• Title/Summary/Keyword: Nonlinear Vibration Analysis

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Nonlinear vibration of nanosheets subjected to electromagnetic fields and electrical current

  • Pourreza, Tayyeb;Alijani, Ali;Maleki, Vahid A.;Kazemi, Admin
    • Advances in nano research
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    • v.10 no.5
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    • pp.481-491
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    • 2021
  • Graphene Nanosheets play an important role in nanosensors due to their proper surface to volume ratio. Therefore, the main purpose of this paper is to consider the nonlinear vibration behavior of graphene nanosheets (GSs) under the influence of electromagnetic fields and electrical current create forces. Considering more realistic assumptions, new equations have been proposed to study the nonlinear vibration behavior of the GSs carrying electrical current and placed in magnetic field. For this purpose, considering the influences of the magnetic tractions created by electrical and eddy currents, new relationships for electromagnetic interaction forces with these nanosheets have been proposed. Nonlinear coupled equations are discretized by Galerkin method, and then solved via Runge-Kutta method. The effect of different parameters such as size effect, electrical current magnitude and magnetic field intensity on the vibration characteristics of GSs is investigated. The results show that the magnetic field increases the linear natural frequency, and decreases the nonlinear natural frequency of the GSs. Excessive increase of the magnetic field causes instability in the GSs.

Internal Resonance and Stability Change for the Two Degree Nonlinear Coupled System (2 자유도 비선형 연성시스템에서 내부공진과 안정성 변화)

  • Kim, Myoung-Gu;Pak, Chul-Hui;Cho, Chong-Du
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2007.11a
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    • pp.853-861
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    • 2007
  • To understand the concept of dynamic motion in two degree nonlinear coupled system, free vibration not including damping and excitation is investigated with the concept of nonlinear normal mode. Stability analysis of a coupled system is conducted, and the theoretical analysis performed for the bifurcation phenomenon in the system. Bifurcation point is estimated using harmonic balance method. When the bifurcation occurs, the saddle point is always found on Poincare's map. Nonlinear phenomenon result in amplitude modulation near the saddle point and the internal resonance in the system making continuous interchange of energy. If the bifurcation in the normal mode is local, the motion remains stable for a long time even when the total energy is increased in the system. On the other hand, if the bifurcation is global, the motion in the normal mode disappears into the chaos range as the range becomes gradually large.

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Random Vibration Analysis of Nonlinear Structure System using Perturbation Method

  • Moon, Byung-Young;Kang, Beom-Soo;Kang, Gyung-Ju
    • Proceedings of the Earthquake Engineering Society of Korea Conference
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    • 2001.09a
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    • pp.243-250
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    • 2001
  • Industrial machines are sometimes exposed to the danger of earthquake. In the design of a mechanical system, this factor should be accounted for from the viewpoint of reliability. A method to analyze a complex nonlinear structure system under random excitation is proposed. First, the actual random excitation, such as earthquake, is approximated to the corresponding Gaussian process far the statistical analysis. The modal equations of overall system are expanded sequentially. Then, the perturbed equations are synthesized into the overall system and solved in probabilistic way. Several statistical properties of a random process that are of interest in random vibration applications are reviewed in accordance with nonlinear stochastic problem. The obtained statistical properties of the nonlinear random vibration are evaluated in each substructure. Comparing with the results of the numerical simulation proved the efficiency of the proposed method.

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Dynamic Characteristics of Linear Motion Supported by Rolling Ball Bearings (볼 베어링을 사용하는 선형 운동 가이드의 동적 특성)

  • Choi Jae Seok;Yi Yong-sub;Kim Yoon Young;Lee Dong Jin;Lee Sung Jin;Yoo Jeonghoon
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.14 no.9 s.90
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    • pp.868-876
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    • 2004
  • The linear motion(LM) guide using ball bearing has many advantages compared with conventional sliding guides. Therefore, LM guide using ball bearing has been widely used to increase the accuracy of the position of a system. This research investigates dynamic characteristics of LM guide through mainly linear analyses. Linear analysis is accomplished by Lagrange equation and the finite element method. And another trial that performs nonlinear analysis about one mode(bouncing mode) of LM guide from Hertzian contact theory is accomplished in the latter half of this research. Through nonlinear analysis we could observe the softening characteristic due to the Hertzian contact nonlinearity.

Reliability-based fragility analysis of nonlinear structures under the actions of random earthquake loads

  • Salimi, Mohammad-Rashid;Yazdani, Azad
    • Structural Engineering and Mechanics
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    • v.66 no.1
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    • pp.75-84
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    • 2018
  • This study presents the reliability-based analysis of nonlinear structures using the analytical fragility curves excited by random earthquake loads. The stochastic method of ground motion simulation is combined with the random vibration theory to compute structural failure probability. The formulation of structural failure probability using random vibration theory, based on only the frequency information of the excitation, provides an important basis for structural analysis in places where there is a lack of sufficient recorded ground motions. The importance of frequency content of ground motions on probability of structural failure is studied for different levels of the nonlinear behavior of structures. The set of simulated ground motion for this study is based on the results of probabilistic seismic hazard analysis. It is demonstrated that the scenario events identified by the seismic risk differ from those obtained by the disaggregation of seismic hazard. The validity of the presented procedure is evaluated by Monte-Carlo simulation.

Analysis and Design of a Pneumatic Vibration Isolation System: Part I. Modeling and Algorithm for Transmissibility Calculation (공압 제진 시스템의 해석과 설계: I. 모델링과 전달율 계산 알고리즘)

  • Moon Jun Hee;Pahk Heui Jae
    • Journal of the Korean Society for Precision Engineering
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    • v.21 no.10
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    • pp.127-136
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    • 2004
  • This paper is the first of two companion papers concerning the analysis and design of a pneumatic vibration isolation system. The design optimization of the pneumatic vibration isolation system is required for the reduction of cost, endeavor and time, and it needs modeling and calculation algorithm. The nonlinear models are devised from the fluid mechanical expression for components of the system and the calculation algorithm is derived from the mathematical relationship between the models. It is shown that the orifice makes the nonlinear property of the transmissibility curve that the resonant frequency changes by the amplitude of excited vibration. Linearization of the nonlinear models is tried to reduce elapsed time and truncation error accumulation and to enable the transmissibility calculation of the system with multi damping chambers. The equivalent mechanical models generated by linearization clarify the function of each component of the system and lead to the linearized transfer function that can give forth to the transmissibility exactly close to that of nonlinear models. The modified successive under-relaxation method is developed to calculate the linearized transfer function.

Nonlinear vibration analysis of carbon nanotube reinforced composite plane structures

  • Rezaiee-Pajand, Mohammad;Masoodi, Amir R.;Rajabzadeh-Safaei, Niloofar
    • Steel and Composite Structures
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    • v.30 no.6
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    • pp.493-516
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    • 2019
  • This paper is dedicated to nonlinear static and free vibration analysis of Uniform Distributed Carbon Nanotube Reinforced Composite (UD-CNTRC) structures under in-plane loading. The authors have suggested an efficient six-node triangular element. Mixed Interpolation of Tensorial Components (MITC) approach is employed to alleviate the membrane locking phenomena. Moreover, the behavior of the well-known LST element is considerably improved by applying an additional linear interpolation on the strain fields. Based on the rule of mixture, the properties of CNTRC are obtained. In this study, only the uniform distributed CNTs are employed through the thickness direction of element. To achieve the natural frequencies and shape modes, the eigenvalue problem is also solved. Using Total Lagrangian Principles, large amplitude free vibration is considered based on the first normalized mode shape of structure. Different well-known plane problem benchmarks and some proposed ones are studied to validate the accuracy and capability of authors' formulations. In addition, the effects of length to the height ratio of beam, CNT's characteristics, support conditions and normalized amplitude parameter on the linear and nonlinear vibration parameters are investigated.

Nonlinear vibration analysis of FG porous shear deformable cylindrical shells covered by CNTs-reinforced nanocomposite layers considering neutral surface exact position

  • Zhihui Liu;Kejun Zhu;Xue Wen;Abhinav Kumar
    • Advances in nano research
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    • v.17 no.1
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    • pp.61-73
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    • 2024
  • This paper presents nonlinear vibration analysis of a composite cylindrical shell. The core of the shell is made of functionally graded (FG) porous materials and layers is fabricated of carbon nanotubes (CNTs) reinforced nanocomposites. To increase the accuracy of results, neutral surface position is considered. First-order shear deformation theory is used as displacement field to derive the basic relations of equation motions. In addition, von-Karman nonlinear strains are employed to account geometric nonlinearity and to enhance the results' precision, the exact position of the neutral surface is considered. To governing the partial equations of motion, the Hamilton's principle is used. To reduce the equation motions into a nonlinear motion equation, the Galerkin's approach is employed. After that the nonlinear motion equation is solved by multiple scales method. Effect of various parameters such as volume fraction and distribution of CNTs along the thickness directions, different patterns and efficiency coefficients of porous materials, geometric characteristics and initial conditions on nonlinear to linear ratio of frequency is investigated.

Nonplanar vibration Phenomenon of the Quadrangle Cantilever Beam (정사각형 외팔보의 비평면 진동현상)

  • Kim, Myoung-Gu;Pak, Chul-Hui;Cho, Chong-Du;Cho, Ho-Joon
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2006.05a
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    • pp.62-65
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    • 2006
  • In this paper, nonlinear nonplanar vibration of a flexible rectangular cantilever beam is analyzed when one-to-one resonance occurs to the beam. The planar and nonplanar motions of the beam are analyzed in time and frequency domains. In frequency domain, FFT analyzer is used to perform autospectrum and cepstrum analyses for nonlinear response of the beam. In time domain, an oscilloscope is used to investigate the phase difference between the planar and nonplanar motions and to perform Torus analysis in the phase space. Through those analyzing process, the main frequencies of superharmonic, subharmonic, and super-subharmonic motions are investigated in the nonplanar motion due to one-to-one resonance. Analyzing the phase difference between the planar and nonplanar motions, it is observed that the phase difference varies in time.

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Nonlinear and nonclassical vibration analysis of double walled piezoelectric cylindrical nanoshell

  • Kachapi, Sayyid H. Hashemi
    • Advances in nano research
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    • v.9 no.4
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    • pp.277-294
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    • 2020
  • In current paper, nonlocal (NLT), nonlocal strain gradient (NSGT) and Gurtin-Murdoch surface/interface (GMSIT) theories with classical theory (CT) are utilized to investigate vibration and stability analysis of Double Walled Piezoelectric Nanosensor (DWPENS) based on cylindrical nanoshell. DWPENS simultaneously subjected to direct electrostatic voltage DC and harmonic excitations, structural damping, two piezoelectric layers and also nonlinear van der Waals force. For this purpose, Hamilton's principle, Galerkin technique, complex averaging and with arc-length continuation methods are used to analyze nonlinear behavior of DWPENS. For this work, three nonclassical theories compared with classical theory CT to investigate Dimensionless Natural Frequency (DNF), pull-in voltage, nonlinear frequency response and stability analysis of the DWPENS considering the nonlocal, material length scale, surface/interface (S/I) effects, electrostatic and harmonic excitation.