• Title/Summary/Keyword: multiple scales

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A multiple scales method solution for the free and forced nonlinear transverse vibrations of rectangular plates

  • Shooshtari, A.;Khadem, S.E.
    • Structural Engineering and Mechanics
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    • v.24 no.5
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    • pp.543-560
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    • 2006
  • In this paper, first, the equations of motion for a rectangular isotropic plate have been derived. This derivation is based on the Von Karmann theory and the effects of shear deformation have been considered. Introducing an Airy stress function, the equations of motion have been transformed to a nonlinear coupled equation. Using Galerkin method, this equation has been separated into position and time functions. By means of the dimensional analysis, it is shown that the orders of magnitude for nonlinear terms are small with respect to linear terms. The Multiple Scales Method has been applied to the equation of motion in the forced vibration and free vibration cases and closed-form relations for the nonlinear natural frequencies, displacement and frequency response of the plate have been derived. The obtained results in comparison with numerical methods are in good agreements. Using the obtained relation, the effects of initial displacement, thickness and dimensions of the plate on the nonlinear natural frequencies and displacements have been investigated. These results are valid for a special range of the ratio of thickness to dimensions of the plate, which is a characteristic of the Multiple Scales Method. In the forced vibration case, the frequency response equation for the primary resonance condition is calculated and the effects of various parameters on the frequency response of system have been studied.

Reliability and Validity of the Korean Version of the Copenhagen Psyco-social Questionnaire Scale (한국어판 코펜하겐 사회심리적 업무환경 측정도구의 타당도와 신뢰도)

  • June, Kyung Ja;Choi, Eun Suk
    • Korean Journal of Occupational Health Nursing
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    • v.22 no.1
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    • pp.1-12
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    • 2013
  • Purpose: This study aims to test the validity and criteria-related reliability of the Korean version of the Copenhagen Psyco-social Questionnaire version II (COPSOQ-K) assessing the psychosocial working environment. Methods: The COPSOQ-K was developed through forward-backward translation techniques, and revision based on feedback from focus groups. Survey data were collected from 311 office workers who worked in one workplace. An internal consistency reliability was estimated by Cronbach's ${\alpha}$. The impacts of the COPSOQ-K scales on job satisfaction, self-rated health, stress, sleeping troubles, burnout, and sickness absence were analyzed with multiple regression model or multiple logistic regression model, adjusted age and gender using SAS version 9.3. The Pearson correlation coefficients between the COPSOQ-K scales and Korean job stress and its subdomain were identified. Results: Cronbach's ${\alpha}$ of COPSOQ-K scales was adequate or good (0.66~0.87). The major COPSOQ-K scales predict job satisfaction, self-rated health, stress, sleeping troubles burnout, and sickness absence. The major COPSOQ-K scales were correlated with Korean job stress and its subdomain. Conclusion: The COPSOQ-K scales have satisfactory reliability and criteria-related validity. The COPSOQ-K scales will be useful for the future studies and practices associated with psychosocial working environment.

Dynamic Analysis of Harmonically Excited Non-Linear System Using Multiple Scales Method

  • Moon, Byung-Young;Kang, Beom-Soo
    • Journal of Mechanical Science and Technology
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    • v.16 no.6
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    • pp.819-828
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    • 2002
  • An analytical method is presented for evaluation of the steady state periodic behavior of nonlinear systems. This method is based on the substructure synthesis formulation and a MS (multiple scales) procedure, which is applied to the analysis of nonlinear responses. The proposed procedure reduces the size of large degrees-of-freedom problem in solving nonlinear equations. Feasibility and advantages of the proposed method are illustrated with the nonlinear rotating machine system as an example of large mechanical structure systems. In addition, its efficiency for nonlinear response prediction will be shown by comparison of other conventional methods.

Vibration analysis of a beam on a nonlinear elastic foundation

  • Karahan, M.M. Fatih;Pakdemirli, Mehmet
    • Structural Engineering and Mechanics
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    • v.62 no.2
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    • pp.171-178
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    • 2017
  • Nonlinear vibrations of an Euler-Bernoulli beam resting on a nonlinear elastic foundation are discussed. In search of approximate analytical solutions, the classical multiple scales (MS) and the multiple scales Lindstedt Poincare (MSLP) methods are used. The case of primary resonance is investigated. Amplitude and phase modulation equations are obtained. Steady state solutions are considered. Frequency response curves obtained by both methods are contrasted with each other with respect to the effect of various physical parameters. For weakly nonlinear systems, MS and MSLP solutions are in good agreement. For strong hardening nonlinearities, MSLP solutions exhibit the usual jump phenomena whereas MS solutions are not reliable producing backward curves which are unphysical.

Near-resonant attitude motion analysis of a spinning satellite via multiple scales method

  • Kang, Ja-Young
    • 제어로봇시스템학회:학술대회논문집
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    • 1994.10a
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    • pp.213-217
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    • 1994
  • The attitude stability of a satellite in spin-stabilized injection mode which contains a liquid pool is investigated. The satellite model for investigation is a two-body system consisting of a the main body, which is symmetric and rigid, representing the spacecraft, and a spherical pendulum, representing the liquid pool. Assuming that both spacecraft and pendulum are in states of steady spin about the symmetry axis of the spacecraft, the coupled nonlinear equations of motion for the system are simplified. In this paper, by using the multiple scales method, the possible resonance conditions in terms of the system parameters are determined and the corresponding near-resonant solutions are derived.

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Nonlinear vibrations of axially moving beams with multiple concentrated masses Part I: primary resonance

  • Sarigul, M.;Boyaci, H.
    • Structural Engineering and Mechanics
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    • v.36 no.2
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    • pp.149-163
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    • 2010
  • Transverse vibrations of axially moving beams with multiple concentrated masses have been investigated. It is assumed that the beam is of Euler-Bernoulli type, and both ends of it have simply supports. Concentrated masses are equally distributed on the beam. This system is formulated mathematically and then sought to find out approximately solutions of the problem. Method of multiple scales has been used. It is assumed that axial velocity of the beam is harmonically varying around a mean-constant velocity. In case of primary resonance, an analytical solution is derived. Then, the effects of both magnitude and number of the concentrated masses on nonlinear vibrations are investigated numerically in detail.

High performance ultrafine-grained Ti-Fe-based alloys with multiple length-scale phases

  • Zhang, Lai-Chang
    • Advances in materials Research
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    • v.1 no.1
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    • pp.13-29
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    • 2012
  • In order to simultaneously enhance the strength and plasticity in nanostructured / ultrafine-grained alloys, a strategy of introducing multiple length scales into microstructure (or called bimodal composite microstructure) has been developed recently. This paper presents a brief overview of the alloy developement and the mechanical behavior of ultrafine-grained Ti-Fe-based alloys with different length-scale phases, i.e., micrometer-sized primary phases (dendrites or eutectic) embedded in an ultrafine-grained eutectic matrix. These ultrafine-grained titanium bimodal composites could be directly obtained through a simple single-step solidification process. The as-prepared composites exhibit superior mechanical properties, including high strength of 2000-2700 MPa, large plasticity up to 15-20% and high specific strength. Plastic deformation of the ultrafine-grained titanium bimodal composites occurs through a combination of dislocation-based slip in the nano-/ultrafine scale matrix and constraint multiple shear banding around the micrometer-sized primary phase. The microstructural charactersitcs associated to the mechanical behaivor have been detailed discussed.

A Theoretical Study on the Measurement of User Information Satisfaction on the Information System (정보시스템 이용자의 정보만족도 측정에 관한 이론적 고찰)

  • Ahn, Sang-Keun;Choi, Min-Ho;Kim, Sung-Soo
    • Journal of Agricultural Extension & Community Development
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    • v.4 no.1
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    • pp.201-209
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    • 1997
  • The objective of this study were 1) to review concepts of user information satisfaction (UIS), 2) to analyze tools for measuring user information satisfaction, 3) to identify factors affecting information satisfaction. The study was carried out by the analysis of literatures related to information system. The construct of UIS has been operationalized in many different ways. Several studies employed single-item rating scales; such scales have been criticized as unreliable. Single-item scales also provide little information as to what the user finds dissatisfying(satisfying) and are thus of limited utility outside a research setting. Multiple-item UIS measures have become increasingly common. Generally, they are of two types. The first focuses on the information system product. With such diverse names as "system acceptance", "output quality", and "appreciation", these scales focus on the content of the information system and the manner in which the information is presented. The second type of multiple-item scale includes the organizational support for developing and maintaining the system as well as the system product itself. This type of instrument contains items concerned with training, documentation, development procedures, systems maintenance, etc., as well as items related to system content. Thus it provides an indicator of the overall quality of information services provided by an information service function. Generally, UIS measures have not been carefully validated. Recently, however, several rigorous attempts have been made to develop valid and reliable UIS measure.

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Validity of the Multiple Intelligence Scales for Young Korean Children (부모-교사용 유아 간편 다중지능척도 타당화 연구)

  • Lee, Chae-Ho;Choe, In-Soo
    • Journal of Gifted/Talented Education
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    • v.21 no.2
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    • pp.449-463
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    • 2011
  • The purpose of this study was to examine the validity of Multiple Intelligence Scales for Young Korean Children (MIS-YKC). Participants of this study were 357 children's parents and teachers from Seoul, Gyeongdo, Jeonlado & Choongchungdo. Data were analyzed by confirmatory factor analysis, Pearson's r and Cronbach's ${\alpha}$. Results are as follows. (1) Confirmatory factor analysis of MIS-YKC for parents MIS-YKC revealed that fit indices such as $X^2$=365.712 (df=168, p=.000), RMSEA=.057, SRMR=.047, NNFI=.935, CFI=.948. and MIS-KYC by teacher's evaluation $X^2$=436.765 (df=168, p=.000), RMSEA=.066, SRMR=.051, NNFI=.917, CFI=.934. (2) Correlations between multiple intelligence scales and IQ were significant. (3) Cronbach's ${\alpha}$ ranged from .80 and .86 for seven intelligence scales and .95 for the total scale by parents' evaluation. Cronbach's ${\alpha}$ is ranged from .76 and .91 for seven intelligence scales and .95 for the total scale by teacher's evaluation. All these results show that the multiple intelligence scales for young Korean children parents and teachers are quite reliable and valid.

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
    • Journal of KSNVE
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    • v.7 no.1
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    • pp.55-60
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    • 1997
  • 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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