• Title/Summary/Keyword: multiple scales method

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Combination resonance analysis of FG porous cylindrical shell under two-term excitation

  • Ahmadi, Habib;Foroutan, Kamran
    • Steel and Composite Structures
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    • v.32 no.2
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    • pp.253-264
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    • 2019
  • This paper presents the combination resonances of FG porous (FGP) cylindrical shell under two-term excitation. The effect of structural damping on the system response is also considered. With regard to classical plate theory of shells, von-$K{\acute{a}}rm{\acute{a}}n$ equation and Hook law, the relations of stress-strain is derived for shell. According to the Galerkin method, the discretized motion equation is obtained. The combination resonances are obtained by using the method of multiple scales. Four types of FGP distributions consist of uniform porosity, non-symmetric porosity soft, non-symmetric porosity stiff and symmetric porosity distribution are considered. The influence of various porosity distributions, porosity coefficients of cylindrical shell and amplitude excitations on the combination resonances for FGP cylindrical shells is investigated.

Nonlinear forced vibration of sandwich plate with considering FG core and CNTs reinforced nano-composite face sheets

  • Rostami, Rasoul;Rahaghi, Mohsen Irani;Mohammadimehr, Mehdi
    • Smart Structures and Systems
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    • v.26 no.2
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    • pp.185-193
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    • 2020
  • Nonlinear vibration of sandwich plate with functionally graded material (FGM) core and carbon nano tubes reinforced (CNTs) nano-composite layers by considering temperature-dependent material properties are studied in this paper. Base on Classical plate theory (CPT), the governing partial differential equations of motion for sandwich plate are derived using Hamilton principle. The Galerkin procedure and multiple scales perturbation method are used to find relation between nonlinear frequency and amplitude of vibration response. The dynamic responses of the sandwich plate are also investigated in both time and frequency domains. Then, the effects of nonlinearity, excitation, power law index of FG core, volume fraction of carbon nanotube, the function of material variations of FG core, temperature changes, scale transformation parameter and damping factor on the frequency responses are investigated.

Steady-state Vibration Responses of a Beam with a Nonlinear Boundary Condition (비선형 경계조건을 가진 보의 정상상태 진동응답)

  • Lee, Won-Kyoung;Yeo, Myeong-Hwan
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.21 no.2
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    • pp.337-345
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    • 1997
  • An analysis is presented for the response of a beam constrained by a nonlinear spring to a harmonic excitation. The system is governed by a linear partial differential equation with a nonlinear boundary condition. The method of multiple scales is used to reduce the nonlinear boundary value problem to a system of autonomous ordinary differential equations of the amplitudes and phases. The case of the third-order subharmonic resonance is considered in this study. The autonomous system is used to determine the steady-state responses and their stability.

Active Nonlinear Vibration Absorber for a Nonlinear System with a Time Delay Acceleration Feedback under the Internal Resonance, Subharmonic, Superharmonic and Principal Parametric Resonance Conditions Simultaneously

  • Mohanty, S;Dwivedy, SK
    • Journal of Aerospace System Engineering
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    • v.13 no.5
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    • pp.9-15
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    • 2019
  • In this paper, dynamic analysis of a nonlinear active vibration absorber is conducted with a time delay acceleration feedback to suppress the vibration of a nonlinear single degree of freedom primary system. The primary system consisting of linear and nonlinear cubic springs, mass, and damper is subjected to the multi-harmonic hard excitation with a parametric excitation. It is proposed to reduce the vibration of the primary system and the absorber by using a lead zirconate titanate (PZT) stack actuator in series with a spring in the absorber which configures as an active vibration absorber. The method of multiple scales (MMS) is used to obtain the approximate solution of the system under the internal resonance, subharmonic, superharmonic, and principal parametric resonance conditions simultaneously. Frequency and time responses of the system are investigated considering a delay in the feedback for the various parameters of the absorber configuration and controlling force.

Large deformations of a flexural frame under nonlinear P-delta effects

  • Afshar, Dana;Afshar, Majid Amin
    • Earthquakes and Structures
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    • v.22 no.5
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    • pp.517-526
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    • 2022
  • In this paper, nonlinear P-delta effects are studied on the seismic performance, and the modal responses of a flexural frame, considering large deformations. Using multiple scales method, the nonlinear differential equations of motion are estimated, and the nonlinear interactions between the frame's degrees of freedom are outcropped. The results of time and frequency domain analyzes of a dynamic model are examined under internal resonance cases, and the linear and nonlinear responses are investigated in each modal cases. Also, changing the modal responses with respect to the amplitude and frequency of the harmonic forces is evaluated. It is shown that the dominant absorption of energy is in the first natural frequency of the frame, in the case of earthquake excitation, and when a harmonic force is applied to the frame, the peaks of the frequency domain responses depending on the frequency of harmonic force are in the first, and second or third natural frequency of the structure.

Nonlinear vibration and primary resonance of multilayer functionally graded shallow shells with porous core

  • Kamran Foroutan;Liming Dai
    • Steel and Composite Structures
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    • v.48 no.3
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    • pp.335-351
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    • 2023
  • This research studies the primary resonance and nonlinear vibratory responses of multilayer functionally graded shallow (MFGS) shells under external excitations. The shells considered with functionally graded porous (FGP) core and resting on two types of nonlinear viscoelastic foundations (NVEF) governed by either a linear model with two parameters of Winkler and Pasternak foundations or a nonlinear model of hardening/softening cubic stiffness augmented by a Kelvin-Voigt viscoelastic model. The shells considered have three layers, sandwiched by functionally graded (FG), FGP, and FG materials. To investigate the influence of various porosity distributions, two types of FGP middle layer cores are considered. With the first-order shear deformation theory (FSDT), Hooke's law, and von-Kármán equation, the stress-strain relations for the MFGS shells with FGP core are developed. The governing equations of the shells are consequently derived. For the sake of higher accuracy and reliability, the P-T method is implemented in numerically analyzing the vibration, and the method of multiple scales (MMS) as one of the perturbation methods is used to investigate the primary resonance. The results of the present research are verified with the results available in the literature. The analytical results are compared with the P-T method. The influences of material, geometry, and nonlinear viscoelastic foundation parameters on the responses of the shells are illustrated.

Validity of the Multiple Scale Solution for a Resonance Response of a Bar with a Nonlinear Boundary Condition (비선형 경계조건을 가진 봉의 공진응답을 위한 다중시간해의 타당성)

  • 이원경;여명환;배상수
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 1996.10a
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    • pp.275-281
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    • 1996
  • In order to examine the validity of an asymptotic solution obtained from the method of multiple scales, we investigate a third-order subharmonic resonance response of a bar constrained by a nonlinear spring to a harmonic excitation. The motion of the bar is governed by a linear partial differential equation with a nonlinear boundary condition. The nonlinear boundary value problem is solved by using the finite difference method. The numerical solution is compared with the asymptotic solution.

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A Study on the Response to Psychiatric Self-Report Rating Scale (SCL-90) of Some Industrial Workers in Korea (일부 산업장 근로자의 간이정신진단 검사(SCL-90)결과에 관한 연구)

  • Choi, Jung-Ae
    • Journal of Preventive Medicine and Public Health
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    • v.15 no.1
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    • pp.219-228
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    • 1982
  • This study aimed at assessing the industrial workers' mental health status and identifing the relationship between mental health status and socio-demographic variables. We administered psychiatric self report rating scale (SCL-90)to 622 manual workers and 191 office workers in a textile .industry. The study began on 1 November, 1981 and lasted for 30 days The results were as follow: 1. Scores of symptom dimension were higher in female rather than male, younger than older, lower income group than higher one, lower educated group than higher one, manual workers than office workers and unmarried group than married one respectively. 2. The result of dimension scores of total samples showed that the score of Obsessive-compulsive scale was highest. The rest symptom dimension showed the order as follows: Interpersonal sensitivity, Depression, Hostility, Anxiety, Paranoid ideation, Somatization, Psychoticism and Phobic anxiety. 3. In order to identify the partial contribution of each socio-demographic variables on the mental health, multiple regression method was applied, and the result was as follows. 1) Sex was the most important one to explain the Somatization, Phobic-anxiety and Psychoticism scales among the 7 variables in the multiple regression equation. 2) Economic status was the most important variable to explein the Obsessive-compulsive, Depression and Hostility scales. 3) Marital status was the most important variable to explain the Interpersonal-sensitivity and Paranoid ideation scales.

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ANTI-PERIODIC SOLUTIONS FOR BAM NEURAL NETWORKS WITH MULTIPLE DELAYS ON TIME SCALES

  • Shu, Jiangye;Li, Yongkun
    • Journal of applied mathematics & informatics
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    • v.29 no.1_2
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    • pp.279-292
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    • 2011
  • In this paper, we consider anti-periodic solutions of the following BAM neural networks with multiple delays on time scales: $$\{{x^\Delta_i(t)=-a_i(t)e_i(x_i(t))+{\sum\limits^m_{j=1}}c_{ji}(t)f_j(y_j(t-{\tau}_{ji}))+I_i(t),\atop y^\Delta_j(t)=-b_j(t)h_j(y_j(t))+{\sum\limits^n_{i=1}}d_{ij}(t)g_i(x_i(t-{\delta}_{ij}))+J_j(t),}\$$ where i = 1, 2, ..., n,j = 1, 2, ..., m. Using some analysis skills and Lyapunov method, some sufficient conditions on the existence and exponential stability of the anti-periodic solution to the above system are established.