear time-varying characteristics in the dynamic equations. When the imbalance is small, the lateral vibration can be degraded to a traditional imbalance problem. Meantime, very small transient torsional vibration with torsional natural frequency ft in frequency domain can be observed at the beginning. The coupling excitation applying on the torsional DOF caused by the lateral synchronous whirling is demonstrated to behave the feature of static torque, consequently, there actually exists no steady-state torsional vibration in small unbalanced rotor. Under largely unbalanced conditions, both resonant and unstable behavior can be observed in the lateral and torsional responses. The combined resonance is induced by the lateral translational–torsional coupling, while the instability is caused by lateral angular–torsional coupling. By increasing the lateral damping, the instability phenomenon can be suppressed, and the lateral amplitude in the resonance region can be effectively reduced.

Participation factors of wind turbine structures under rotor blade wind loads

A participation factor formulation is developed to determine the importance of each natural frequency due to rotor blades induced forces and moments. This factor can be used to realize the quantitative influence of a mode due to rotor-induced responses and know which active degree of freedom of that mode at the tower top. For jacket support structures, the participation factor of the first torsional mode is often large, so the multiple of the 3P frequency (nF3p) approaching the first torsional mode will cause serious resonance conditions. Thus, appropriate small yaw stiffness and large yaw damping are suggested to avoid resonance and reduce high-frequency fatigue damage. The participation factors of the second and third bending rotational natural frequencies often between 10% and 30% are not concentrated compared to the first torsional natural frequency. The resonance of this mode with nF3p may not be severe for fatigue issues, but it is still necessary to avoid it. The tuned mass damping can be used to reduce the rotor-induced forces and moments, while the proposed participation factor is useful to know which mode and location should be first reduced.

Analysis of Torsional Vibrations of Rotary Winding Machines

This work is chosen to analyze the rotary winding machines because these machines are existed in our country and this analysis is practical from the side of input values and getting the results. Good rotary winding machine design practice demands the analysis of the system to insure that the reaction due to operation of the machine will not cause damaging vibrations. The widest phenomenon in vibration forms in mechanical transmission is the torsional vibration. The aim of this work is the analysis of the torsional vibrations of these rotary winding machines and to minimize that vibrations and to alleviate recurring costly maintenance problems. 
 To minimize system dynamic torques it is necessary to spread the torsional natural frequencies. This is best achieved by lowering the fundamental torsional natural frequency. In main rotary winding machine drives this is most readily accomplished by lowering the torsional stiffness at the lead spindle location or, by making the lead spindle torsional flexibility greater by increasing the shaft separation or, if necessary, by using a torsionally flexible spacer. Torsional stiffness is inversely proportional to shaft length. For the solution of the problem one must first of all estimate the physical system parameters taking into consideration the real set of components of a rotary winding machine and then to transform them into a mathematical model. In this work there was also the method of calculation model presented. 
 The equations of motion of the whole vibrating system are defined and the study include solution of torsional vibration of this machine by using Jacobi method as method of solution because it is easy to program and accurate. A computer program (Math Lab) has been used in order to Facilitate the solution because it is contain already comments specialized to solve the vibration problems. Finally, finding the final results gave a good vision to forecast the failure of the machine that could caused either by errors in design or operating conditions. 

Auxetic meta-disk for independent control of flexural and torsional waves

Locally resonant elastic metamaterials have a unique characteristic of forming a low-frequency bandgap where wave propagation is inhibited. In this study, we present an auxetic meta-disk, a novel design of a local resonator capable of independent control of the flexural and torsional wave propagation in a pipe. The auxetic meta-disks are perforated with rationally designed auxetic patterns, whose mode-dependent deformation is the key mechanism enabling to manipulate the flexural and torsional natural frequencies of the meta-disks simultaneously. The capabilities of auxetic meta-disks in controlling wave propagation are thoroughly investigated using finite element analysis, and its applicability to elastic wave mode filtering is presented. Because of the simplicity in design and installation, the proposed concept is expected to be practical and applicable to various fields of vibration isolation or non-destructive inspection that require considering more than one vibration mode.

A three-axis modular horizontal vibration isolation system with adjustable stiffness: Design, analysis and experimental validation

In this study, a modular vibration isolator design is introduced in which the horizontal stiffness of the system can be adjusted in three axes (translational stiffness in the horizontal x and y axes and torsional stiffness about the vertical z-axis) by changing the compressive forces on the leg modules, which are composed of elastic stepped columns and a string. A novel multi-string tensioning mechanism is developed to change the axial compressive forces on all the elastic stepped columns simultaneously, which in turn vary the translational and torsional stiffness of the system. Consequently, the translational and torsional natural frequencies of the system can be tuned to a targeted value by increasing/decreasing the tension forces in the strings for light/heavy payloads. With the use of multiple leg modules in the isolator, the torsional natural frequency can be kept close to the translational natural frequencies at any value of the tension forces in the strings even if the payload masses vary over a wide range. To investigate the relationship between the tension forces and natural frequencies, a leg module is produced. Analytical and finite element models of the leg module are formed, and the results of these models are found to be in good agreement with the experimental results. It is shown that the translational and torsional natural frequencies of the isolator with multiple leg modules can be adjusted to 0.5 Hz and 0.6 Hz, respectively, keeping the lower limits of the isolation bandwidth in the translational and torsional axes less than 1 Hz. Moreover, the upper limit of the isolation bandwidths can be kept above 135 Hz. Therefore, the proposed isolation system has a very wide isolation bandwidth at low frequencies.

ОЦЕНКА РЕЗОНАНСНЫХ РЕЖИМОВ ПРИВОДА ГЛАВНОГО ДВИЖЕНИЯ ТОКАРНОГО СТАНКА С БЕССТУПЕНЧАТЫМ РЕГУЛИРОВАНИЕМ

The study objective is to define and evaluate the resonant drive modes of the lathe primary motion continuously rated. The problem to which the paper is devoted is to draw up a design scheme of a dynamic torsional drive system for the lathe primary motion with the spindle speed continuously rated and to make a calculation that allows finding out the lowest natural torsional vibration frequencies of the drive. Research methods: analysis of a multi-mass analytical model of the lathe drive primary motion, followed by its reduction to models with a smaller number of masses (inertial elements). The novelty of the work is in the development of software that allows simplifying linear dynamic systems and finding out natural frequencies. Study results: the dynamic quality of the drive is analyzed, which gives the opportunity to find non-resonant zones of the drive by the rotational and toothed frequencies of forced vibrations with the help of the frequency ranges of shafts. Conclusions: the developed software makes it possible at the design stage to simplify the dynamic system, find the lowest natural frequencies of torsional vibrations and take measures to exclude resonant phenomena.

Experimental Determination of Torsional Coefficients of Torsion Shafts Used in Heavy Commercial Vehicle Hydraulic Steering

Bu çalışmada ağır ticari araç hidrolik direksiyonlarında geri toplamayı sağlayan burulma millerinin burulma katılıkları teorik, numerik ve deneysel olarak hesaplanmıştır. Numerik çalışmada ANSYS programı kullanılarak burulma milinin maksimum burulma miktarı olan 7° burulma halinde oluşan tork değeri elde edilmiştir. Tork-açı sensörü kullanılarak oluşturulan test düzeneğinde numunelerin tork-açı grafikleri elde edilmiş ve ekstrem burulma olan +/-7° aralığında burulma için burulma katsayıları deneysel olarak hesaplanmıştır. Elde edilen deneysel burulma katsayısı değerleri teorik ve numerik değerler ile karşılaştırıldığında deneysel ölçüm teorik değerlere göre yüksek sonuç vermiştir. Efektif burulma katsayısının teorik değere göre yaklaşık %5 daha yüksek olduğu görülmüştür. Çalışmamızda ayrıca burulma katılığına bağlı olarak burulma doğal titreşim frekansı 5 farklı numune için teorik ve numerik olarak elde edilmiş, burulma mili rezonansının direksiyon düzeneğine etkileri tartışılmıştır.

Experimental evidence of coupled-mode flutter in a two-meter-long non-rotating wind turbine blade

We have conducted a series of experiments on a 30:1 scale wind turbine blade and observed coupled-mode flutter. This observation validates the theoretical studies that predict larger wind turbine blades are susceptible to coupled-mode flutter. To conduct these experiments, we built a scaled-down model of the 61-meter NREL 5 MW blade. The blade was approximately 2 meters long and was built such that the ratios between its first torsional natural frequency and the flapwise natural frequencies were similar to those of the full-scale blade. This was important, because the theoretical predictions suggest that coupled-mode flutter occurs when one of the flapwise modes and the first torsional mode of the blade coalesce. In our experiments, as the wind speed was increased, turbulence induced vibrations were observed initially in the form of oscillations of the blade’s first flapwise mode, and then its second flapwise mode, with a region of multi-modal oscillations in between. It was observed that the first torsional natural frequency of the blade decreased with increasing wind speed and the second flapwise natural frequency increased slightly. Then at a critical wind speed, the second flapwise mode and the first torsional mode merged into a flutter mode, indicating coupled-mode flutter has occurred at this wind speed.

A Parametric Study of the Free Undamped Torsional Vibration of One-Dimensional Structural Elements using the Differential Quadrature Method (DQM)

Recently, structures prone to torsional vibration have grabbed the interest of the structural engineering field whose aim has become to design structures with increased torsional stiffness. To the author’s limited knowledge, studies researching this topic couldn’t provide a simplified method to obtain the natural torsional frequencies and the corresponding mode shapes of structures providing ease of use by structural engineers having limited mathematical backgrounds. The purpose of this study is to establish a simplified numerical model of the torsional vibration of rods with non-uniform geometry and material with classical boundary conditions using the differential quadrature method (DQM). To account for geometric and material non- uniformity, any space varying functions in the longitudinal direction of a one- dimensional structural element can be used in the model. The numerical results obtained are compared with previously obtained analytical results in cases of rods with uniform cross sections and linearly non-uniform ones. The comparison proved significant agreement with the analytical results. The illustrated use of the DQM showed efficiency and acceptable accuracy that made it legible to create an alternative to the time-consuming analytical solutions that require a unique solution technique for every type of structural variation where a strong mathematical background of the user is needed.

Method for Adjusting Torsional Natural Frequencies of Powertrains with Novel Coupling Design

Torsional vibrations are inherently present in every rotating powertrain. In resonant conditions, torsional vibrations can be significantly amplified. A typical method to reduce the torsional vibration particularly at resonance is to modify the torsional natural frequencies with the component design. Commonly, a straightforward method for the modification is the adjustment of the torsional stiffness of a coupling. This study presents a method to modify the torsional natural frequencies using a coupling design with continuously adjustable torsional stiffness. The presented coupling design is investigated with torsional analysis and experimental measurements. Torsional analysis was utilized to predict the effects of varying the coupling stiffness to the torsional natural frequencies of a powertrain. The experimental measurements were conducted by attaching the adjustable stiffness coupling to the powertrain and measuring the change in the torsional natural frequencies while the torsional stiffness of the coupling was adjusted. The torsional natural frequencies were determined from the measurements by identifying the resonance induced torsional vibrations from the vibration response of the powertrain. The torsional vibrations were excited to the system by a load motor. The measurements showed that the first torsional natural frequency of the powertrain changed from 15.6 Hz to 43.0 Hz as the torsional stiffness of the coupling was adjusted. The results of the torsional analysis and the experimental measurements were compared to determine the performance of the realized coupling. The results indicated that the torsional natural frequencies determined by torsional analysis agree well with the experimentally measured results. The prediction errors were generally below ±5%, which is typically considered as a margin for accurate torsional analysis.

Coupled Flexural–Torsional Forced Vibration Analysis of a Piezoelectrically Actuated Double-Cantilever Structure

Abstract In this paper, the forced coupled flexural–torsional vibration of a piezoelectrically actuated double-cantilever structure is investigated. The double-cantilever structure is composed of two uniform and identical Euler–Bernoulli cantilever beams connected by a rigid tip connection at their free ends. There is also a piezoelectric layer attached on the top surface of each cantilever beam. The characteristic equation for the coupled flexural–torsional vibrations of the structure is derived and solved to determine the natural frequencies. The time response to the forced vibrations of the structure is studied using the Galerkin approximation method. The effects of dimensional parameters, including the length of the cantilever beams and the length of the tip connection, and the piezoelectric input voltage on the coupled flexural–torsional natural frequencies and amplitude of vibrations of the structure are investigated analytically and experimentally. The results show that the coupled flexural–torsional fundamental frequency of the piezoelectrically actuated double-cantilever structure decreases as either the length of the cantilever beams or the tip connection is increased. Moreover, the amplitude of the coupled flexural–torsional vibrations of the structure is proportional to the piezoelectric input voltage; however, the slope of the curves depends on dimensional parameters. For a given voltage, the effect of either of the aforementioned dimensional parameters on the amplitude of vibrations depends on the other dimensional parameter such that there is a turning point in all the curves, whose location depends on the configuration of the structure.

Process Monitoring of a Vibration Dampening CFRP Drill Tube in BTA deep hole drilling using Fibre-Bragg-Grating Sensors

The large tool length in BTA deep hole drilling often leads to strong torsional vibrations of the tool system, leading to a reduced bore hole quality failures. When substituting steel drill tubes with tubes from composite material, the laminate structure dampens these vibrations. Secondly, the integration of sensors allow to monitor process vibrations. This contribution introduces a new sensor platform to measure process vibrations, feed force and drilling torque using Fibre-Bragg Grating Sensors. The presented experimental results focus on characteristic frequency spectra with natural torsional and compression frequencies of the CFRP drill tube, which show variations due to changed feed.

Study on the flow-induced vibration of a two-tandem cylinder system in rigid body motion

The flow-induced vibration (FIV) of a cylinder cluster is often observed in subsea pipelines and marine risers. The motion of the cylinder clusters was often modeled as the equation of motion of a particle, which has ignored the torsion freedom. Hence, the answers to the following questions are still unavailable—what are the impacts of torsion on the FIV of a cylinder cluster? Does torsional freedom facilitate the development of new features in FIV? In the present work, the FIV of a two-tandem cylinder system was numerically studied under the consideration of torsional freedom. It was found that six well-defined regimes were formed in the FIV of the cylinder system with the increase in the reduced velocity. The formation of different regimes mainly occurred by the accouplement of two frequencies—the vortex shedding frequency and the natural frequency of the cylinder system. A quirky low frequency dominated the cross-flow vibration at some reduced velocities, significantly magnifying the cross-flow vibration and the torsional vibration. The two cylinders acted as two feet treading water alternatively, enabling the cylinder system to move further on one side at such low frequencies. The characteristics of the amplitudes and frequency responses vs Ur* were qualitatively similar when the stiffness ratio k* was in the range of 10 ≤ k* ≤ 50, where Ur* was the torsional reduced velocity which was defined by the uniform velocity U divided torsional natural frequency frn and diameter of the cylinder D.

Analysis and design of an adjustable stiffness three-axis horizontal vibration isolator using elastic columns and a string in tension

The aim of this study is to design a horizontal vibration isolation system with adjustable quasi-zero-stiffness along three axes (translational stiffness in the horizontal x and y axes and torsional stiffness about the vertical z-axis). For this purpose, a string is placed in the central axis of the system, and a string tensioning mechanism is developed to tune the horizontal (lateral) stiffness of the elastic columns that support the top platform on which a payload is placed. By increasing/decreasing the tension force in the string for smaller/larger payloads, axial compressive forces on all the elastic columns can be varied simultaneously, which in turn enables to adjust translational and torsional natural frequencies of the system. Various parametric studies are conducted by using normalized length and force quantities such as the ratio of string length to column length, and the ratio of critical buckling force due to a tension force directed towards a fixed point to critical buckling force due to an external vertical load. Robustness of the system against eccentric payload placement is quantified. Moreover, transmissibility of the system is calculated for translational and torsional excitations. Implicit and explicit analytical, and finite element models demonstrate that by selecting the parameters of the system appropriately, the lower limit of the isolation bandwidth for both translational and torsional excitations can be kept below 1 Hz, and the upper limit can be kept above 250 Hz even if the payload mass and its mass moment of inertia change in a wide range. Thus, the system is capable of achieving a very large isolation bandwidth at low frequencies.