Nonlinear Vibration Analysis of Viscoelastic Isolator

2012 ◽  
Vol 160 ◽  
pp. 140-144
Author(s):  
Chao Zhou ◽  
Cai Mao Zhong
Keyword(s):  
Dynamic Response ◽  
Fractional Derivative ◽  
Nonlinear Dynamic ◽  
Harmonic Balance Method ◽  
Nonlinear Damping ◽  
Vibration Isolator ◽  
Response Characteristics ◽  
Nonlinear Dynamic Equation ◽  
The Stability ◽  
Stiffness And Damping

Research on nonlinear dynamic response of passive vibration isolator, which was excited by foundation vibration and isolated by viscoelastic material was done. Nonlinear stiffness was expressed by the cubic polynomial function of deformation and nonlinear damping was characterized by viscoelastic fractional derivative operator. Then the fractional derivative nonlinear dynamic equation of passive vibration isolator was established. The dynamic response characteristics were analyzed by harmonic balance method and the frequency response equation and amplitude-frequency curve were obtained, and furthermore, the influence of nonlinearity on system was analyzed. Finally, the stability and the stable interval of the periodic solution were argued by the Floquet theory. The result s indicates that the proposed equation can precisely describe the dynamic characteristics of viscoelastic vibration isolator. The ignorance of nonlinearity of stiffness and damping will result in obvious error. The proposed method provides theoretic reference for design of viscoelastic isolator and the evaluation of its effect.

Nonlinear Dynamic Response of FG Graphene Platelets Reinforced Composite Beam with Edge Cracks in Thermal Environment

2020 ◽  
pp. 2043005 ◽  
Author(s):  
Zhicheng Yang ◽  
Meifung Tam ◽  
Yingyan Zhang ◽  
Sritawat Kitipornchai ◽  
Jiangen Lv ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Thermal Environment ◽  
Crack Depth ◽  
Functionally Graded ◽  
Nonlinear Dynamic Response ◽  
Response Characteristics ◽  
Reinforced Composite ◽  
Edge Cracks ◽  
Graphene Platelets

This paper presents a numerical investigation on the nonlinear dynamic response of multilayer functionally graded graphene platelets reinforced composite (FG-GPLRC) beam with open edge cracks in thermal environment. It is assumed that graphene platelets (GPLs) in each GPLRC layer are uniformly distributed and randomly oriented with its concentration varying layer-wise along the thickness direction. The effective material properties of each GPLRC layer are predicted by Halpin-Tsai micromechanics-based model. Finite element method is employed to calculate the dynamic response of the cracked FG-GPLRC beam. It is found that the maximum dynamic deformation of the cracked FG-GPLRC beam under dynamic loading is quite sensitive to the crack location and grows with an increase in the crack depth ratio (CDR) and temperature rise. The influences of GPL distribution, concentration, geometry as well as the boundary conditions on the dynamic response characteristics of cracked FG-X-GPLRC beams are also investigated comprehensively.

Investigation of nonlinear landing gear behavior and dynamic responses on high performance aircraft

2019 ◽  
Vol 233 (15) ◽  
pp. 5674-5688
Author(s):  
PS Suresh ◽  
Niranjan K Sura ◽  
K Shankar
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Landing Gear ◽  
Flight Mechanics ◽  
Dynamic Responses ◽  
Nonlinear Stiffness ◽  
Response Model ◽  
Nonlinear Dynamic Response ◽  
Vertical Descent ◽  
Stiffness And Damping

The dynamic responses simulation of aircraft as rigid body considering heave, pitch, and roll motions, coupled onto a tricycle landing gear arrangement is presented. Equation of motion for each landing gear consists of un-sprung mass vertical and longitudinal motions considering strut nonlinear stiffness and damping combined with strut bending flexibility. Initially, the nonlinear dynamic response model is subjected to an input of riding over staggered bump and the responses are compared with linear landing gear model. It is observed that aircraft dynamics and important landing gear events such as vertical, spin-up and spring-back are truly represented with nonlinear stiffness and damping model considering strut bending flexibility. Later, landing response analysis is performed, with the input from nonlinear flight mechanics model for several vertical descent rate cases. The aircraft and landing gear dynamic responses such as displacement, velocity, acceleration, and reaction forces are obtained. The vertical and longitudinal drag forces from the nonlinear dynamic response model is compared with “Book-case method” outlined in landing gear design technical specifications. From the reaction force ratio calculation, it is shown that for lower vertical descent rate case the predicted loads are lesser using nonlinear dynamic response model. The same model for higher vertical descent rate cases predicts higher ratios on vertical reaction for main landing gear and longitudinal reaction for nose landing gear, respectively. The scope for increase in fatigue life for low vertical descent rate landing covering major design spectrum and the concern for static strength and structural integrity consideration for higher vertical descent rate cases are discussed in the context of event monitoring on aircraft in services.

Stability of uniform electronic wavepackets in chains and fullerenes

2015 ◽  
Vol 26 (12) ◽  
pp. 1550133 ◽  
Author(s):  
Valdemir L. Chaves Filho ◽  
Rodrigo P. A. Lima ◽  
F. A. B. F. de Moura ◽  
Marcelo L. Lyra
Keyword(s):  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Modulational Instability ◽  
The Other ◽  
Nonlinear Coupling ◽  
Phonon Coupling ◽  
Instability Analysis ◽  
Nonlinear Dynamic Equation ◽  
Electron Phonon Coupling ◽  
The Stability

In this paper, we investigate the influence of electron-lattice interaction on the stability of uniform electronic wavepackets on chains as well as on several types of fullerenes. We will use an effective nonlinear Schrödinger equation to mimic the electron–phonon coupling in these topologies. By numerically solving the nonlinear dynamic equation for an initially uniform electronic wavepacket, we show that the critical nonlinear coupling above which it becomes unstable continuously decreases with the chain size. On the other hand, the critical nonlinear strength saturates on a finite value in large fullerene buckyballs. We also provide analytical arguments to support these findings based on a modulational instability analysis.

scholarly journals An Asymmetric Quasi-zero Stiffness Vibration Isolator with Long Stroke and Large Bearing Capacity

2021 ◽  
Author(s):  
Xinghua Zhou ◽  
Dingxuan Zhao ◽  
Xiao Sun ◽  
Xiao Yang ◽  
Jianhai Zhang ◽  
...  
Keyword(s):  
Bearing Capacity ◽  
Vibration Isolation ◽  
Geometrical Nonlinearity ◽  
Harmonic Balance Method ◽  
Nonlinear Damping ◽  
Vibration Isolator ◽  
Plate Spring ◽  
Supporting Force ◽  
Vibration Isolation Performance ◽  
Isolation Performance

Abstract A novel passive asymmetric quasi-zero stiffness vibration isolator (AQZS-VI) comprising two linear springs acting in parallel with one negative stiffness element (NSE) is proposed, of which the NSE is mainly constructed by the combination of cantilever plate spring and L-shaped lever (CPS-LSL). The static model of the isolator is deduced considering the geometrical nonlinearity of the NSE and the bending deformation of plate spring. The nonlinear stiffness properties of the CPS-LSL and the AQZS-VI, as well as the nonlinear damping properties of the AQZS-VI are discussed. The absolute displacement transmissibility of the AQZS-VI under base displacement excitation is obtained using Harmonic Balance Method, and the effects of different excitation amplitudes and damping factors on the vibration isolation performance are analyzed. Better than other quasi-zero stiffness vibration isolators (QZS-VI) whose NSEs do not provide supporting force at zero stiffness point, the NSE of the AQZS-VI provides more supporting force than the parallel connected linear springs, which is very beneficial for improving the bearing capacity of the isolator. Compared with a typical symmetric QZS-VI with same damping property, the AQZS-VI has longer stroke with low stiffness and lower peak value of displacement transmissibility. The prototype experiments indicate that the AQZS-VI outperforms the linear counterpart with much smaller starting frequency of vibration isolation and lower displacement transmissibility. The proposed AQZS-VI has great potential for applying in various engineering practices with superior vibration isolation performance.

Study on the Pair’s Characteristics of Web Press’s Fold System in High Speed

2011 ◽  
Vol 311-313 ◽  
pp. 1398-1403
Author(s):  
Ying Cai Yuan ◽  
Yan Li ◽  
Yi Ming Wang
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
High Speed ◽  
Dynamic Performance ◽  
Dynamics Model ◽  
Nonlinear Dynamic Response ◽  
Response Characteristics ◽  
Fold System ◽  
Main Factors ◽  
Dynamic Response Characteristics

In high speed, the web press’s fold mechanism appears nonlinear dynamic response characteristics, which seriously affect the fold system’s stability and precision. The clearance and roller’s deformation are the main factors to cause the nonlinear dynamic response. To study the influence of clearance and roller’s deformation, the hypothesis of rigid role and spring combination is put forward. Based on the hypothesis, the dynamics model of fold system with clearance is established by kinematics and dynamics analysis. Through the dynamics model of fold system, the situation of pair clearance and roller’s deformation can be obtained, and the influence to the dynamic performance of fold system can be easily got.

A Floquet-Based Analysis of Parametric Excitation Through the Damping Coefficient

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Fatemeh Afzali ◽  
Gizem D. Acar ◽  
Brian F. Feeny
Keyword(s):  
Floquet Theory ◽  
Initial Conditions ◽  
Harmonic Balance Method ◽  
Damping Coefficient ◽  
Periodic Part ◽  
Response Characteristics ◽  
Floquet Solution ◽  
Mathieu’S Equation ◽  
Truncated Fourier Series ◽  
The Stability

Abstract The Floquet theory has been classically used to study the stability characteristics of linear dynamic systems with periodic coefficients and is commonly applied to Mathieu’s equation, which has parametric stiffness. The focus of this article is to study the response characteristics of a linear oscillator for which the damping coefficient varies periodically in time. The Floquet theory is used to determine the effects of mean plus cyclic damping on the Floquet multipliers. An approximate Floquet solution, which includes an exponential part and a periodic part that is represented by a truncated Fourier series, is then applied to the oscillator. Based on the periodic part, the harmonic balance method is used to obtain the Fourier coefficients and Floquet exponents, which are then used to generate the response to the initial conditions, the boundaries of instability, and the characteristics of the free response solution of the system. The coexistence phenomenon, in which the instability wedges disappear and the transition curves overlap, is recovered by this approach, and its features and robustness are examined.

Research the Layered Structure Affect on Seismic Dynamic Response of Rock Slope

2011 ◽  
Vol 382 ◽  
pp. 439-443
Author(s):  
Fa You A ◽  
Ji Ming Kong ◽  
Zhen Qiang Ni
Keyword(s):  
Dynamic Response ◽  
Layered Structure ◽  
Rock Slope ◽  
Dynamic Responses ◽  
Deformation And Failure ◽  
Response Characteristics ◽  
The Stability ◽  
Bedding Slope ◽  
Dip Slope ◽  
Better Than

The deformation and failure induced by Wenchuan earthquake between bedding and anti-dip slope existence very big difference. The number and size of the bedding slope deformation and failure are much more than the anti-dip slope according to the investigation and analysis. In order to analyze the layered structure affect on seismic dynamic response of rock Slope. As bedding and anti-dip slope is the study object and the seismic dynamic responses of different layered structure slope have been studied by using ANSYS finite element method in this study. Analysis shows that slope as a structure, the internal structure different lead to the slope seismic dynamic response is also different. The bedding and anti-dip slope seismic dynamic response is discontinuous or mutations in the slope as layered structure interface the boundary. And the seismic dynamic stress, displacement and acceleration of the bedding slope are always greater than the anti-dip slope. The seismic response characteristics further increased the deformation and failure probability of bedding slope. The results consistent with the investigation conclusion that the stability of anti-dip better than the anti-dip slope

scholarly journals Stability and bifurcation analysis of super- and sub-harmonic responses in a torsional system with piecewise-type nonlinearities

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jong-Yun Yoon ◽  
Byeongil Kim
Keyword(s):  
Nonlinear Dynamic ◽  
Continuation Method ◽  
Harmonic Balance Method ◽  
Period Doubling ◽  
Stability Conditions ◽  
Arc Length ◽  
Dynamic Behaviors ◽  
Variational Stability ◽  
Time Histories ◽  
The Stability

AbstractThe nonlinear dynamic behaviors induced by piecewise-type nonlinearities generally reflect super- and sub-harmonic responses. Various inferences can be drawn from the stability conditions observed in nonlinear dynamic behaviors, especially when they are projected in physical motions. This study aimed to investigate nonlinear dynamic characteristics with respect to variational stability conditions. To this end, the harmonic balance method was first implemented by employing Hill’s method, and the time histories under stable and unstable conditions were examined using a numerical simulation. Second, the super- and sub-harmonic responses were investigated according to frequency upsweeping based on the arc-length continuation method. While the stability conditions vary along the arc length, the bifurcation phenomena also show various characteristics depending on their stable or unstable status. Thus, the study findings indicate that, to determine the various stability conditions along the direction of the arc length, it is fairly reasonable to determine nonlinear dynamic behaviors such as period-doubling, period-doubling cascade, and quasi-periodic (or chaotic) responses. Overall, this study suggests analytical and numerical methods to understand the super- and sub-harmonic responses by comparing the arc length of solutions with the variational stability conditions.

An Approximate Analytical Solution for Dynamic Response of a Large Nonlinear Rotor-Bearing System

2016 ◽  
Vol 693 ◽  
pp. 445-452
Author(s):  
Xiao Ying Liu ◽  
Cai Jing Yang ◽  
Li Ping Zhou ◽  
Yu Wang ◽  
Jia Sheng Wang
Keyword(s):  
Analytical Solution ◽  
Dynamic Response ◽  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Harmonic Balance Method ◽  
Rotating Machinery ◽  
Nonlinear Dynamic Response ◽  
Reduced Order ◽  
Rotor Bearing ◽  
Bearing System

Large nonlinear rotor-bearing system is an important structure in rotating machinery, such as NC machine. Due to the mass imbalance of the system, vibrations induced by centrifugal forces inevitably exist in rotating machinery. So, nonlinear dynamic response of a complex rotor-bearing system was dealt with in this paper. The system considered was modeled using the finite element method and has 124 DOFs (degrees of freedom). A linear reduction method was used and a reduced-order dynamic model of the system with two DOFs had been obtained. Harmonic balance method was applied to the reduced-order dynamic model of the system and an approximate analytical expression of the solution for nonlinear dynamic response of the system at steady state was derived. The analytical solution obtained from the reduced-order dynamic model of the system was compared with the numerical one obtained from the direct integration of the equations of motion of the original system.

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