Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method

We present an analysis of the free vibration of plates with internal discontinuities due to central cut-outs. A numerical formulation for a basic L-shaped element which is divided into appropriate sub-domains that are dependent upon the location of the cut-out is used as the basic building element. Trial functions formed to satisfy certain boundary conditions are employed to define the transverse deflection of each sub-domain. Mathematical treatments in terms of the continuities in displacement, slope, moment, and higher derivatives between the adjacent sub-domains are enforced at the interconnecting edges. The energy functional results, from the proper assembly of the coupled strain and kinetic energy contributions of each sub-domain, are minimized via the Ritz procedure to extract the vibration frequencies and. mode shapes of the plates. The procedures are demonstrated by considering plates with central cut-outs that are subjected to two types of boundary conditions. (C) 2003 Elsevier Ltd. All rights reserved.

A semi-analytical solution for vibration of rectangular plates with abrupt thickness variation

A semi-analytical analysis of free vibration of plates with cross-sectional discontinuities due to abrupt changes in thickness is presented. A basic square element divided into suitable subdomains dependent upon the positions of these abrupt changes is used as the basic building element, Admissible functions that satisfy the essential or geometric boundary conditions are used to define the transverse deflection of each subdomain. Continuities in the displacement, slope, moment and higher derivatives between adjacent subdomains are enforced at the interconnecting edges. The resulting global energy functional from the proper assembly of the coupled strain and kinetic energy contributions of each subdomain is then minimized via the Ritz procedure to extract the frequencies and mode shapes. Contour plots of a range of new mode shapes are presented for the enhancement of understanding the dynamic behavior of this class of plates, (C) 2001 Elsevier Science Ltd, All rights reserved.

Modal Analysis of a Beam with a Tip Rotor by Using a Fundamental Response

The shape modes of a damped-free beam model with a tip rotor are determined by using a dynamical basis that is generated by a fundamental spatial free response. This is a non-classical distributed model for the displacements in the transverse directions of the beam which turns out to be coupled through boundary conditions due to rotation. Numerical calculations are performed by using the Ritz-Rayleigh method with several approximating basis.

Analytical investigation of squeeze film dampers

Squeeze film damping effects naturally occur if structures are subjected to loading situations such that a very thin film of fluid is trapped within structural joints, interfaces, etc. An accurate estimate of squeeze film effects is important to predict the performance of dynamic structures. Starting from linear Reynolds equation which governs the fluid behavior coupled with structure domain which is modeled by Kirchhoff plate equation, the effects of nondimensional parameters on the damped natural frequencies are presented using boundary characteristic orthogonal functions. For this purpose, the nondimensional coupled partial differential equations are obtained using Rayleigh-Ritz method and the weak formulation, are solved using polynomial and sinusoidal boundary characteristic orthogonal functions for structure and fluid domain respectively. In order to implement present approach to the complex geometries, a two dimensional isoparametric coupled finite element is developed based on Reissner-Mindlin plate theory and linearized Reynolds equation. The coupling between fluid and structure is handled by considering the pressure forces and structural surface velocities on the boundaries. The effects of the driving parameters on the frequency response functions are investigated. As the next logical step, an analytical method for solution of squeeze film damping based upon Green’s function to the nonlinear Reynolds equation considering elastic plate is studied. This allows calculating modal damping and stiffness force rapidly for various boundary conditions. The nonlinear Reynolds equation is divided into multiple linear non-homogeneous Helmholtz equations, which then can be solvable using the presented approach. Approximate mode shapes of a rectangular elastic plate are used, enabling calculation of damping ratio and frequency shift as well as complex resistant pressure. Moreover, the theoretical results are correlated and compared with experimental results both in the literature and in-house experimental procedures including comparison against viscoelastic dampers.

On the flexural vibration of cylinders under axial loads:Numerical and experimental study

The flexural vibration of a homogeneous isotropic linearly elastic cylinder of any aspect ratio is analysed in this paper. Natural frequencies of a cylinder under uniformly distributed axial loads acting on its bases are calculated numerically by the Ritz method with terms of power series in the coordinate directions as approximating functions. The effect of axial loads on the flexural vibration cannot be described by applying infinitesimal strain theory, therefore, geometrically nonlinear strain–displacement relations with second-order terms are considered here. The natural frequencies of free–free, clamped–clamped, and sliding–sliding cylinders subjected to axial loads are calculated using the proposed three-dimensional Ritz approach and are compared with those obtained with the finite element method and the Bernoulli–Euler theory. Different experiments with cylinders axially compressed by a hydraulic press are carried out and the experimental results for the lowest flexural frequency are compared with the numerical results. An approach based on the Ritz formulation is proposed for the flexural vibration of a cylinder between the platens of the press with constraints varying with the intensity of the compression. The results show that for low compressions the cylinder behaves similarly to a sliding–sliding cylinder, whereas for high compressions the cylinder vibrates as a clamped–clamped one.

Updating of Finite Element Models using static and dynamic optical strains with application to damage assessment

In the recent years, vibration-based structural damage identification has been subject of significant research in structural engineering. The basic idea of vibration-based methods is that damage induces mechanical properties changes that cause anomalies in the dynamic response of the structure, which measures allow to localize damage and its extension. Vibration measured data, such as frequencies and mode shapes, can be used in the Finite Element Model Updating in order to adjust structural parameters sensible at damage (e.g. Young’s Modulus). The novel aspect of this thesis is the introduction into the objective function of accurate measures of strains mode shapes, evaluated through FBG sensors. After a review of the relevant literature, the case of study, i.e. an irregular prestressed concrete beam destined for roofing of industrial structures, will be presented. The mathematical model was built through FE models, studying static and dynamic behaviour of the element. Another analytical model was developed, based on the ‘Ritz method’, in order to investigate the possible interaction between the RC beam and the steel supporting table used for testing. Experimental data, recorded through the contemporary use of different measurement techniques (optical fibers, accelerometers, LVDTs) were compared whit theoretical data, allowing to detect the best model, for which have been outlined the settings for the updating procedure.

A Highly Improved Method For Sensitive Determination Of Amitriptyline In Pharmaceutical Formulations Using An Unmodified Carbon Nanotube Electrode In The Presence Of Sulfuric Acid.

The present paper describes a novel, simple and reliable differential pulse voltammetric method for determining amitriptyline (AMT) in pharmaceutical formulations. It has been described for many authors that this antidepressant is electrochemically inactive at carbon electrodes. However, the procedure proposed herein consisted in electrochemically oxidizing AMT at an unmodified carbon nanotube paste electrode in the presence of 0.1 mol L(-1) sulfuric acid used as electrolyte. At such concentration, the acid facilitated the AMT electroxidation through one-electron transfer at 1.33 V vs. Ag/AgCl, as observed by the augmentation of peak current. Concerning optimized conditions (modulation time 5 ms, scan rate 90 mV s(-1), and pulse amplitude 120 mV) a linear calibration curve was constructed in the range of 0.0-30.0 μmol L(-1), with a correlation coefficient of 0.9991 and a limit of detection of 1.61 μmol L(-1). The procedure was successfully validated for intra- and inter-day precision and accuracy. Moreover, its feasibility was assessed through analysis of commercial pharmaceutical formulations and it has been compared to the UV-vis spectrophotometric method used as standard analytical technique recommended by the Brazilian Pharmacopoeia.

Influence Of Delivery Method On Neuroprotection By Bone Marrow Mononuclear Cell Therapy Following Ventral Root Reimplantation With Fibrin Sealant.

The present work compared the local injection of mononuclear cells to the spinal cord lateral funiculus with the alternative approach of local delivery with fibrin sealant after ventral root avulsion (VRA) and reimplantation. For that, female adult Lewis rats were divided into the following groups: avulsion only, reimplantation with fibrin sealant; root repair with fibrin sealant associated with mononuclear cells; and repair with fibrin sealant and injected mononuclear cells. Cell therapy resulted in greater survival of spinal motoneurons up to four weeks post-surgery, especially when mononuclear cells were added to the fibrin glue. Injection of mononuclear cells to the lateral funiculus yield similar results to the reimplantation alone. Additionally, mononuclear cells added to the fibrin glue increased neurotrophic factor gene transcript levels in the spinal cord ventral horn. Regarding the motor recovery, evaluated by the functional peroneal index, as well as the paw print pressure, cell treated rats performed equally well as compared to reimplanted only animals, and significantly better than the avulsion only subjects. The results herein demonstrate that mononuclear cells therapy is neuroprotective by increasing levels of brain derived neurotrophic factor (BDNF) and glial derived neurotrophic factor (GDNF). Moreover, the use of fibrin sealant mononuclear cells delivery approach gave the best and more long lasting results.

Uv-vis Spectra As An Alternative To The Lowry Method For Quantify Hair Damage Induced By Surfactants.

It is well known that long term use of shampoo causes damage to human hair. Although the Lowry method has been widely used to quantify hair damage, it is unsuitable to determine this in the presence of some surfactants and there is no other method proposed in literature. In this work, a different method is used to investigate and compare the hair damage induced by four types of surfactants (including three commercial-grade surfactants) and water. Hair samples were immersed in aqueous solution of surfactants under conditions that resemble a shower (38 °C, constant shaking). These solutions become colored with time of contact with hair and its UV-vis spectra were recorded. For comparison, the amount of extracted proteins from hair by sodium dodecyl sulfate (SDS) and by water were estimated by the Lowry method. Additionally, non-pigmented vs. pigmented hair and also sepia melanin were used to understand the washing solution color and their spectra. The results presented herein show that hair degradation is mostly caused by the extraction of proteins, cuticle fragments and melanin granules from hair fiber. It was found that the intensity of solution color varies with the charge density of the surfactants. Furthermore, the intensity of solution color can be correlated to the amount of proteins quantified by the Lowry method as well as to the degree of hair damage. UV-vis spectrum of hair washing solutions is a simple and straightforward method to quantify and compare hair damages induced by different commercial surfactants.

Graded Meshes In Bio-thermal Problems With Transmission-line Modeling Method.

In this study, the transmission-line modeling (TLM) applied to bio-thermal problems was improved by incorporating several novel computational techniques, which include application of graded meshes which resulted in 9 times faster in computational time and uses only a fraction (16%) of the computational resources used by regular meshes in analyzing heat flow through heterogeneous media. Graded meshes, unlike regular meshes, allow heat sources to be modeled in all segments of the mesh. A new boundary condition that considers thermal properties and thus resulting in a more realistic modeling of complex problems is introduced. Also, a new way of calculating an error parameter is introduced. The calculated temperatures between nodes were compared against the results obtained from the literature and agreed within less than 1% difference. It is reasonable, therefore, to conclude that the improved TLM model described herein has great potential in heat transfer of biological systems.

Trichomes Related To An Unusual Method Of Water Retention And Protection Of The Stem Apex In An Arid Zone Perennial Species.

It is well known that trichomes protect plant organs, and several studies have investigated their role in the adaptation of plants to harsh environments. Recent studies have shown that the production of hydrophilic substances by glandular trichomes and the deposition of this secretion on young organs may facilitate water retention, thus preventing desiccation and favouring organ growth until the plant develops other protective mechanisms. Lychnophora diamantinana is a species endemic to the Brazilian 'campos rupestres' (rocky fields), a region characterized by intense solar radiation and water deficits. This study sought to investigate trichomes and the origin of the substances observed on the stem apices of L. diamantinana. Samples of stem apices, young and expanded leaves were studied using standard techniques, including light microscopy and scanning and transmission electron microscopy. Histochemical tests were used to identify the major groups of metabolites present in the trichomes and the hyaline material deposited on the apices. Non-glandular trichomes and glandular trichomes were observed. The material deposited on the stem apices was hyaline, highly hydrophilic and viscous. This hyaline material primarily consists of carbohydrates that result from the partial degradation of the cell wall of uniseriate trichomes. This degradation occurs at the same time that glandular trichomes secrete terpenoids, phenolic compounds and proteins. These results suggest that the non-glandular trichomes on the leaves of L. diamantinana help protect the young organ, particularly against desiccation, by deposition of highly hydrated substances on the apices. Furthermore, the secretion of glandular trichomes probably repels herbivore and pathogen attacks.

Tissue Microarray Is A Reliable Method For Immunohistochemical Analysis Of Pleomorphic Adenoma.

To determine the most adequate number and size of tissue microarray (TMA) cores for pleomorphic adenoma immunohistochemical studies. Eighty-two pleomorphic adenoma cases were distributed in 3 TMA blocks assembled in triplicate containing 1.0-, 2.0-, and 3.0-mm cores. Immunohistochemical analysis against cytokeratin 7, Ki67, p63, and CD34 were performed and subsequently evaluated with PixelCount, nuclear, and microvessel software applications. The 1.0-mm TMA presented lower results than 2.0- and 3.0-mm TMAs versus conventional whole section slides. Possibly because of an increased amount of stromal tissue, 3.0-mm cores presented a higher microvessel density. Comparing the results obtained with one, two, and three 2.0-mm cores, there was no difference between triplicate or duplicate TMAs and a single-core TMA. Considering the possible loss of cylinders during immunohistochemical reactions, 2.0-mm TMAs in duplicate are a more reliable approach for pleomorphic adenoma immunohistochemical study.

Use Of Experimental Design To Optimize A Triple-potential Waveform To Develop A Method For The Determination Of Streptomycin And Dihydrostreptomycin In Pharmaceutical Veterinary Dosage Forms By Hplc-pad.

An HPLC-PAD method using a gold working electrode and a triple-potential waveform was developed for the simultaneous determination of streptomycin and dihydrostreptomycin in veterinary drugs. Glucose was used as the internal standard, and the triple-potential waveform was optimized using a factorial and a central composite design. The optimum potentials were as follows: amperometric detection, E1=-0.15V; cleaning potential, E2=+0.85V; and reactivation of the electrode surface, E3=-0.65V. For the separation of the aminoglycosides and the internal standard of glucose, a CarboPac™ PA1 anion exchange column was used together with a mobile phase consisting of a 0.070 mol L(-1) sodium hydroxide solution in the isocratic elution mode with a flow rate of 0.8 mL min(-1). The method was validated and applied to the determination of streptomycin and dihydrostreptomycin in veterinary formulations (injection, suspension and ointment) without any previous sample pretreatment, except for the ointments, for which a liquid-liquid extraction was required before HPLC-PAD analysis. The method showed adequate selectivity, with an accuracy of 98-107% and a precision of less than 3.9%.

A Rapid And Simple Capillary Electrophoresis Method For Indirect Determination Of The Biocide 2,2-dibromo-3-nitrilo-propionamide (dbnpa) In Cooling Waters.

A capillary zone electrophoresis (CE) method was developed for the determination of the biocide 2,2-dibromo-3-nitrilo-propionamide (DBNPA) in water used in cooling systems. The biocide is indirectly determined by CE measurement of the concentration of bromide ions produced by the reaction between the DBNPA and bisulfite. The relationship between the bromide peak areas and the DBNPA concentrations showed a good linearity and a coefficient of determination (R(2)) of 0.9997 in the evaluated concentration range of 0-75 μmol L(-1). The detection and quantification limits for DBNPA were 0.23 and 0.75 μmol L(-1), respectively. The proposed CE method was successfully applied for the analysis of samples of tap water and cooling water spiked with DBNPA. The intra-day and inter-day (intermediary) precisions were lower than 2.8 and 6.2%, respectively. The DBNPA concentrations measured by the CE method were compared to the values obtained by a spectrophotometric method and were found to agree well.

Flow injection green method for the quantitative analysis of ketoconazole in pharmaceutical preparations

A flow injection method for the quantitative analysis of ketoconazole in tablets, based on the reaction with iron (III) ions, is presented. Ketoconazole forms a red complex with iron ions in an acid medium, with maximum absorbance at 495 nm. The detection limit was estimated to be 1×10--4 mol L-1; the quantitation limit is about 3×10--4 mol L-1 and approximately 30 determinations can be performed in an hour. The results were compared with those obtained with a reference HPLC method. Statistical comparisons were done using the Student's t procedure and the F test. Complete agreement was found at the 0.95 significance level between the proposed flow injection and the HPLC procedures. The two methods present similar precision, i.e., for HPLC the mean relative standard deviation was ca. 1.2% and for FIA ca. 1.6%.