scholarly journals Basic Constraints for Design Optimization of Cubic and Bistable NES

2021 ◽  
pp. 1-51
Author(s):  
Zhenhang Wu ◽  
Sebastien Seguy ◽  
Manuel Paredes
Keyword(s):  
Multiple Scales ◽  
Energy Levels ◽  
Conservative System ◽  
Harmonic Excitation ◽  
Absorption Efficiency ◽  
Complex Variables ◽  
Maximum Efficiency ◽  
Nonlinear Stiffness ◽  
Optimal Efficiency ◽  
Different Response

Abstract This work mainly concentrates on the optimization of cubic and bistable NES to find the maximum efficiency point under harmonic excitation. The conservative system is considered to reveal the inner property of the damping system. With the application of the multiple scales method and the complex variables method, the threshold of excitation and different response regimes are distinguished under the assumption of 1:1 resonance. The maximum efficiency point of cubic and bistable NES occurs when SMR disappears. The factors that affect the optimal efficiency limit are explored. The result indicates that the maximum absorption efficiency level is mainly determined by the damping parameters. Compared with the cubic case, the bistable case involves more complex regimes in terms of chaos oscillation. The influence of damping parameters on the chaos threshold is discussed to adopt different energy levels. With the help of analytical predictions, the proper nonlinear stiffness is determined for certain harmonic excitation. This work offers some fundamental insights into the optimal design of cubic and bistable NES.

Thermal Effect on Dynamics of Beam with Variable-Stiffness Nonlinear Energy Sink

2020 ◽  
Vol 21 (1) ◽  
pp. 1-10 ◽  
Author(s):  
J. E. Chen ◽  
W. Zhang ◽  
M. H. Yao ◽  
J. Liu ◽  
M. Sun
Keyword(s):  
Variable Stiffness ◽  
Nonlinear Energy Sink ◽  
Excitation Amplitude ◽  
Harmonic Excitation ◽  
Absorption Efficiency ◽  
Nonlinear Stiffness ◽  
Vibration Absorption ◽  
Low Stiffness ◽  
Energy Sink ◽  
Nonlinear Energy

AbstractIn this study, we investigate the targeted energy transfer (TET) from a simply supported beam that is subjected to thermal variations and external excitations to a local nonlinear energy sink (NES). We derive the governing equation of motion for the beam with an NES device and study the influences of NES parameters on the vibration-suppressing effect. We obtain the optimized parameters of the NES under constant-amplitude harmonic excitation at room temperature. The optimized NES gradually loses its vibration absorption efficiency as the excitation amplitude and temperature increase. We change the nonlinear stiffness of the NES to mitigate the influence of temperature variation and show that NES efficiency can be enhanced by reducing the nonlinear stiffness. We propose a variable-stiffness NES, and the results demonstrate this NES is best for maintaining efficiency over the whole temperature range. We also analyze the transient responses of the system under impulse loads. Results indicate that, like the performance of the system subjected to harmonic excitation, an NES with relatively low stiffness can better suppress vibration with increasing impulse amplitude and temperature.

scholarly journals Highly Photoluminescent and Stable N-Doped Carbon Dots as Nanoprobes for Hg2+ Detection

Nanomaterials ◽  
2018 ◽  
Vol 8 (11) ◽  
pp. 900 ◽  
Author(s):  
Longshi Rao ◽  
Yong Tang ◽  
Hanguang Lu ◽  
Shudong Yu ◽  
Xinrui Ding ◽  
...  
Keyword(s):  
Photoelectron Spectroscopy ◽  
Carbon Dots ◽  
Limit Of Detection ◽  
Energy Levels ◽  
Orbital Energy ◽  
Synthesis Conditions ◽  
Porous Copper ◽  
Different Response ◽  
Doped Carbon Dots ◽  
Nitrogen Doped Carbon

We developed a microreactor with porous copper fibers for synthesizing nitrogen-doped carbon dots (N-CDs) with a high stability and photoluminescence (PL) quantum yield (QY). By optimizing synthesis conditions, including the reaction temperature, flow rate, ethylenediamine dosage, and porosity of copper fibers, the N-CDs with a high PL QY of 73% were achieved. The PL QY of N-CDs was two times higher with copper fibers than without. The interrelations between the copper fibers with different porosities and the N-CDs were investigated using X-ray photoelectron spectroscopy (XPS) and Fourier Transform infrared spectroscopy (FTIR). The results demonstrate that the elemental contents and surface functional groups of N-CDs are significantly influenced by the porosity of copper fibers. The N-CDs can be used to effectively and selectively detect Hg2+ ions with a good linear response in the 0~50 μM Hg2+ ions concentration range, and the lowest limit of detection (LOD) is 2.54 nM, suggesting that the N-CDs have great potential for applications in the fields of environmental and hazard detection. Further studies reveal that the different d orbital energy levels of Hg2+ compared to those of other metal ions can affect the efficiency of electron transfer and thereby result in their different response in fluorescence quenching towards N-CDs.

Nonlinear Harmonic Vibration Analysis of a Fully Clamped Micro-Beam

2015 ◽  
Author(s):  
Mehran Sadri ◽  
Davood Younesian ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Vibration Analysis ◽  
Multiple Scales ◽  
Special Kind ◽  
Equation Of Motion ◽  
Harmonic Excitation ◽  
Harmonic Vibration ◽  
Potential Wells ◽  
State Response ◽  
Nonlinear Forced Vibration ◽  
First Time

Nonlinear harmonic vibration analysis of a clamped-clamped micro-beam is studied in this paper. Nonlinear forced vibration of a special kind of micro-actuators is examined for the first time. Galerkin method is employed to derive the equation of motion of the micro-beam with two symmetric potential wells. An electric force composed of DC and AC components is applied to the structure. Multiple Scales method (MSM) is used to solve the nonlinear equation of motion. Primary and secondary resonances are taken into account and steady-state response of the microbeam is obtained. A parametric study is then carried out to investigate the effects of different parameters on the amplitude-frequency curves. Finally, phase plot and Poincare map have been taken into consideration to investigate the influence of the amplitude of the harmonic excitation on stability of the microelectromechanical system.

Vibration Control of Horizontally Excited Structures Utilizing Internal Resonance of Liquid Sloshing in Nearly Square Tanks

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Takashi Ikeda ◽  
Yuji Harata
Keyword(s):  
Frequency Response ◽  
Internal Resonance ◽  
Passive Control ◽  
Harmonic Excitation ◽  
Liquid Sloshing ◽  
Maximum Efficiency ◽  
System Response ◽  
Response Curves ◽  
System Parameters ◽  
Theoretical Results

Passive control of vibrations in an elastic structure subjected to horizontal, harmonic excitation by utilizing a nearly square liquid tank is investigated. When the natural frequency ratio 1:1:1 is satisfied among the natural frequencies of the structure and the two predominant sloshing modes (1,0) and (0,1), the performance of a nearly square tank as a tuned liquid damper (TLD) is expected to be superior to rectangular TLDs due to internal resonance. In the theoretical analysis, Galerkin's method is used to determine the modal equations of motion for liquid sloshing considering the nonlinearity of sloshing. Then, van der Pol's method is used to obtain the expressions for the frequency response curves for the structure and sloshing modes. Frequency response curves and bifurcation set diagrams are shown to investigate the influences of the aspect ratio of the tank cross section and the tank installation angle on the system response. From the theoretical results, the optimal values of the system parameters can be determined in order to achieve maximum efficiency of vibration suppression for the structure. Hopf bifurcations occur and amplitude modulated motions (AMMs) may appear depending on the values of the system parameters. Experiments were also conducted, and the theoretical results agreed well with the experimental data.

A Unique Formulation of Piecewise Exact Method to Analyze a Nonlinear Spring System under Harmonic Excitation

2014 ◽  
Vol 31 (3) ◽  
pp. 337-344
Author(s):  
P.-S. Xie ◽  
P.-J. Shih
Keyword(s):  
Exact Solution ◽  
Numerical Approximation ◽  
Piecewise Linear ◽  
Equilibrium Points ◽  
Harmonic Excitation ◽  
Exact Method ◽  
Nonlinear Stiffness ◽  
Time Error ◽  
Single Degree Of Freedom ◽  
Spring System

AbstractThis paper introduces a unique, efficient, and exact formulation for solving a single-degree-of-freedom system with nonlinear stiffness under a harmonic loading. This formulation is one kind of the piecewise exact method, and its benefit lies in providing the closed-form exact solution in each displacement segment. Since the exact solution is given in each segment, the continuity between two segments can be confirmed. Consequently, no instability errors affect the analysis. To determine the exact solutions in these segments, this research develops a technique that shifts the equilibrium points of the piecewise linear segments, which are discretized from a nonlinear stiffness curve, to new equilibrium points in order to satisfy the typical linear exact solution. Thus, positive- and negative-stiffness linear segments can be solved with this technique. This formulation saves roughly 60% of the calculation time (error < 10−10) as compared to the numerical approximation.

Superharmonic and Subharmonic Resonances of Spiral Stiffened Functionally Graded Cylindrical Shells under Harmonic Excitation

2019 ◽  
Vol 19 (10) ◽  
pp. 1950114 ◽  
Author(s):  
Habib Ahmadi ◽  
Kamran Foroutan
Keyword(s):  
Multiple Scales ◽  
Plate Theory ◽  
Cylindrical Shells ◽  
Harmonic Excitation ◽  
Functionally Graded ◽  
Classical Plate Theory ◽  
Geometrical Properties ◽  
Hardening Nonlinearity ◽  
Subharmonic Resonances ◽  
Theory Of Shells

This paper presents the superharmonic and subharmonic resonances of spiral stiffened functionally graded (SSFG) cylindrical shells under harmonic excitation. The stiffeners are considered to be externally or internally added to the shell. Also, it is assumed that the material properties of the stiffeners are continuously graded in the thickness direction. In order to model the stiffeners, the smeared stiffener technique is used. Within the context of the classical plate theory of shells, the von Kármán nonlinear equations are derived for the shell and stiffeners based on Hooke’s law and the relations of stress-strain. Using Galerkin’s method, the equation of motion is discretized. The superharmonic and subharmonic resonances are analyzed by the method of multiple scales. The influence of the material parameters and various geometrical properties on the superharmonic and subharmonic resonances of SSFG cylindrical shells is investigated. Considering these results, the hardening nonlinearity behavior and jump value of cylindrical shell is less and more than others, when the angle of stiffeners is [Formula: see text] and [Formula: see text], respectively.

Nonlinear Vibration Analysis of a Fractional Viscoelastic Euler-Bernoulli Microbeam

2018 ◽  
Author(s):  
Firooz Bakhtiari-Nejad ◽  
Ehsan Loghman ◽  
Mostafa Pirasteh
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibration ◽  
Multiple Scales ◽  
Scale Effects ◽  
Viscoelastic Model ◽  
Harmonic Excitation ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Harmonic Resonance

Nonlinear vibration of a simply-supported Euler-Bernoulli microbeam with fractional Kelvin-Voigt viscoelastic model subjected to harmonic excitation is investigated in this paper. For small scale effects the modified strain gradient theory is used. For take into account geometric nonlinearities the Von karman theory is applied. Beam equations are derived from Hamilton principle and the Galerkin method is used to convert fractional partial differential equations into fractional ordinary differential equations. Problem is solved by using the method of multiple scales and amplitude-frequency equations are obtained for primary, super-harmonic and sub-harmonic resonance. Effects of force amplitude, fractional parameters and nonlinearity on the frequency responses for primary, super-harmonic and sub-harmonic resonance are investigated. Finally results are compared with ordinary Kelvin-Voigt viscoelastic model.

Multimodal Resonances in Suspended Cables via a Direct Perturbation Approach

1997 ◽  
Author(s):  
Giuseppe Rega ◽  
Walter Lacarbonara ◽  
Ali H. Nayfeh ◽  
Char-Ming Chin
Keyword(s):  
Internal Resonance ◽  
Multiple Scales ◽  
A Priori ◽  
Three Dimensional ◽  
Primary Resonance ◽  
Harmonic Excitation ◽  
Finite Amplitude ◽  
Perturbation Approach ◽  
Plane Symmetric ◽  
Complex Valued

Abstract We analyze the nonlinear three–dimensional response of an elastic suspended cable with small sag-to-span ratio to a harmonic excitation. We investigate the case of primary resonance of the first in-plane symmetric mode when it is involved in a one–to–one internal resonance with the first antisymmetric planar and nonplanar modes and a two–to–one internal resonance with the first symmetric nonplanar mode. We apply the method of multiple scales directly to the governing two integro–partial–differential equations and associated boundary conditions with no a priori assumption on the shape of the motion. The result is a system of four coupled nonlinear complex–valued equations describing the modulation of the amplitudes and phases of the four interacting modes. The spatial-temporal corrections to the displacement field at higher orders show that the solution is not separable in space and time. Prelimary comparisons with a companion Galerkin-type discretized model show that the latter must be used with some care in studying finite–amplitude motions of cables.

scholarly journals Power Flow in a Two-Stage Nonlinear Vibration Isolation System with High-Static-Low-Dynamic Stiffness

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Ze-Qi Lu ◽  
Dong Shao ◽  
Hu Ding ◽  
Li-Qun Chen
Keyword(s):  
Nonlinear Vibration ◽  
Power Flow ◽  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Harmonic Balance Method ◽  
Harmonic Excitation ◽  
Resonant Peak ◽  
Nonlinear Stiffness ◽  
Two Stage ◽  
Force Transmissibility

The manuscript concerns the power flow characterization in a two-stage nonlinear vibration isolator comprising three springs, which are configured so that each stage of the system has a high-static-low-dynamic stiffness. To demonstrate the distinction of evaluation for vibration isolation using power flow, force transmissibility is used for comparison. The dynamic behavior of the isolator subject to harmonic excitation, however, is of interest here. The harmonic balance method (HBM) could be used to analyze the frequency response curve (FRC) of the strong nonlinear vibration system. A suggested stability analysis to distinguish the stable and the unstable HBM solutions is described. Increasing both upper and lower nonlinear stiffness could bend the first resonant peak to the left. The isolation range in the power and the force transmissibility plot could be extended to the lower frequencies when the nonlinear stiffness is increased, but the rate of roll-off for the power transmissibility is twice the rate for the force transmissibility at each horizontal stiffness setting. An explanation for this phenomenon is given in the paper.

The Nonlinear Response of a Simply Supported Rectangular Metallic Plate to Transverse Harmonic Excitation

2000 ◽  
Vol 67 (3) ◽  
pp. 621-626 ◽  
Author(s):  
O. Elbeyli and ◽  
G. Anlas
Keyword(s):  
Critical Points ◽  
Internal Resonance ◽  
Nonlinear Response ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Primary Resonance ◽  
Harmonic Excitation ◽  
Stability Of Solutions ◽  
Metallic Plate ◽  
Simply Supported

In this study, the nonlinear response of a simply supported metallic rectangular plate subject to transverse harmonic excitations is analyzed using the method of multiple scales. Stability of solutions, critical points, types of bifurcation in the presence of a one-to-one internal resonance, together with primary resonance, are determined. [S0021-8936(00)00603-6]

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