Nonlinear free vibration analysis of the functionally graded beams

Nonlinear natural oscillations of beams made from functionally graded material (FGM) are studied in this paper. The equation of motion is derived according to the EulerBernoulli beam theory and von Karman geometric nonlinearity. Subsequently, Galerkin’s solution technique is applied to obtain the corresponding ordinary differential equation (ODE) for the FGM beam. This equation represents a kind of a nonlinear ODE containing quadratic and cubic nonlinear terms. This nonlinear equation is then solved by means of three efficient approaches. Homotopy perturbation method is applied at the first stage and the corresponding frequency-amplitude relationship is obtained. Frequency-amplitude formulation and Harmonic balance method are then employed and the consequent frequency responses are determined. In addition, Parameter Expansion Method is utilized for evaluating the nonlinear vibration of the system. A parametric study is then conducted to evaluate the influence of the geometrical and mechanical properties of the FGM beam on its frequency responses. Different types of material properties and boundary conditions are taken into account and frequency responses of the system are evaluated for different gradient indexes. The frequency ratio (nonlinear to linear natural frequency) is obtained in terms of the initial amplitude and compared for different materials and end conditions

Declining incidence of esophageal cancer in the Turkmen Plain, eastern part of the Caspian Littoral of Iran: A retrospective cancer surveillance

Background: Previous studies have shown that upper gastrointestinal cancers are the most common cancers in Caspian Littoral, and rate of esophageal cancer (EC) in Iranian Turkmens residing in the Eastern part of littoral are among the highest in the world. Our aim was to reassess the rate 30 years later and following socioeconomic changes in the region. Methods: A comprehensive retrospective search was undertaken to find all new cancer cases during the 1996-2000 period. Diagnosis of cancer was based on histopathological reports in 68.2, clinical and/or radiological evidence in 29.7 and death certificate only (DCO) in 2.1 of the cases. Results: A total of 5143 new cancer cases were registered of whom 3063 (59.6) were males. The median (IQR) age was 60 (44-69) years. Age-standardized rates (ASR) for all cancers in males and females were 134.7 and 104.5 per 100,000, respectively. Based on ASR, the top five common cancers in males (excluding skin cancer) were cancers of esophagus (43.4), stomach (27.8), colorectal (10.7), bladder (7.8) and oral cavity (6.3), while in females cancer of esophagus (36.3) was followed by cancers of breast (15.7), stomach (8.3) colorectal (6.6) and cervix (3.6). Conclusion: We conclude that EC incidence rate has decreased to less than half the rate reported 30 years ago, while the incidence rates of colorectal and breast cancers have increased significantly. © 2006 International Society for Preventive Oncology. Published by Elsevier Ltd. All rights reserved

Analityczne rozwiązania problemu drgań swobodnych belek umieszczonych na sprężystym podłożu wyznaczone za pomocą iteracyjnej metody wariacyjnej

Closed form expressions are obtained for the dynamic response of an elastic beam rested on a nonlinear foundation in this paper. The nonlinear governing equation is solved using the Variational Iteration Method (VIM). An iteration formulation is constructed based on the VIM and the dynamic responses are then obtained. Frequency responses are presented in a closed form and their sensitivity with respect to the initial amplitudes are investigated. A number of numerical simulations are then carried out and performance and validity of the solution procedure is evaluated in the time domain. It is proved that the VIM is quite a reliable and straightforward technique to solve the corresponding set of coupled nonlinear differential equations.W pracy przedstawiono zamknięte formy rozwiązań opisujących odpowiedź dynamiczną elastycznej belki spoczywającej na nieliniowo sprężystym podłożu. Równanie ruchu rozwiązano przy pomocy iteracyjnej metody wariacyjnej (VIM). Sformułowanie iteracyjne skonstruowane w oparciu o tę metodę pozwoliło na wyznaczenie odpowiedzi dynamicznej belki. Charakterystyki częstościowe przedstawiono w zamkniętej formie i podkreślono ich wrażliwość na wartość amplitud początkowych. Następnie zaprezentowano wyniki kilku symulacji numerycznych w celu oszacowania wydajności i dokładności zastosowanej procedury rozwiązywania równań ruchu w dziedzinie czasu. Wykazano, że metoda VIM jest wystarczająco prosta i wiarygodna w rozwiązywaniu układu sprzężonych, nieliniowych równań różniczkowych

Analysis of nonlinear oscillations of a punctual charge in the electric field of a charged ring via a Hamiltonian approach and the energy balance method

WOS: 000292853300047The method of Hamiltonian approach and the energy balance method are applied to obtain the periodic solutions of nonlinear oscillations of a punctual charge in the electric field of charged ring. The obtained approximate frequencies are accurate for the entire range of oscillation amplitudes. A good agreement of the approximate frequencies and periodic solutions with the exact ones are demonstrated and discussed. It is also proved that the results of the energy balance method are better than the Hamiltonian approach for solving this equation.(C) 2011 Elsevier Ltd. All rights reserved

Higher order approximate periodic solutions for nonlinear oscillators with the Hamiltonian approach

WOS: 000294886000015In this work, the Hamiltonian approach is applied to obtain the natural frequency of the Duffing oscillator, the nonlinear oscillator with discontinuity and the quintic nonlinear oscillator. The Hamiltonian approach is then extended to the second and third orders to find more precise results. The accuracy of the results obtained is examined through time histories and error analyses for different values for the initial conditions. Excellent agreement of the approximate frequencies and the exact solution is demonstrated. It is shown that this method is powerful and accurate for solving nonlinear conservative oscillatory systems. (C) 2011 Elsevier Ltd. All rights reserved

Approximate periodic solutions for the Helmholtz-Duffing equation

WOS: 000297140300022Approximate periodic solutions for the Helmholtz-Duffing oscillator are obtained in this paper. He's Energy Balance Method (HEBM) and He's Frequency Amplitude Formulation (HFAF) are adopted as the solution methods. Oscillation natural frequencies are analytically analyzed. Error analysis is carried out and accuracy of the solution methods is evaluated. (C) 2011 Elsevier Ltd. All rights reserved

Opium Addiction and Ischemic Stroke in Isfahan, Iran: A Case-Control Study

Background: The effect of opium addiction (OA) on cerebrovascular disease is controversial. The aim of this study was to clarify this relationship in Iranian patients with ischemic stroke. Methods: In a case-control study, 672 patients with ischemic stroke and 293 controls without a previous history of cerebrovascular or cardiovascular diseases were compared. OA as well as other risk factors such as diabetes mellitus (DM), hypertension (HTN), hyperlipidemia, tobacco smoking (TS) were compared between the 2 groups. Results: OA percentage, TS, TS amount (pack/year), HTN and DM history were significantly higher in the case group compared to controls (p < 0.05). After regression analysis between risk factors, a significant difference remained between 2 groups with regards to HTN (OR 4.21, 95% CI 3.05-5.81, p < 0.001), TS (OR 2.33, 95% CI 1.51-3.59, p < 0.001), and OA (OR 2.36, 95% CI 1.16-4.85, p = 0.018). Conclusion: Our study showed OA is a risk factor for stroke. However, a follow-up study with a larger cohort is required to confirm the results. © 2017 S. Karger AG, Basel. Copyright: All rights reserve

Analytical Solutions for Autonomous Conservative Nonlinear Oscillator

WOS: 000286696600008This paper adapts the Energy Balance Method (EBM) and Frequency Amplitude Formulation to solve the free vibrations of a conservative oscillator with inertia and static cubic non-linearities. Case studies on the effects of the time response are presented. The results that obtained from the EBM and FAF are then compared with those from the numerical solution in order to verify the accuracy of the proposed method