Coupled purely nonlinear oscillators: normal modes and exact solutions for free and forced responses

Nonlinear Dynamics - This article is concerned first with free vibrations in a chain of two-mass oscillators with purely nonlinear springs whose power of nonlinearity can be any real number higher...     

Normal modes of a double pendulum at low energy levels

Nonlinear Dynamics - This study is concerned with a double pendulum and its regular behaviour associated with low energy levels and the influence of the associated initial conditions on the...     

Modelling and analysis of the nonlinear string-mass structure of the vibration absorber

ABSTRACT

In this paper a nonlinear string-mass structure of the vibration absorber is analyzed. This structure is convenient to be installed in vibration damping systems of high buildings for their protection in the case of earthquake. The considered string-mass structure contains a translator movable mass connected with two strings. Due to nonlinear geometric properties of the system the motion of the mass is described with a strong nonlinear second order differential equation. In the paper the approximate procedure for solving of the nonlinear equation of motion is developed. Based on the solution the influence of the string preloading force, slider mass and friction force on the vibration property of the string-mass system is investigated. It is concluded that variation of the preloading string force may be applied as a control parameter for vibration absorption and as the regulator of vibration decay time.     

Influence of ultrasonic processing on the macromolecular properties of poly (d,l-lactide-co-glycolide) alone and in its biocomposite with hydroxyapatite

In this work poly(d,l-lactide-co-glycolide) (PLGA) and a poly(d,l-lactide-co-glycolide)/hydroxyapatite (PLGA/HAp) composite processed in an ultrasonic field at higher (25 °C) and lower (8 °C) temperatures were studied with respect to the molecular properties of the obtained materials. The processing of the PLGA and the PLGA/HAp composite in an ultrasonic field resulted in a change of molar mass averages of the polymer/polymeric part of these materials, while an amorphous structure and a 50:50 lactide-to-glycolide co-monomer ratio were preserved without the formation of crystalline oligomers. However, mobility of polymeric chains obtained after ultrasonic processing was lower indicating ordering the structure of polymeric chains as a result of processing. Additionally, it was observed that the mobility of the PLGA macromolecules was lower within the composite in comparison with the mobility of the chains within the PLGA alone in the case when both were obtained after ultrasonic processing. This was a consequence of the structure formation through the interactions between the PLGA and the HAp. Based on these results different degradation rate of PLGA in composite can be expected, which is important in the application of this material for the controlled drug delivery of medicaments.     

Dynamic study of Schröder’s families of first and second kind

The Schröder iterative families of the first and second kind are of great importance in the theory and practice of iterative processes for solving nonlinear equations f(x) = 0. In both cases, the methods E _r (first kind) and S _r (second kind) converge locally to a zero α of f as O(|x _k ? α| ^r ). Although characteristics of these families have been studied in many papers, their dynamic and chaotic behavior has not been completely investigated. In this paper, we compare convergence properties of both iterative schemes using the two methodologies: (i) comparison by numerical examples and (ii) comparison using dynamic study of methods by basins of attraction that enable their graphic visualization. Apart from the visualization of iterative processes, basins of attraction reveal very useful features on iterations such as consumed CPU time and average number of iterations, both as functions of starting points. We demonstrate by several examples that the Schröder family of the second kind S _r possesses better convergence characteristics than the Schröder family of the first kind E _r .     

A class of three-point root-solvers of optimal order of convergence

The construction of a class of three-point methods for solving nonlinear equations of the eighth order is presented. These methods are developed by combining fourth order methods from the class of optimal two-point methods and a modified Newton’s method in the third step, obtained by a suitable approximation of the first derivative based on interpolation by a nonlinear fraction. It is proved that the new three-step methods reach the eighth order of convergence using only four function evaluations, which supports the Kung-Traub conjecture on the optimal order of convergence. Numerical examples for the selected special cases of two-step methods are given to demonstrate very fast convergence and a high computational efficiency of the proposed multipoint methods. Some computational aspects and the comparison with existing methods are also included.     

Surface Chemistry Studies of Quantum Dots (QDs) Modified with Surfactants

Since luminescent CdSe quantum dots (QDs) have shown great potential in biological labeling, the surface chemistry behavior of QDs at interfaces is of great research interest. In the present study, CdSe QDs with green luminescence were modified with hydrophobic chains of varying lengths [from C6 to C18]. These modified QDs can be utilized to form stable monolayers at the air/water interface. Surface pressure-area isotherms of modified QDs have been measured and limiting molecular areas have also been extrapolated in order to analyze the size of the QDs. UV absorption spectra of modified QDs at various surface pressures were also determined. Surface chemistry, as well as the topographic properties, of modified QDs in Langmuir and L-B films was discussed.