Chaotic Oscillations of a Post-Buckled Beam Constrained by an Axial Spring: Part 2 — Analysis

2004 ◽  
Author(s):  
Shinichi Maruyama ◽  
Ken-ichi Nagai ◽  
Takao Yamaguchi ◽  
Kazuaki Hoshi
Keyword(s):  
Principal Component Analysis ◽  
Lyapunov Exponent ◽  
Principal Component ◽  
Component Analysis ◽  
Degree Of Freedom ◽  
Chaotic Oscillations ◽  
Harmonic Response ◽  
Chaotic Response ◽  
Buckled Beam ◽  
Modes Of Vibration

To compare with corresponding experiment, analytical results are presented on chaotic oscillations of a post-buckled beam constrained by an axial spring. The beam with an initial deflection is clamped at both ends. The beam is compressed to a post-buckled configuration by the axial spring. Then, the beam is subjected to both accelerations of gravity and periodic lateral excitation. Basic equations of motion includes geometrical nonlinearity of deflection and in-plane displacement. Applying the Galerkin procedure to the basic equation and using the mode shape function proposed by the author, a set of nonlinear ordinary differential equations is obtained with a multiple-degree-of-freedom system. Linear natural frequency due to the axial compression and restoring force of the post-buckled beam are obtained. Next, periodic responses of the beam are inspected by the harmonic balance method. Chaotic responses are obtained by the numerical integration of the Runge-Kutta-Gill method. Chaotic time responses are inspected by the Fourier spectra, the Poincare´ projections, the maximum Lyapunov exponents. Contribution of the number of modes of vibration to the chaos is also discussed by the principal component analysis. Chaotic response is generated within the sub-harmonic resonance responses of 1/2 and 1/3 orders. The maximum Lyapunov exponent corresponded to the sub-harmonic response of 1/2 order is greater than that of the sub-harmonic response of 1/3 order. By the inspection of the Lyapunov exponent on the chaotic response and the analysis with the multiple-degree-of-freedom system, more than three modes of vibration contribute to the chaos. Using the principal component analysis to the chaotic responses at multiple positions of the beam, the lowest mode of vibration contributes dominantly. Higher modes of vibration contribute to the chaos with small amount of amplitude.

Chaotic Vibrations on a Coupled Vibrating System of a Post-Buckled Cantilevered Beam and an Axial Vibrating Body Connected With a Stretched String

2009 ◽  
Author(s):  
Shinichi Maruyama ◽  
Ken-ichi Nagai ◽  
Kota Muto ◽  
Takao Yamaguchi
Keyword(s):  
Principal Component Analysis ◽  
Vibration Mode ◽  
Harmonic Balance Method ◽  
Principal Component ◽  
Component Analysis ◽  
Axial Displacement ◽  
Chaotic Vibrations ◽  
Vibrating System ◽  
Chaotic Response ◽  
Cantilevered Beam

Analytical results are presented on chaotic vibrations on a coupled vibrating system of a post-buckled cantilevered beam and an axial vibrating body connected with a stretched string. The string is stretched between the top end of the cantilevered beam and the axial vibrating body which consists of a mass and a spring. As an initial axial displacement is applied to the spring, the beam is buckled by the tensile force of the string. The main scope of this paper is to investigate the effects of the axial inertia of the vibrating body on the chaotic vibrations of the system. The dynamical model involves nonlinear geometrical coupling between the deformation and the axial force of the beam at the boundary. Furthermore, the problem includes the static buckling and the nonlinear vibration. By using the mode shape function, which was proposed by the senior author, as a coordinate function of the governing equations, nonlinear ordinary differential equations in multiple-degree-of-freedom system are derived by the modified Galerkin procedure. Periodic responses of the beam are calculated with the harmonic balance method, while chaotic responses are integrated numerically. Chaotic time responses are inspected with the Fourier spectra, the Poincare´ projections, the maximum Lyapunov exponents and the principal component analysis. Chaotic responses are generated from the sub-harmonic resonance responses of 1/2 and 1/3 orders. The results of the principal component analysis shows that the lowest mode of vibration contributes to the chaotic response dominantly, while the second mode of vibration also contribute to the chaos with small amount of amplitude. Inspection of the kinetic energy of each vibration mode shows that the vibration mode with large axial displacement is also dominant in the chaotic response.

Chaotic Oscillations of a Post-Buckled Beam Constrained by an Axial Spring: Part 1 — Experiment

2004 ◽  
Author(s):  
Ken-ichi Nagai ◽  
Shinichi Maruyama ◽  
Kazuya Sakaimoto ◽  
Takao Yamaguchi
Keyword(s):  
Principal Component ◽  
Lateral Acceleration ◽  
Maximum Lyapunov Exponent ◽  
Chaotic Oscillations ◽  
Test Beam ◽  
Restoring Force ◽  
Concentrated Load ◽  
Chaotic Response ◽  
Buckled Beam ◽  
Exciting Frequency

Experimental results are presented on chaotic oscillations of a post-buckled beam subjected to periodic lateral acceleration. A thin steel beam of thickness 0.198mm, breath 12.7 mm and length 106mm is used as a test beam. Both ends of the beam are clamped and one end is connected to an axial spring. First, natural frequencies of the beam are measured under an axial compression. Under the post-buckled configuration of the beam, characteristics of static deflection by a concentrated load on the beam are obtained. The post-buckled beam shows the soften-and-hardening characteristics of restoring force. The frequency regions of chaotic responses are inspected. The chaotic responses around these domains are examined carefully by time histories, the Poincare´ maps, the Fourier spectra, the maximum Lyapunov exponents and the principal component analysis. The predominant chaotic responses of the beam are generated by the jump phenomena. The chaotic responses are related to the sub-harmonic resonances of 1/2 and 1/3 orders with the lowest mode of vibration. The maximum Lyapunov exponent of the former chaotic response of 1/2 order is larger than that of the latter chaotic response of 1/3 order. Onsets of the chaotic responses are also confirmed by the Poincare´ projection in the variation of exciting frequency.

A German version of the Intermittent Claudication Questionnaire (ICQ): cultural adaptation and validation

VASA ◽  
2012 ◽  
Vol 41 (5) ◽  
pp. 333-342 ◽  
Author(s):  
Kirchberger ◽  
Finger ◽  
Müller-Bühl
Keyword(s):  
Principal Component Analysis ◽  
Intermittent Claudication ◽  
Completion Time ◽  
Short Form ◽  
Principal Component ◽  
Component Analysis ◽  
German Version ◽  
Average Completion Time ◽  
Sf 36 ◽  
Related Quality

Background: The Intermittent Claudication Questionnaire (ICQ) is a short questionnaire for the assessment of health-related quality of life (HRQOL) in patients with intermittent claudication (IC). The objective of this study was to translate the ICQ into German and to investigate the psychometric properties of the German ICQ version in patients with IC. Patients and methods: The original English version was translated using a forward-backward method. The resulting German version was reviewed by the author of the original version and an experienced clinician. Finally, it was tested for clarity with 5 German patients with IC. A sample of 81 patients were administered the German ICQ. The sample consisted of 58.0 % male patients with a median age of 71 years and a median IC duration of 36 months. Test of feasibility included completeness of questionnaires, completion time, and ratings of clarity, length and relevance. Reliability was assessed through a retest in 13 patients at 14 days, and analysis of Cronbach’s alpha for internal consistency. Construct validity was investigated using principal component analysis. Concurrent validity was assessed by correlating the ICQ scores with the Short Form 36 Health Survey (SF-36) as well as clinical measures. Results: The ICQ was completely filled in by 73 subjects (90.1 %) with an average completion time of 6.3 minutes. Cronbach’s alpha coefficient reached 0.75. Intra-class correlation for test-retest reliability was r = 0.88. Principal component analysis resulted in a 3 factor solution. The first factor explained 51.5 of the total variation and all items had loadings of at least 0.65 on it. The ICQ was significantly associated with the SF-36 and treadmill-walking distances whereas no association was found for resting ABPI. Conclusions: The German version of the ICQ demonstrated good feasibility, satisfactory reliability and good validity. Responsiveness should be investigated in further validation studies.

Multifactorial analysis of clinical laboratory signs, the levels of IL-17A, IL-23, IL-33, IL-35, and specific antibodies in the serum of patients with Lyme borreliosis without erythema migrans

2020 ◽  
Vol 4 (11) ◽  
pp. 676-681
Author(s):  
V.V. Sapozhnikova ◽  
◽  
A.L. Bondarenko ◽  
Keyword(s):  
Principal Component Analysis ◽  
Lyme Borreliosis ◽  
Clinical Laboratory ◽  
Acute Infection ◽  
Erythema Migrans ◽  
Principal Component ◽  
Component Analysis ◽  
Control Group ◽  
Multifactorial Analysis ◽  
Specific Antibodies

Aim: to determine the association between clinical laboratory parameters, the production of cytokines (IL-17A, -23, -33, -35), and specific IgM and IgG in the serum of patients with Lyme borreliosis without erythema migrans. Patients and Methods: complete blood count, the concentrations of IL-17A, -23, -33, -35, and the levels of specific IgM and IgG were measured during acute infection and convalescence (n=30). The control group included age- and sex-matched healthy individuals (n=30). Statistical analysis was performed using the StatSoft Statistica v 10.0 software (parametric and non-parametric methods and multifactorial analysis, i.e., principal component analysis). Results: most (80%) patients with Lyme borreliosis without erythema migrans are the people of working age. In most patients, the combination of the specific antibodies against Borrelia afzelii and Borrelia garinii (76.7%) and severe intoxication and inflammatory process (100%) were detected. Moderate and severe disease associated with meningism was diagnosed in 90% and 10%, respectively. The mean duration of hectic period was 8.3±1.27 days. Abnormal ECG was reported in 40% of patients, i.e., conduction abnormalities in 20%, sinus bradycardia in 16.7%,and sinus tachycardia in 3.3%. The clinical laboratory signs of hepatitis without jaundice were identified in 26.7%. During treatment, the significant reduction in band and segmented neutrophil counts as well as the significant increase in platelet count were revealed compared to these parameters at admission. Abnormal cytokine levels (i.e., the increase in IL-17A, -23, -33 and the deficiency of IL-35) were detected. Conclusions: multifactorial analysis has demonstrated that the severity of immunological abnormalities in patients with Lyme borreliosis without erythema migrans is associated with fever, cardiac and liver disorders, the high levels of IL-23 and IL-33, and the lack of IL-35 and specific IgM and IgG. KEYWORDS: tick-borne borreliosis, Lyme disease without erythema migrans, clinical laboratory signs, cytokines, specific antibodies, multifactorial analysis, principal component analysis. FOR CITATION: Sapozhnikova V.V., Bondarenko A.L. Multifactorial analysis of clinical laboratory signs, the levels of IL-17A, IL-23, IL-33, IL-35, and specific antibodies in the serum of patients with Lyme borreliosis without erythema migrans. Russian Medical Inquiry. 2020;4(11):676–681. DOI: 10.32364/2587-6821-2020-4-11-676-681.

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