Kuvvetli Nonlineer Sistemler İçin Çok Ölçekli Lindstedt Poincare Tekniği

Konferans Bildirisi -- Teorik ve Uygulamalı Mekanik Türk Milli Komitesi, 2013Conference Paper -- Theoretical and Applied Mechanical Turkish National Committee, 2013Çok ölçekli metot ve Lindstedt-Poincare tekniğinin birleştirilmesi esasına dayanan yeni bir perturbasyon metodu ortaya atılmıştır. Yeni metot lineer sönümlü osilatör, Duffing denklemi, sönümlü kübik nonlineer denklem, kuadratik ve kübik nonlineer denklem ve zorlamalı Duffing denklemine uygulanmıştır. Klasik çok ölçekli metot ve yeni metodu kullanarak yaklaşık analitik çözümler elde edilmiştir. Bu çözümler ana denklemin sayısal çözümü ile karşılaştırılmıştır. Yeni metot kuvvetli nonlineer sistemler için çok iyi sonuçlar vermiştir.A new perturbation method combining the Method of Multiple Scales and Lindstedt Poincare techniques is proposed. The new method is applied to Linear damped oscillator, Duffing equation, damped cubic nonlinear equation, an equation with quadratic and cubic nonlinearities and forced Duffing equation. Approximate analytical solutions are obtained using the classical Multiple scales method and the new method. Both solutions are contrasted with the direct numerical solutions of the original equation. The new method produces much better results for strong nonlinearities

Escape from COVID-19 pandemic to safe haven

Gold, which is accepted as a safe haven by households, is known as an investment tool that is preferred especially in times of crisis and uncertainty. Especially in recent days, the uncertainty caused by the COVID-19 pandemic and the visible increase in Turkey's 5-year CDS data has led investors in Turkey to grams of gold, which is considered a safe haven. In this context, this study aims to test the long-term relationship between daily case-related deaths and Turkey's 5-year CDS data with gram gold prices in Turkish lira during the COVID-19 pandemic. The long-term relationship between the variables was tested with the autoregressive distributed lag bound test (ARDL bound test) applied to the daily data for the period March 17, 2020-April 11, 2020. For the application of ARDL bound test, the stationarity of the variables was tested with unit root tests such as augmented Dickey-Fuller test (ADF) and Phillips-Perron (PP). According to the ARDL bound test findings, there is a statistically significant and positive relationship between the number of case-related deaths and the gram gold prices in Turkish lira in the long run. However, it has been found that Turkey's 5-year CDS data does not have a significant long-term relationship with gram gold prices in Turkish lira

Continuous Systems with Odd Nonlinearities: A General Solution Procedure

A generalized equation of motion with odd nonlinearities is considered. The nonlinearities of cubic and fifth order are represented in the form of arbitrary operators. The equation of motion, in its general form, may model a class of partial differential equations encountered in vibrations of continuous systems. Approximate analytical solutions are sought using the method of multiple scales, a perturbation technique. Forced vibrations with viscous damping are considered. Frequency-response relation is derived in its most general form. Finally, an application to a specific problem is given

A New Perturbation-Iteration Approach for First Order Differential Equations

Two new perturbation-iteration algorithms for solving differential equations of first order are proposed. Variants of the algorithm are developed depending on the differential order of Taylor series expansions. The iteration algorithms are tested on a number of first order equations. Much better solutions than the regular perturbation solutions are achieved

Strength of Wheat and Barley Stems and Design of New Beam/Columns

In this study, physical and mechanical properties of wheat and barley stems are examined. Transverse sections of the stems are magnified by a microscope and the material structure in the transverse sections are analysed with image processing programs. Geometric properties such as inner, outer radius, stem wall thickness and density variation of the material along the radius are measured and density variations are approximated by a mathematical model. Moment of inertia of the cross-sectional area which plays a vital role in resistance against bending and buckling is calculated approximately. Using the material density variations of the wheat (Triticum sativum L.) stems, new beam/columns are designed. Stress distributions in this new design and conventional designs of equivalent weight are compared using ANSYS program. It is found that stresses are more uniformly distributed in the new design with maximum stresses being lower than the conventional designs