scholarly journals Design and Characteristics Analysis of a Nonlinear Isolator Using a Curved-Mount-Spring-Roller Mechanism as Negative Stiffness Element

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Han Junshu ◽  
Meng Lingshuai ◽  
Sun Jinggong
Keyword(s):  
Damping Ratio ◽  
Harmonic Balance Method ◽  
Excitation Amplitude ◽  
Negative Stiffness ◽  
Response Curves ◽  
Restoring Force ◽  
Characteristics Analysis ◽  
Stiffness Softening ◽  
Isolation Performance ◽  
Cubic Stiffness

The characteristics of a passive nonlinear isolator are developed by combining a curved-mount-spring-roller mechanism as a negative stiffness corrector in parallel with a vertical linear spring. The static characteristics of the isolator are presented, and the configurative parameters are optimized to achieve a wider displacement range at the equilibrium position where the isolator has a low stiffness and the stiffness changes slightly. The restoring force of the isolator is approximated using a Taylor expansion to a cubic stiffness. Considering the overload and underload conditions, a dynamic equation is established as a Helmholtz-Duffing equation, and the resonance response of the nonlinear system is determined by employing the harmonic balance method (HBM). The frequency response curves (FRCs) are obtained for displacement excitations. The absolute displacement and acceleration transmissibility are defined and investigated to evaluate the performance of the nonlinear isolator, and they are compared with an equivalent linear isolator that can support the same mass with the same static deflection as the proposed isolator. The effects of the amplitude of the excitation, the offset displacement, and the damping ratio on the dynamic characteristics and the transmissibility performance are considered, and experiments are carried out to verify the above analysis. The results show that the overload and underload system can outperform the counterparts with the linear stiffness, softening stiffness, softening-hardening stiffness, and hardening stiffness with the magnitude of the excitation amplitude, and that its isolation performance is generally better than that of a linear system. The transmissibility, response, and resonance frequency of the system are affected by the excitation amplitude, offset displacement, cubic stiffness, and damping ratio. To obtain a better isolation performance, an appropriate mass, not-too-large amplitude, and larger damper are necessary for the proposed isolator.

scholarly journals Theoretical Design and Characteristics Analysis of a Quasi-Zero Stiffness Isolator Using a Disk Spring as Negative Stiffness Element

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
Lingshuai Meng ◽  
Jinggong Sun ◽  
Wenjuan Wu
Keyword(s):  
Damping Ratio ◽  
Low Frequency ◽  
Harmonic Balance Method ◽  
Steady State Solution ◽  
Excitation Amplitude ◽  
Response Curves ◽  
Disk Spring ◽  
Performance Effects ◽  
Characteristics Analysis ◽  
Isolation Performance

This paper presents a novel quasi-zero stiffness (QZS) isolator designed by combining a disk spring with a vertical linear spring. The static characteristics of the disk spring and the QZS isolator are investigated. The optimal combination of the configurative parameters is derived to achieve a wide displacement range around the equilibrium position in which the stiffness has a low value and changes slightly. By considering the overloaded or underloaded conditions, the dynamic equations are established for both force and displacement excitations. The frequency response curves (FRCs) are obtained by using the harmonic balance method (HBM) and confirmed by the numerical simulation. The stability of the steady-state solution is analyzed by applying Floquet theory. The force, absolute displacement, and acceleration transmissibility are defined to evaluate the isolation performance. Effects of the offset displacement, excitation amplitude, and damping ratio on the QZS isolator and the equivalent system (ELS) are studied. The results demonstrate that the QZS isolator for overloaded or underloaded can exhibit different stiffness characteristics with changing excitation amplitude. If loaded with an appropriate mass, excited by not too large amplitude, and owned a larger damper, the QZS isolator can possess better isolation performance than its ELS in low frequency range.

Nonlinear Dynamic Response of an Isolation System With Negative Stiffness and Shape Memory-Based Damping

2020 ◽  
Author(s):  
Andrea Salvatore ◽  
Biagio Carboni ◽  
Walter Lacarbonara
Keyword(s):  
Shape Memory ◽  
Damping Ratio ◽  
Dynamic Performance ◽  
Excitation Amplitude ◽  
Negative Stiffness ◽  
Response Curves ◽  
Nonlinear Dynamic Response ◽  
Isolation System ◽  
Hysteretic Damping ◽  
Different Levels

Abstract The negative stiffness offered by bi-stable mechanisms can improve the dynamic performance of a structure. In this work the effects of adding negative stiffness and shape memory alloy (SMA) damping in base-isolated structures are explored through the study of the stationary response for different values of negative stiffness and SMA hysteretic damping ratio. The frequency response curves of the isolated structure, with and without the negative stiffness contribution, are numerically obtained for different levels of excitation amplitude in order to evaluate the acceleration and displacement transmissibility curves. The benefits of negative stiffness, damping amplification and reduced transmissibility of accelerations and displacements, as well as the existence of dynamic instabilities, are illustrated.

Shock isolation characteristics of a bistable vibration isolator with tunable magnetic controlled stiffness

2021 ◽  
pp. 1-28
Author(s):  
Bo Yan ◽  
Peng Ling ◽  
Yanlin Zhou ◽  
Chuan-yu Wu ◽  
Wen-Ming Zhang
Keyword(s):  
Damping Ratio ◽  
Excitation Amplitude ◽  
Relative Displacement ◽  
Vibration Isolator ◽  
Maximum Acceleration ◽  
Vibration Isolators ◽  
Displacement Ratio ◽  
Shock Isolation ◽  
Maximum Relative Displacement ◽  
Isolation Performance

Abstract This paper investigates the shock isolation characteristics of an electromagnetic bistable vibration isolator (BVI) with tunable magnetic controlled stiffness. The theoretical model of the BVI is established. The maximum acceleration ratio (MAR), maximum absolute displacement ratio (MADR) and maximum relative displacement ratio (MRDR) are introduced to evaluate the shock isolation performance of the BVI. The kinetic and potential energy are observed to further explore the performance of the BVI. The effects of the potential barrier, shape of potential well, damping ratio on the BVI are discussed compared to the linear vibration isolators (LVI). The results demonstrate that the intrawell oscillations and snap-through oscillations are determined by the excitation amplitude and duration time of main pulse. MADR and MRDR of the BVI are smaller than those of the LVI. The maximum acceleration peak amplitude of the BVI is far below that of the LVI, especially when the snap-through oscillation occurs. In brief, the proposed BVI has a better shock isolation performance than the LVI and has the potential to suppress the shock of space structures during the launch and on-orbit deploying process.

Non-resonant response of the novel airborne photoelectric quasi-zero stiffness platform with friction damping

2020 ◽  
Vol 64 (1-4) ◽  
pp. 315-324
Author(s):  
Guangxu Dong ◽  
Chicheng Ma ◽  
Feng Zhang ◽  
Yajun Luo ◽  
Chuanxing Bi
Keyword(s):  
Current Model ◽  
Excitation Frequency ◽  
Low Frequency ◽  
Harmonic Balance Method ◽  
Negative Stiffness ◽  
The Novel ◽  
Friction Damping ◽  
Improve Measurement ◽  
Photoelectric System ◽  
Isolation Performance

To suppress the low frequency vibrations of airborne photoelectric system and improve measurement accuracy, a novel passive airborne photoelectric quasi-zero stiffness platform (APQZSP), which is composed of upper/bottom planes, anti-shaking structure and six quasi-zero stiffness (QZS) legs, is designed. The QZS leg is constructed by connecting the folded beam spring with magnetic negative stiffness spring (MNSS) in parallel. According to current model, the magnetic force and negative stiffness of MNSS are derived. As the friction damping is introduced with anti-shaking structure, the isolation performance of the platform under friction damping is investigated based on harmonic balance method. Then the effect of damping and excitation on the isolation performance is analyzed. The results indicate that with the QZS technology, the resonant frequency of the platform is reduced and the low frequency vibrations can be effectively isolated with APQZSP. Moreover, the friction damping can maintain the displacement transmissibility at unity as long as the excitation frequency is lower than the break-loose frequency, and then the resonance can be avoided.

Numerical Study of a New Variable Friction TMD

2011 ◽  
Vol 243-249 ◽  
pp. 5450-5457 ◽  
Author(s):  
Li Qin ◽  
Wei Ming Yan ◽  
Sheng Bo Guo
Keyword(s):  
Frequency Response ◽  
Numerical Study ◽  
Damping Ratio ◽  
Harmonic Balance Method ◽  
Structural Response ◽  
Harmonic Excitation ◽  
Response Curves ◽  
Equivalent Damping ◽  
Response Characteristics ◽  
Variable Friction

The paper proposes a new variable friction system, of which the friction force can increase linearly with the displacement of system. This new system can be used in TMD to avoid the disadvantage of Coulomb friction TMD. Using first order harmonic balance method, the equivalent damping ratio and frequency of SDOF variable friction system is deduced and analyzed. The frequency response characteristics of SDOF variable friction system is discussed. The control effectiveness of variable friction TMD under harmonic excitation is analyzed theoretically. The results demonstrate that the frequency response curves of variable friction TMD and classically damped TMD are similar and both can effectively reduce structural response under harmonic excitation.

scholarly journals Nonlinear isolation performance of 6 × 19 wire rope of different lengths under compression

2021 ◽  
Vol 13 (6) ◽  
pp. 168781402110280
Author(s):  
Genlin Mo ◽  
Jing Liu ◽  
Yongxi Jin ◽  
Wenmin Yan
Keyword(s):  
Hysteresis Loop ◽  
Vibration Amplitude ◽  
Steel Wire ◽  
Damping Ratio ◽  
Excitation Amplitude ◽  
Wire Rope ◽  
Equivalent Damping ◽  
Wire Rope Isolator ◽  
The Wire ◽  
Isolation Performance

Stainless steel wire rope isolator is widely used in engineering. To optimize design of the isolator, loading, and unloading characteristics of the 6 × 19 6 mm wire rope under compression are investigated. Ropes of different lengths are tested to get the force-displacement relations. The stiffness, the equivalent damping ratio, and the hysteresis loop of the wire rope are derived. The stiffness decreases with both the length of the rope and the vibration amplitude. It has an approximate linear relationship with the reciprocal of length and amplitude. The equivalent damping ratio has an approximate quadratic relationship with the reciprocal of length and amplitude. The hysteresis loop of the wire rope is described using the proposed quadrilateral model. The loading stage is found to be determined by the length of the rope. The unloading stage is influenced by both the vibration amplitude and the length of the rope. Influences of the excitation amplitude and the frequency on the isolation performance for both steady-state vibration and transient impact vibration are revealed based on the models. The work would help engineers to design the isolators and predict responses of the structures.

Identification of Non-Linear Parameters of a Nuclear Fuel Rod

2017 ◽  
Author(s):  
Giovanni Ferrari ◽  
Stanislas Le Guisquet ◽  
Prabakaran Balasubramanian ◽  
Marco Amabili ◽  
Brian Painter ◽  
...  
Keyword(s):  
Circular Cylindrical Shell ◽  
Harmonic Balance Method ◽  
Excitation Amplitude ◽  
Resonance Phenomenon ◽  
Response Curves ◽  
Pressurized Water ◽  
Fuel Rods ◽  
Fuel Rod ◽  
Safety Margins ◽  
Fuel Assemblies

In Pressurized Water Reactors (PWR), fuel assemblies are made up of fuel rods, long slender tubes filled with uranium pellets, bundled together using spacer grids. These structures are subjected to fluid-structure interactions, due to the flowing coolant surrounding the fuel assemblies inside the core, coupled with large-amplitude vibrations in case of external seismic excitation. Therefore, understanding the nonlinear response of the structure, and, particularly, its dissipation, is of paramount importance for the choice of safety margins, in the design of fuel assemblies, to ensure their functionality and safety in the worst external condition scenarios. To model the nonlinear dynamic response of fuel rods, the identification of the nonlinear stiffness and damping parameters is required. A tool based on harmonic balance method was developed to identify these parameters from the experimentally obtained force-response curves, considering one-to-one internal resonance phenomenon present in axisymmetric structures such as cylindrical tubes and shells. To validate the tool, it was applied to the reference case of circular cylindrical shell filled with water, which revealed an increase of damping with the excitation amplitude. In the following paper, the more realistic case of a single fuel rod with clamped-clamped boundary condition was investigated by applying harmonic excitation at various force levels. The nonlinear parameters including damping were extracted from experimental results by means of the adapted tool. An increase in damping with excitation amplitude has been shown according to earlier studies.

Bifurcation Modes of Periodic Solution in a Duffing System Under Constant Force as Well as Harmonic Excitation

2019 ◽  
Vol 29 (13) ◽  
pp. 1950173 ◽  
Author(s):  
Lei Hou ◽  
Xiaochao Su ◽  
Yushu Chen
Keyword(s):  
Frequency Response ◽  
Damping Ratio ◽  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Harmonic Excitation ◽  
Nonlinearity Parameter ◽  
Constant Force ◽  
Response Curves ◽  
Duffing System ◽  
Singularity Method

This paper focuses on the classification of the bifurcation modes of a Duffing system under the combined excitations of constant force and harmonic excitation. The Harmonic Balance method combined with the arc-length continuation is used to obtain the periodic solutions of the system, and the Floquet theory is employed to analyze the stability of the corresponding solutions. Accordingly, the frequency-response curves affected respectively by the constant force and the magnitude of the harmonic excitation are analyzed to show the basic dynamical properties of the system. Afterwards, the bifurcation investigations are carried out with the aid of the two-state variable singularity method. It is derived that there are a total of six different types of bifurcation modes due to the effects of the constant force and the magnitude of the harmonic excitation. At last, the effects of the nonlinearity parameter and the damping ratio on the bifurcation modes of the system are also discussed. The results obtained in this paper extend the findings in reference that the system can have markedly three types of frequency-response curves: with only one solution, or with maximum three or five solutions for a certain excitation frequency, and contribute to a better understanding of the significant influence of the constant force.

scholarly journals Experimental Characterization of Friction in a Negative Stiffness Nonlinear Oscillator

Vibration ◽  
2020 ◽  
Vol 3 (2) ◽  
pp. 132-148
Author(s):  
Dario Anastasio ◽  
Stefano Marchesiello
Keyword(s):  
Dynamical Behavior ◽  
Harmonic Balance Method ◽  
Nonlinear Behavior ◽  
Nonlinear Damping ◽  
Negative Stiffness ◽  
Experimental Characterization ◽  
Restoring Force ◽  
Wide Range ◽  
Energy Dissipated

Nonlinear dissipative phenomena are common features of many dynamical systems and engineering applications, and their experimental characterization has always been a challenge among the research community. Within the wide range of nonlinear damping mechanisms, friction is surely one of the most common, and with a high impact on the dynamical behavior of structures. In this paper, the nonlinear identification of friction in a negative stiffness oscillator is pursued. The structure exhibits a strong nonlinear behavior, mainly due to its polynomial elastic restoring force with a negative stiffness region. This leads to an asymmetric double-well potential with two stable equilibrium positions, and the possibility of switching between them in a chaotic way. Friction plays a crucial role in this context, as it derives from the continuous sliding between the central guide and the moving mass. The system is driven through harmonic tests with several input amplitudes, in order to estimate the variations in the energy dissipated per cycle. The identification of the frictional behavior is then pursed by minimizing the errors between the experimental measurements and the model predictions, using the harmonic balance method in conjunction with a continuation technique on the forcing amplitudes.

Design and experiments of a quasi–zero-stiffness isolator with a noncircular cam-based negative-stiffness mechanism

2020 ◽  
Vol 26 (21-22) ◽  
pp. 1935-1947
Author(s):  
Ming Li ◽  
Wei Cheng ◽  
Ruili Xie
Keyword(s):  
Harmonic Balance ◽  
Experimental Studies ◽  
Approximation Error ◽  
Low Frequency ◽  
Harmonic Balance Method ◽  
Negative Stiffness ◽  
Restoring Force ◽  
Stiffness Characteristic ◽  
Physical Prototype ◽  
Negative Stiffness Mechanism

This article presents a quasi–zero-stiffness isolator with a cam-based negative-stiffness mechanism, where the cam has a user-defined noncircular profile to generate negative stiffness to counterbalance the positive stiffness of the vertical spring and yield the quasi–zero-stiffness characteristic around the equilibrium position. Unlike previous studies, the proposed quasi–zero-stiffness isolator has the preferable feature that the desired cubic restoring force can be directly obtained through the well-designed profile of the cam in the negative-stiffness mechanism with the friction considered during the model design, rather than through the Taylor expansion and friction-ignoring assumption, which can avoid the approximation error between the theoretical design and the specific realization. The pure-cubic nonlinear differential equation of motion of the quasi–zero-stiffness isolator is derived and solved with the harmonic balance method, followed by the discussion of the relevant dynamic characteristics. Experimental studies are carried out based on the physical prototype of the quasi–zero-stiffness isolator. The results show that the quasi–zero-stiffness isolator can greatly extend the isolation frequency bandwidth and has a much lower resonance peak. In the low-frequency band, the quasi–zero-stiffness isolator greatly outperforms the corresponding linear system but is equivalent or even inferior in the high-frequency range with the increase of excitation force.

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