Discrete fractional order system vibrations

A theory of free vibrations of discrete fractional order (FO) systems with a finite number of degrees of freedom (dof) is developed. A FO system with a finite number of dof is defined by means of three matrices: mass inertia, system rigidity and FO elements. By adopting a matrix formulation, a mathematical description of FO discrete system free vibrations is determined in the form of coupled fractional order differential equations (FODE). The corresponding solutions in analytical form, for the special case of the matrix of FO properties elements, are determined and expressed as a polynomial series along time. For the eigen characteristic numbers, the system eigen main coordinates and the independent eigen FO modes are determined. A generalized function of visoelastic creep FO dissipation of energy and generalized forces of system with no ideal visoelastic creep FO dissipation of energy for generalized coordinates are formulated. Extended Lagrange FODE of second kind, for FO system dynamics, are also introduced. Two examples of FO chain systems are analyzed and the corresponding eigen characteristic numbers determined. It is shown that the oscillatory phenomena of a FO mechanical chain have analogies to electrical FO circuits. A FO electrical resistor is introduced and its constitutive voltage–current is formulated. Also a function of thermal energy FO dissipation of a FO electrical relation is discussed.

Bending of stochastic Kirchhoff plates on Winkler foundations via the Galerkin method and the Askey-Wiener scheme

In this paper, the method of Galerkin and the Askey-Wiener scheme are used to obtain approximate solutions to the stochastic displacement response of Kirchhoff plates with uncertain parameters. Theoretical and numerical results are presented. The Lax-Milgram lemma is used to express the conditions for existence and uniqueness of the solution. Uncertainties in plate and foundation stiffness are modeled by respecting these conditions, hence using Legendre polynomials indexed in uniform random variables. The space of approximate solutions is built using results of density between the space of continuous functions and Sobolev spaces. Approximate Galerkin solutions are compared with results of Monte Carlo simulation, in terms of first and second order moments and in terms of histograms of the displacement response. Numerical results for two example problems show very fast convergence to the exact solution, at excellent accuracies. The Askey-Wiener Galerkin scheme developed herein is able to reproduce the histogram of the displacement response. The scheme is shown to be a theoretically sound and efficient method for the solution of stochastic problems in engineering. (C) 2009 Elsevier Ltd. All rights reserved.

Aplicación de Métodos Meshless al Análisis de Problemas de Autovalores

La presente Tesis Doctoral aborda la aplicación de métodos meshless, o métodos sin malla, a problemas de autovalores, fundamentalmente vibraciones libres y pandeo. En particular, el estudio se centra en aspectos tales como los procedimientos para la resolución numérica del problema de autovalores con estos métodos, el coste computacional y la viabilidad de la utilización de matrices de masa o matrices de rigidez geométrica no consistentes. Además, se acomete en detalle el análisis del error, con el objetivo de determinar sus principales fuentes y obtener claves que permitan la aceleración de la convergencia. Aunque en la actualidad existe una amplia variedad de métodos meshless en apariencia independientes entre sí, se han analizado las diferentes relaciones entre ellos, deduciéndose que el método Element-Free Galerkin Method [Método Galerkin Sin Elementos] (EFGM) es representativo de un amplio grupo de los mismos. Por ello se ha empleado como referencia en este análisis. Muchas de las fuentes de error de un método sin malla provienen de su algoritmo de interpolación o aproximación. En el caso del EFGM ese algoritmo es conocido como Moving Least Squares [Mínimos Cuadrados Móviles] (MLS), caso particular del Generalized Moving Least Squares [Mínimos Cuadrados Móviles Generalizados] (GMLS). La formulación de estos algoritmos indica que la precisión de los mismos se basa en los siguientes factores: orden de la base polinómica p(x), características de la función de peso w(x) y forma y tamaño del soporte de definición de esa función. Se ha analizado la contribución individual de cada factor mediante su reducción a un único parámetro cuantificable, así como las interacciones entre ellos tanto en distribuciones regulares de nodos como en irregulares. El estudio se extiende a una serie de problemas estructurales uni y bidimensionales de referencia, y tiene en cuenta el error no sólo en el cálculo de autovalores (frecuencias propias o carga de pandeo, según el caso), sino también en términos de autovectores. This Doctoral Thesis deals with the application of meshless methods to eigenvalue problems, particularly free vibrations and buckling. The analysis is focused on aspects such as the numerical solving of the problem, computational cost and the feasibility of the use of non-consistent mass or geometric stiffness matrices. Furthermore, the analysis of the error is also considered, with the aim of identifying its main sources and obtaining the key factors that enable a faster convergence of a given problem. Although currently a wide variety of apparently independent meshless methods can be found in the literature, the relationships among them have been analyzed. The outcome of this assessment is that all those methods can be grouped in only a limited amount of categories, and that the Element-Free Galerkin Method (EFGM) is representative of the most important one. Therefore, the EFGM has been selected as a reference for the numerical analyses. Many of the error sources of a meshless method are contributed by its interpolation/approximation algorithm. In the EFGM, such algorithm is known as Moving Least Squares (MLS), a particular case of the Generalized Moving Least Squares (GMLS). The accuracy of the MLS is based on the following factors: order of the polynomial basis p(x), features of the weight function w(x), and shape and size of the support domain of this weight function. The individual contribution of each of these factors, along with the interactions among them, has been studied in both regular and irregular arrangement of nodes, by means of a reduction of each contribution to a one single quantifiable parameter. This assessment is applied to a range of both one- and two-dimensional benchmarking cases, and includes not only the error in terms of eigenvalues (natural frequencies or buckling load), but also of eigenvectors

Shake-table tests of a reinforced concrete frame designed following modern codes: seismic performance and damage evaluation

This paper presents shake-table tests conducted on a two-fifths-scale reinforced concrete frame representing a conventional construction design under current building code provisions in the Mediterranean area. The structure was subjected to a sequence of dynamic tests including free vibrations and four seismic simulations in which a historical ground motion record was scaled to levels of increasing intensity until collapse. Each seismic simulation was associated with a different level of seismic hazard, representing very frequent, frequent, rare and very rare earthquakes. The structure remained basically undamaged and within the inter-story drift limits of the "immediate occupancy" performance level for the very frequent and frequent earthquakes. For the rare earthquake, the specimen sustained significant damage with chord rotations of up to 28% of its ultimate capacity and approached the upper bound limit of inter-story drift associated with "life safety". The specimen collapsed at the beginning of the "very rare" seismic simulation. Besides summarizing the experimental program, this paper evaluates the damage quantitatively at the global and local levels in terms of chord rotation and other damage indexes, together with the energy dissipation demands for each level of seismic hazard. Further, the ratios of column-to-beam moment capacity recommended by Eurocode 8 and ACI-318 to guarantee the formation of a strong column-weak beam mechanism are examined.

Dynamic analysis of translational shells

In this paper a dynamic analysis of transnational shells is presented. The general linear shell theory is used in conjunction with additional shallow and curved plate approximations. In order to apply some type of extended Levy solution, the shell is assumed to be limited by a rectangular plan form, with two opposite edges simply supported (gable boundary conditions). First, the shells free vibrations are studied in the usual way, obtaining for each Fourier term the natural frequencies as solutions of a transcendental equation. However, solving these equations arises enormous computational difficulties. This paper deals specifically with this problem, trying to reduce its dimension by a discretization procedure. In the shell dynamic characteristics, namely the mass. The shell mass is lumped along a family of coordinate lines. Therefore, the natural frequencies for each harmonic term can be found from the solution of a typical matrix eigenvalues problem and standard numerical techniques can be applied. The shell response to forced vibrations, particularly to earthquake excitation, can be determined by using conventional procedure either in the time or in the frequency domain. Finally, extending the above procedure, any system of translational shells under dynamic loading can be studied. Then, by using matrix methods, a general computer program is written and applied to some illustrative examples. Numerical results has been obtained in two cases: circular cylindrical shell and box girder bridge.

Intermolecular vibrations and fast relaxations in supercooled ionic liquids

Short-time dynamics of ionic liquids has been investigated by low-frequency Raman spectroscopy (4 < omega < 100 cm(-1)) within the supercooled liquid range. Raman spectra are reported for ionic liquids with the same anion, bis(trifluoromethylsulfonyl)imide, and different cations: 1-butyl-3-methylimidazolium, 1-hexyl-3-methylimidazolium, 1-butyl-1-methylpiperidinium, trimethylbutylammonium, and tributylmethylammonium. It is shown that low-frequency Raman spectroscopy provides similar results as optical Kerr effect (OKE) spectroscopy, which has been used to study intermolecular vibrations in ionic liquids. The comparison of ionic liquids containing aromatic and non-aromatic cations identifies the characteristic feature in Raman spectra usually assigned to librational motion of the imidazolium ring. The strength of the fast relaxations (quasi-elastic scattering, QES) and the intermolecular vibrational contribution (boson peak) of ionic liquids with non-aromatic cations are significantly lower than imidazolium ionic liquids. A correlation length assigned to the boson peak vibrations was estimated from the frequency of the maximum of the boson peak and experimental data of sound velocity. The correlation length related to the boson peak (similar to 19 angstrom) does not change with the length of the alkyl chain in imidazolium cations, in contrast to the position of the first-sharp diffraction peak observed in neutron and X-ray scattering measurements of ionic liquids. The rate of change of the QES intensity in the supercooled liquid range is compared with data of excess entropy, free volume, and mean-squared displacement recently reported for ionic liquids. The temperature dependence of the QES intensity in ionic liquids illustrates relationships between short-time dynamics and long-time structural relaxation that have been proposed for glass-forming liquids. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3604533]

Finite field treatment of vibrational polarizabilities and hyperpolarizabilities: on the role of the Eckart conditions, their implementation, and their use in characterizing key vibrations

In the finite field (FF) treatment of vibrational polarizabilities and hyperpolarizabilities, the field-free Eckart conditions must be enforced in order to prevent molecular reorientation during geometry optimization. These conditions are implemented for the first time. Our procedure facilities identification of field-induced internal coordinates that make the major contribution to the vibrational properties. Using only two of these coordinates, quantitative accuracy for nuclear relaxation polarizabilities and hyperpolarizabilities is achieved in π-conjugated systems. From these two coordinates a single most efficient natural conjugation coordinate (NCC) can be extracted. The limitations of this one coordinate approach are discussed. It is shown that the Eckart conditions can lead to an isotope effect that is comparable to the isotope effect on zero-point vibrational averaging, but with a different mass-dependence

Vibration free machining tools

Appearance of the vibration is the very important problem in long tool turning and milling. Current solutions of minimizing vibrations provided by different tool suppliers are very expensive. This Master’s Thesis is presenting the new type of vibration free machining tools produced by Konepaja ASTEX Gear Oy that have cheaper production costs compare to competitors’ products. Vibration problems in machining and their today’s solutions are analyzed in this work. The new vibration damping invention is presented and described. Moreover, the production, laboratory experimental modal analysis and practical testing of the new vibration free prototypes are observed and analyzed on the pages of this Thesis. Based on the testing results the new invention is acknowledged to be successful and approved for further studies and developments.

Finite field treatment of vibrational polarizabilities and hyperpolarizabilities: on the role of the Eckart conditions, their implementation, and their use in characterizing key vibrations

In the finite field (FF) treatment of vibrational polarizabilities and hyperpolarizabilities, the field-free Eckart conditions must be enforced in order to prevent molecular reorientation during geometry optimization. These conditions are implemented for the first time. Our procedure facilities identification of field-induced internal coordinates that make the major contribution to the vibrational properties. Using only two of these coordinates, quantitative accuracy for nuclear relaxation polarizabilities and hyperpolarizabilities is achieved in π-conjugated systems. From these two coordinates a single most efficient natural conjugation coordinate (NCC) can be extracted. The limitations of this one coordinate approach are discussed. It is shown that the Eckart conditions can lead to an isotope effect that is comparable to the isotope effect on zero-point vibrational averaging, but with a different mass-dependence

Vocal folds vibrations with a three-dimensional deformable model

In this work a computational method is presented to simulate the movements of vocal folds in three dimensions. The proposed model consists of a mesh free structure where each vertex is connected its neighbor through a group spring-damper. Forced oscillations were studied by time varying surface forces. The preliminary results using this model are similar with the literature and with the experimental stroboscopic observations of larynx. © 2006 IEEE.

On nonlinear dynamics in a free fluid surface of a tank excited by a non-ideal power source

We investigate the nonlinear oscillations in a free surface of a fluid in a cylinder tank excited by non-ideal power source, an electric motor with limited power supply. We study the possibility of parametric resonance in this system, showing that the excitation mechanism can generate chaotic response. Additionally, the dynamics of parametrically excited surface waves in the tank can reveal new characteristics of the system. The fluid-dynamic system is modeled in such way as to obtain a nonlinear differential equation system. Numerical experiments are carried out to find the regions of chaotic solutions. Simulation results are presented as phase-portrait diagrams characterizing the resonant vibrations of free fluid surface and the existence of several types of regular and chaotic attractors. We also describe the energy transfer in the interaction process between the hydrodynamic system and the electric motor. Copyright © 2011 by ASME.

Added mass and wave radiation damping for flow-induced rotational vibrations of skinplates of hydraulic gates

One observed vibration mode for Tainter gate skinplates involves the bending of the skinplate about a horizontal nodal line. This vibration mode can be approximated as a streamwise rotational vibration about the horizontal nodal line. Such a streamwise rotational vibration of a Tainter gate skinplate must push away water from the portion of the skinplate rotating into the reservoir and draw water toward the gate over that portion of the skinplate receding from the reservoir. The induced pressure is termed the push-and-draw pressure. In the present paper, this push-and-draw pressure is analyzed using the potential theory developed for dissipative wave radiation problems. In the initial analysis, the usual circular-arc skinplate is replaced by a vertical, flat, rigid weir plate so that theoretical calculations can be undertaken. The theoretical push-and-draw pressure is used in the derivation of the non-dimensional equation of motion of the flow-induced rotational vibrations. Non-dimensionalization of the equation of motion permits the identification of the dimensionless equivalent added mass and the wave radiation damping coefficients. Free vibration tests of a vertical, flat, rigid weir plate model, both in air and in water, were performed to measure the equivalent added mass and the wave radiation damping coefficients. Experimental results compared favorably with the theoretical predictions, thus validating the theoretical analysis of the equivalent added mass and wave radiation damping coefficients as a prediction tool for flow-induced vibrations. Subsequently, the equation of motion of an inclined circular-arc skinplate was developed by incorporating a pressure correction coefficient, which permits empirical adaptation of the results from the hydrodynamic pressure analysis of the vertical, flat, rigid weir plate. Results from in-water free vibration tests on a 1/31-scale skinplate model of the Folsom Dam Tainter gate are used to demonstrate the utility of the equivalent added mass coefficient.

N-H center dot center dot center dot pi hydrogen-bonding and large-amplitude tipping vibrations in jet-cooled pyrrole-benzene

The N-H center dot center dot center dot pi hydrogen bond is an important intermolecular interaction in many biological systems. We have investigated the infrared (IR) and ultraviolet (UV) spectra of the supersonic-jet cooled complex of pyrrole with benzene and benzene-d(6) (Pyr center dot Bz, Pyr center dot Bz-d(6)). DFT-D density functional, SCS-MP2 and SCS-CC2 calculations predict a T-shaped and (almost) C(s) symmetric structure with an N-H center dot center dot center dot pi hydrogen bond to the benzene ring. The pyrrole is tipped by omega(S(0)) = +/- 13 degrees relative to the surface normal of Bz. The N center dot center dot center dot ring distance is 3.13 angstrom. In the S(1) excited state, SCS-CC2 calculations predict an increased tipping angle omega(S(1)) = +/- 21 degrees. The IR depletion spectra support the T-shaped geometry: The NH stretch is redshifted by -59 cm(-1), relative to the "free" NH stretch of pyrrole at 3531 cm(-1), indicating a moderately strong N-H center dot center dot center dot pi interaction. The interaction is weaker than in the (Pyr)(2) dimer, where the NH donor shift is -87 cm(-1) [Dauster et al., Phys. Chem. Chem. Phys., 2008, 10, 2827]. The IR C-H stretch frequencies and intensities of the Bz subunit are very similar to those of the acceptor in the (Bz)(2) dimer, confirming that Bz acts as the acceptor. While the S(1) <- S(0) electronic origin of Bz is forbidden and is not observable in the gas-phase, the UV spectrum of Pyr center dot Bz in the same region exhibits a weak 0(0)(0) band that is red-shifted by 58 cm(-1) relative to that of Bz (38 086 cm(-1)). The origin appears due to symmetry-breaking of the p-electron system of Bz by the asymmetric pyrrole NH center dot center dot center dot pi hydrogen bond. This contrasts with (Bz)(2), which does not exhibit a 0(0)(0) band. The Bz moiety in Pyr center dot Bz exhibits a 6a(0)(1) band at 0(0)(0) + 518 cm(-1) that is about 20x more intense than the origin band. The symmetry breaking by the NH center dot center dot center dot pi hydrogen bond splits the degeneracy of the v(6)(e(2g)) vibration, giving rise to 6a' and 6b' sub-bands that are spaced by similar to 6 cm(-1). Both the 0(0)(0) and 6(0)(1) bands of Pyr center dot Bz carry a progression in the low-frequency (10 cm(-1)) excited-state tipping vibration omega', in agreement with the change of the omega tipping angle predicted by SCS-MP2 and SCS-CC2 calculations.

Supercapattery based on binder-free Co3 (PO4)2·8H2O multilayer nano/microflakes on nickel foam

A binder-free cobalt phosphate hydrate (Co3(PO4)2·8H2O) multilayer nano/microflake structure is synthesized on nickel foam (NF) via a facile hydrothermal process. Four different concentrations (2.5, 5, 10, and 20 mM) of Co2+ and PO4–3 were used to obtain different mass loading of cobalt phosphate on the nickel foam. The Co3(PO4)2·8H2O modified NF electrode (2.5 mM) shows a maximum specific capacity of 868.3 C g–1 (capacitance of 1578.7 F g–1) at a current density of 5 mA cm–2 and remains as high as 566.3 C g–1 (1029.5 F g–1) at 50 mA cm–2 in 1 M NaOH. A supercapattery assembled using Co3(PO4)2·8H2O/NF as the positive electrode and activated carbon/NF as the negative electrode delivers a gravimetric capacitance of 111.2 F g–1 (volumetric capacitance of 4.44 F cm–3). Furthermore, the device offers a high specific energy of 29.29 Wh kg–1 (energy density of 1.17 mWh cm–3) and a specific power of 4687 W kg–1 (power density of 187.5 mW cm–3).

An Efficient Protocol For The Generation Of Monocyte Derived Dendritic Cells Using Serum-free Media For Clinical Applications In Post Remission Aml Patients.

Protocols for the generation of dendritic cells (DCs) using serum as a supplementation of culture media leads to reactions due to animal proteins and disease transmissions. Several types of serum-free media (SFM), based on good manufacture practices (GMP), have recently been used and seem to be a viable option. The aim of this study was to evaluate the results of the differentiation, maturation, and function of DCs from Acute Myeloid Leukemia patients (AML), generated in SFM and medium supplemented with autologous serum (AS). DCs were analyzed by phenotype characteristics, viability, and functionality. The results showed the possibility of generating viable DCs in all the conditions tested. In patients, the X-VIVO 15 medium was more efficient than the other media tested in the generation of DCs producing IL-12p70 (p=0.05). Moreover, the presence of AS led to a significant increase of IL-10 by DCs as compared with CellGro (p=0.05) and X-Vivo15 (p=0.05) media, both in patients and donors. We concluded that SFM was efficient in the production of DCs for immunotherapy in AML patients. However, the use of AS appears to interfere with the functional capacity of the generated DCs.