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Abstract

Based on the V-function method, the properties of wave nature of object motion are studied for object uniform motion with constant speed and for harmonic oscillator. It follows from the V-function method that object wave motion is inseparably linked with its trajectory motion. The V-function method consists of the principle of local variation and a new statement of the direct and inverse dynamics problems. The proposed approach made it possible to make the optico-mechanical analogy that obtained a new continuation. A comparison is made with the results obtained by Schrödinger for a harmonic oscillator.

Chapter 10 The Simple Harmonic Oscillator The infinite square well is useful to illustrate many concepts including energy quantization, but the infinite square well is a limiting case of a realistic potential. The simple harmonic oscillator (SHO), in contrast, is a realistic and commonly encountered potential energy function. It is one of the most important problems in quantum mechanics and physics in general. It is often used as a first approximation to more complex phenomena. It is dominantly popular in modeling a multitude of cooperative phenomena. The

Abstract

In Blade Tip Timing several sensors installed circumferentially in the casing are used to record times of arrival (TOA) and observe deflections of blade tips. This paper aims to demonstrate methodology of model-based processing of aliased data. It focuses on the blade vibration excited by the forces synchronous with engine rotation, which are called integral responses. The driven harmonic oscillator with single degree of freedom (SDOF) is used to analyse blade vibration measured by tip-timing sensors during engine deceleration. When integral engine order EO is known, the linear sine fitting techniques can be used to process data from sensors to estimate amplitude, phase and frequency of blade vibration in each rotation. The oscillator model is implemented in MATLAB and used to generate resonance curves and simulate blade responses observed with tip sensors, installed in the axial compressor. Generated TOA data are fitted to the sine function to estimate vibration parameters. The validated procedure is then employed to analyze real test data.

Abstract

Blade Tip Timing (BTT) is a non-intrusive method to measure blade vibration in turbomachinery. Time of Arrival (TOA) is recorded when a blade is passing a stationary sensor. The measurement data, in form of undersampled (aliased) tip-deflection signal, are difficult to analyze with standard signal processing methods like digital filters or Fourier Transform. Several indirect methods are applied to process TOA sequences, such as reconstruction of aliased spectrum and Least-Squares Fitting to harmonic oscillator model. We used standard sine fitting algorithms provided by IEEE-STD-1057 to estimate blade vibration parameters. Blade-tip displacement was simulated in time domain using SDOF model, sampled by stationary sensors and then processed by the sinefit.m toolkit. We evaluated several configurations of different sensor placement, noise level and number of data. Results of the linear sine fitting, performed with the frequency known a priori, were compared with the non-linear ones. Some of non-linear iterations were not convergent. The algorithms and testing results are aimed to be used in analysis of asynchronous blade vibration.

Abstract

In this study an interesting symmetric linear system is considered. As a first step we obtain the Lagrangian of the system. Secondly, we derive the classical Euler- Lagrange equations of the system. Finally, numerical and analytic solution for these equations have been presented for some chosen initial conditions.

Abstract

This paper deals with stability analysis of pin-jointed beams that are affected to random pulsating load. The stability conditions of a pin-jointed beam are analysed using a mathematical model of the beam characterised by longitudinal force with Poisson characteristics and applying the stochastic modification of the second Lyapunov method.

., Crisis Economics: A Crash Course In The Future Of Finance, Penguin. Sandoval L. Jr., Franca I.P., 2011, Shocks In Financial Markets, Price Expectation, And Damped Harmonic Oscillators, Http://Arxiv.Org/Abs/1103.1992v2. Scanlon K., Whitehead C., 2011, The Uk Mortgage Market: Responding To Volatility, Journal Of Housing And The Built Environment, 26(3), 277-293. Skifter A. H., Andersson R., Wessel T., Vilkama K., 2016, The Impact Of Housing Policies And Housing Markets On Ethnic Spatial Segregation: Comparing The Capital Cities Of Four Nordic Welfare States

Abstract

We consider the Schrödinger equation with pseudo-Gaussian potential and point out that it is basically made up by a term representing the harmonic oscillator potential and an additional term, which is actually a power series that converges rapidly. Based on this observation the system can be considered as a perturbation of harmonic oscillator. The perturbation method is used to approximate the energy levels of pseudo- Gaussian oscillator. The results are compared with those obtained in the analytic and numeric case.

Abstract

The information-theoretical entropy, also called the “classical” entropy, was introduced by Wehrl in terms of the Glauber coherent states (CSs) | z > , i.e. the CSs corresponding to the one-dimensional harmonic oscillator (HO-1D). In the present paper, we have focused our attention on the examination of the information-theoretical entropy, i.e. the Wehrl entropy, for both the pure and the mixed (thermal) states of some quantum oscillators.

Abstract

A computational study using density functional theory is reported for the coronene monomer and selected linear cata-benzocoronene oligomers. Local aromaticity was discussed and analysed using the theoretical Harmonic Oscillator Model of the Electron Delocalisation (HOMED) index and its geometric (GEO) and energetic (EN) contributions. The [n]acenes (n = 3, 7, 11 and 15) served as reference molecules. Local aromaticity of individual superbenzene rings has oscillating character. On the other hand, the highest HOMED parameters which are practically independent on the molecular lengths were found for the smallest molecules including condensed benzene rings in their structure. For the largest structure of [n]acenes (n = 15), the inner rings are less aromatic than the outer ones. Depending on the molecular length, the energy gaps between the B3LYP energy levels of the highest occupied and lowest unoccupied molecular orbitals vary from 2.71 eV to 4.04 eV for coronene series and from 0.61 eV to 3.59 eV for [n]acenes.