• Title/Summary/Keyword: eigenvalue problem.

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Three-Dimensional Vibration Analysis of Deep, Nonlinearly Tapered Rods and Beams with Circular Cross-Section (원형단면의 깊은 비선형 테이퍼 봉과 보의 3차원 진동해석)

  • 심현주;강재훈
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.16 no.3
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    • pp.251-260
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    • 2003
  • A three dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of deep, tapered rods and beams with circular cross section. Unlike conventional rod and beam theories, which are mathematically one-dimensional (1-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components u/sup r/, u/sub θ/ and u/sub z/, in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in , and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the rods and beams are formulated, the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the rods and beams. Novel numerical results are tabulated for nine different tapered rods and beams with linear, quadratic, and cubic variations of radial thickness in the axial direction using the 3D theory. Comparisons are also made with results for linearly tapered beams from 1-D classical Euler-Bernoulli beam theory.

Three Dimensional Vibration Analysis of Thick, Circular and Annular Plates with Nonlinear Thickness Variation (비선형 두께 변분을 갖는 두꺼운 원형판과 환형판의 3차원적 진동해석)

  • 장승환;심현주;강재훈
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.17 no.2
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    • pp.119-129
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    • 2004
  • A three dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, circular and annular plates with nonlinear thickness variation along the radial direction. Unlike conventional plate theories, which are mathematically two dimensional (2D), the present method is based upon the 3D dynamic equations of elasticity. Displacement components u/sub s/, u/sub z/, and u/sub θ/ in the radial, thickness, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the s and z directions. Potential (strain) and kinetic energies of the plates are formulated, and the Ritz method is used to solve the eigenvalue problem thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four digit exactitude is demonstrated for the first five frequencies of the plates. Numerical results we presented for completely free, annular and circular plates with uniform linear, and quadratic variations in thickness. Comparisons are also made between results obtained from the present 3D and previously published thin plate (2D) data.

Vibration Analysis of Thick Hyperboloidal Shells of Revolution from a Three-Dimensional Analysis (두꺼운 축대칭 쌍곡형 쉘의 3차원 진동해석)

  • 심현주;강재훈
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.16 no.4
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    • pp.419-429
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    • 2003
  • A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of thick, hyperboloidal shells of revolution. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components u/sub r/, u/sub θ/, u/sub z/ in the radial, circumferential, and axial directions, respectively, we taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the r and z directions. Potential(strain) and kinetic energies of the hyperboloidal shells are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four digit exactitude is demonstrated for the first five frequencies of the hyperboloidal shells of revolution. Numerical results are tabulated for eighteen configurations of completely free hyperboloidal shells of revolution having two different shell thickness ratios, three variant axis ratios, and three types of shell height ratios. Poisson's ratio (ν) is fixed at 0.3. Comparisons we made among the frequencies for these hyperboloidal shells and ones which ate cylindrical or nearly cylindrical( small meridional curvature. ) The method is applicable to thin hyperboloidal shells, as well as thick and very thick ones.

Critical Elastic Buckling Load Investigation of Aluminium Alloy A6082-T6 Square plate Subjected to Patch Loading (패치 로딩을 받는 알루미늄 합금 A6082-T6 사각형 판의 임계 탄성좌굴하중 검토)

  • Oh, Young-Cheol;Ko, Jae-Yong
    • Journal of the Korean Society of Marine Environment & Safety
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    • v.20 no.4
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    • pp.451-460
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    • 2014
  • In this paper, we examined the problem of the structural stability according to the patch load of a rectangular plate that reflects the material properties of A6082-T6 is used primarily for marine plant structure. it applied to the four patch loading shapes, the effect of aspect ratio, a boundary condition and calculated the critical elastic buckling load. Calculating the critical elastic buckling load, During the eigenvalue buckling analysis it is applied to the shell181 as 4 node shell element. when the plate subjected to patch loading compare to the plate under a uniform axial compression load, it is possible observed to occur the different elastic buckling behaviour and it could be confirmed that it is affected significantly on a variable position and type of loadings, such as the effect of the aspect ratio. Also, Critical elastic buckling load according to th patch loading type in simply supported rectangular plate a/b=1.0, ${\gamma}b$=200mm are calculated 67%(Loading type I), 119 %(Loading type II), 76 %(Loading type III), 160 %(Loading type IV), respectively. Loading type I and III could be determined with the strong elastic buckling behavior much more than Loading type II and IV.

Topology Design Optimization of Plate Buckling Problems Considering Buckling Performance (좌굴성능을 고려한 평판 좌굴문제의 위상설계최적화)

  • Lee, Seung-Wook;Ahn, Seung-Ho;Cho, Seonho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.28 no.5
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    • pp.441-449
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    • 2015
  • In this paper we perform a linearized buckling analysis using the Kirchhoff plate theory and the von Karman nonlinear strain-displacement relation. Design sensitivity analysis(DSA) expressions for plane elasticity and buckling problems are derived with respect to Young's modulus and thickness. Using the design sensitivity, we can formulate the topology optimization method for minimizing the compliance and maximizing eigenvalues. We develop a topology optimization method applicable to plate buckling problems using the prestress for buckling analysis. Since the prestress is needed to assemble the stress matrix for buckling problem using the von Karman nonlinear strain, we introduced out-of-plane motion. The design variables are parameterized into normalized bulk material densities. The objective functions are the minimum compliance and the maximum eigenvalues and the constraint is the allowable volume. Through several numerical examples, the developed DSA method is verified to yield very accurate sensitivity results compared with the finite difference ones and the topology optimization yields physically meaningful results.

Free Vibration Analysis of Horizontally Curved I-Girder Bridges using the Finite Element Method (유한요소법을 이용한 수평곡선 I형교의 자유진동해석)

  • Yoon, Ki Yong;Kang, Young Jong
    • Journal of Korean Society of Steel Construction
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    • v.10 no.1 s.34
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    • pp.47-61
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    • 1998
  • The behavior of horizontally curved I-girder bridges is complex because the flexural and torsional behavior of curved girders are coupled due to their initial curvature. Also, the behavior is affected by cross beams. To investigate the behavior of horizontally curved I-girder bridges, it is necessary to consider curved girders with cross beams. In order to perform free vibration analyses of horizontally curved I-girder bridges, a finite element formulation is presented here and a finite element analysis program is developed. The formulation that is presented here consists of curved and straight beam elements, including the warping degree of freedom. Based on the theory of thin-walled curved beams, the shape functions of the curved beam elements are derived from homogeneous solutions of the static equilibrium equations. Third-order hermits polynomials are used to form the shape functions of the straight beam elements. In the finite element analysis program, global stiffness and mass matrix are composed, based on the Cartesian coordinate system. The Gupta method is used to efficiently solve the eigenvalue problem. Comparing the results of several examples here with those of previous studies, the formulation presented is verified. The validity of the program developed is shown by comparing results with those analyzed by the shell element.

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Application of a Fictitious Axial Force Factor to Determine Elastic and Inelastic Effective Lengths for Column Members of Steel Frames (강프레임 기둥 부재의 탄성 및 비탄성 유효좌굴길이 산정을 위한 가상축력계수의 적용)

  • Choi, Dong Ho;Yoo, Hoon;Lee, Yoon Seok
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.30 no.2A
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    • pp.81-92
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    • 2010
  • In design of steel frames, it is generally believed that elastic system buckling analysis cannot predict real behaviors of structures, while inelastic system buckling analysis can give informative buckling behaviors of individual members considering inelastic material behavior. However, the use of Euler buckling equation with these system buckling analyses have the inherent problem that the methods evaluate unexpectedly large effective lengths of members having relatively small axial forces. This paper proposes a new method of obtaining elastic and inelastic effective lengths of all members in steel frames. Considering a fictitious axial force factor for each story of frames, the proposed method determines the effective lengths using the inelastic stiffness reduction factor and the iterative eigenvalue analysis. In order to verify the validity of the proposed method, the effective lengths of example frames by the proposed method were compared to those of previously established methods. As a result, the proposed method gives reasonable effective lengths of all members in steel frames. The effect of inelastic material behavior on the effective lengths of members was also discussed.

The Development of the Korean Form of Childhood Attention Problem(CAP) Scale: A Study on the Reliability and Validity (한국형 소아기 집중력 문제척도: 신뢰도 및 타당도 연구)

  • Seo, Wan-Seok;Lee, Jong-Bum;Park, Hyung-Bae;Suh, Hyea-Soo;Lee, Kwang-Hun;SaKong, Jeong-Kyu
    • Journal of Yeungnam Medical Science
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    • v.14 no.1
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    • pp.123-136
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    • 1997
  • The purpose of this study was to examine the reliability and validity of a Korean form of Childhood Attention Problem(CAP) scale. CAP were administered to 98 normal elementary school students as control group and 98 attention deficit hyperactivity disorder patients. Male students showed high scores than female students in both subscale and total scores, but not statistically significant. There were no significant difference in CAP scale between male students and female students in attention deficit hyperactivity disorder patients. In the reliability test, the test-retest reliability coefficient was highly satisfactory and that of inattention subscale was 0.83, impulsivity subscale was 0.70 and total score was 0.82. In the reliability test by internal consistency, the Cronbach $\alpha$ coefficient was highly satisfactory and that of inattention subscale was 0.91, overactivity subscale was 0.89(p<0.05). The concurrent validity between CAP scale and ADDES-BV scale was 0.85 in attention deficit hyperactivity disorder patient group and 0.73 in normal control group(p<0.05). In discriminant validity test between attention deficit hyperactivity disorder patient group and normal control group, the patient group showed higher score(p<0.05). The total discriminant capacity of the patient group in CAP was 93.4%. In this point of view, CAP scale showed high reliability and validity in applying to Korean subjects and was proved to be the good and simple screening test tool for attention deficit hyperactivity disorder research and can help many young patient to treat early.

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A Study on Qulity Perceptions and Satisfaction for Medical Service Marketing (의료서비스 마케팅을 위한 품질지각과 만족에 관한 연구)

  • Yoo, Dong-Keun
    • Journal of Korean Academy of Nursing Administration
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    • v.2 no.1
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    • pp.97-114
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    • 1996
  • INSTRODUCTION Service quality is, unlike goods quality, an abstract and elusive constuct. Service quality and its requirements are not easily understood by consumers, and also present some critical research problems. However, quality is very important to marketers and consumers in that it has many strategic benefits in contributing to profitability of marketing activities and consumers' problem-solving activities. Moreover, despite the phenomenal growth of medical service sector, few researchers have attempted to define and model medical service quality. Especially, little research has focused on the evaluation of medical service quality and patient satisfaction from the perspectives of both the provider and the patient. As competition intensifies and patients are demanding higher quality of medical service, medical service quality and patient satisfaction has emerged as a critical research topic. The major purpose of this article is to explore the concept of medical service quality and its evaluation from both nurse and patient perspectives. This article attempts to achieve its purpose by (1)classfying critical service attibutes into threecategories(satisfiers, hygiene factors, and performance factors). (2)measuring the relative importance of need criteria, (3)evaluating SERVPERF model and SERVQUAL model in medical service sector, and (4)identifying the relationship between perceived quality and overall patient satisfaction. METHOD Data were gathered from a sample of 217 patients and 179 nurses in Seoul-area general hospitals. From the review of previous literature, 50 survey items representing various facets of the medical service quality were developed to form a questionnaire. A five-point scale ranging from "Strongly Agree"(5) to "Strongly Disagree"(1) accompanied each statement(expectation statements, perception statements, and importance statements). To measure overall satisfaction, a seven-point scale was used, ranging from "Very Satisfied"(7) to "Very Dissatisfied"(1) with no verbal labels for scale points 2 through 6 RESULTS In explaining the relationship between perceived performance and overall satisfaction, only 31 variables out of original 50 survey items were proven to be statistically significant. Hence, a penalty-reward analysis was performed on theses 31 critical attributes to find out 17 satisfiers, 8 hygiene factors, and 4 performance factors in patient perspective. The role(category) of each service quality attribute in relation to patient satisfaction was com pared across two groups, that is, patients and nurses. They were little overlapped, suggesting that two groups had different sets of 'perceived quality' attributes. Principal components factor analyses of the patients' and nurses' responses were performed to identify the underlying dimensions for the set of performance(experience) statements. 28 variables were analyzed by using a varimax rotation after deleting three obscure variables. The number of factors to be extracted was determined by evaluating the eigenvalue scores. Six factors wereextracted, accounting for 57.1% of the total variance. Reliability analysis was performed to refine the factors further. Using coefficient alpha, scores of .84 to .65 were obtained. Individual-item analysis indicated that all statements in each of the factors should remain. On 26 attributes of 31 critical service quality attributes, there were gaps between actual patient's importance of need criteria and nurse perceptions of them. Those critical attributes could be classified into four categories based on the relative importance of need criteria and perceived performance from the perspective of patient. This analysis is useful in developing strategic plans for performance improvement. (1) top priorities(high importance and low performance) (in this study)- more health-related information -accuracy in billing - quality of food - appointments at my convenience - information about tests and treatments - prompt service of business office -adequacy of accommodations(elevators, etc) (2) current strengths(high importance and high performance) (3)unnecessary strengths(low importance and high performance) (4) low priorities(low importance and low performance) While 26 service quality attributes of SERPERF model were significantly related to patient satisfation, only 13 attributes of SERVQUAL model were significantly related. This result suggested that only experience-based norms(SERVPERF model) were more appropriate than expectations to serve as a benchmark against which service experiences were compared(SERVQUAL model). However, it must be noted that the degree of association to overall satisfaction was not consistent. There were some gaps between nurse percetions and patient perception of medical service performance. From the patient's viewpoint, "personal likability", "technical skill/trust", and "cares about me" were most significant positioning factors that contributed patient satisfaction. DISCUSSION This study shows that there are inconsistencies between nurse perceptions and patient perceptions of medical service attributes. Also, for service quality improvement, it is most important for nurses to understand what satisfiers, hygiene factors, and performance factors are through two-way communications. Patient satisfaction should be measured, and problems identified should be resolved for survival in intense competitive market conditions. Hence, patient satisfaction monitoring is now becoming a standard marketing tool for healthcare providers and its role is expected to increase.

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