Numerical Determination of the Response of a Linear Vibration System With a Singular Mass Matrix

1972 ◽  
Vol 94 (1) ◽  
pp. 64-69
Author(s):  
K. D. Willmert
Keyword(s):  
Multistep Methods ◽  
Mass Matrix ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Vibrational System ◽  
Wide Range ◽  
Mass Matrices ◽  
The Stability ◽  
The Many

In numerically determining the response of a linear second-order multidegree-of-freedom vibrational system subjected to a general excitation, the common approach of applying one of the many multistep methods of numerical analysis (e.g., Milne-Simpson, Adams-Bashforth, etc.) leads ultimately to the solution of a system of linear equations. However, when the mass matrix of the original vibrational system is singular, the coefficient matrix of the system of equations also becomes singular and thus the response cannot be determined. Presented is a means of applying these multistep methods to vibrational systems which results in a method that is capable of obtaining the response independent of the singularity of the mass matrix. This technique is particularly useful in optimization where the values of the parameters of the system are unknown in advance, and thus the method of determining the response must be applicable for a wide range of values of the parameters. In the development and investigation of this technique, the causes of the stability problems which develop from the application of multistep methods to systems with nearly singular mass matrices become apparent.

Determination of Modal Parameters Using Finite Element Modeling Considering the Compliance at the Clamping End

2020 ◽  
Author(s):  
Aditya Saraf ◽  
Rinku K. Mittal ◽  
Ramesh K. Singh
Keyword(s):  
Finite Element ◽  
Material Removal ◽  
Removal Rate ◽  
Modal Parameters ◽  
Machining Parameters ◽  
Wide Range ◽  
The Stability ◽  
Stability Limits ◽  
Quality Surface

Abstract Micromilling process is widely used in biomedical and aerospace industries to produce complex 3D microscale features and components. The benefits of the micromilling process are ability of processing of wide range of materials, high quality surface finish, high material removal rate and submicron accuracy. One of the key limitations of micromachining is the low flexural stiffness of the microtool which can lead to chatter. Chatter in micromilling can be avoided by using the machining parameters within the stability limits. To predict the accurate stability limits, the tool tip dynamics need to be determined precisely. In this paper, a finite element method for determination of modal parameters has been proposed which considers the machine tool compliance at the clamping. The modeling of micro endmill and machine compliance is achieved by introducing elastic foundation interaction at the clamping interface. The model is further validated using experimental modal analysis on micro endmill at various locations and the results obtained were found to be in agreement with simulated results.

scholarly journals A QP-Free Algorithm for Finite Minimax Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Daolan Han ◽  
Jinbao Jian ◽  
Qinfeng Zhang
Keyword(s):  
Minimax Problems ◽  
Linear Equations ◽  
Inequality Constraints ◽  
Coefficient Matrix ◽  
Systems Of Linear Equations ◽  
Full Dimension ◽  
Finite Minimax ◽  
The Stability ◽  
Nonlinear Minimax Problems ◽  
Nonlinear Minimax

The nonlinear minimax problems without constraints are discussed. Due to the expensive computation for solving QP subproblems with inequality constraints of SQP algorithms, in this paper, a QP-free algorithm which is also called sequential systems of linear equations algorithm is presented. At each iteration, only two systems of linear equations with the same coefficient matrix need to be solved, and the dimension of each subproblem is not of full dimension. The proposed algorithm does not need any penalty parameters and barrier parameters, and it has small computation cost. In addition, the parameters in the proposed algorithm are few, and the stability of the algorithm is well. Convergence property is described and some numerical results are provided.

Influences of experimental parameters on the stability of a benzoporphyrin drug in water/ethanol mixtures: a statistical approach investigation

2005 ◽  
Vol 09 (09) ◽  
pp. 609-616 ◽  
Author(s):  
André Luiz Tessaro ◽  
Daniela Martins Fernandes ◽  
Ailton José Terezo ◽  
Vagner Roberto de Souza ◽  
Noboru Hioka
Keyword(s):  
Water Content ◽  
Aqueous Media ◽  
Solvent Mixtures ◽  
Wide Range ◽  
Experimental Parameters ◽  
Carboxylic Groups ◽  
Minimum Number ◽  
Set Up ◽  
The Stability

The benzoporphyrin derivative, named B3B, is a promising new drug for application in photodynamic therapy. In aqueous organic solvent mixtures, B3B, can be used in topical application for superficial diseases, like for skin cancer. In this paper, the self-aggregation phenomena of porphyrin molecules in aqueous media was investigated using a chemometric tool to evaluate the effects of experimental variables on the stability of the B3B monomer in water/ethanol mixtures. A 23 factorial design was employed which permitted determination of the magnitude of experimental parameters which influence aggregation of the drug at different pHs using the minimum number of experiments. At first, the pK a values of the B3B in water/ethanol mixtures were determined by spectrophotometric measurements, resulting in pK a1 = 3.3 and pK a2 = 5.7, corresponding to the imino nitrogens and carboxylic groups, respectively. The experimental variables (B3B concentration, time and water/ethanol composition) were evaluated in three protonation states of the drug, at pH 7.0, 4.1 and 2.6. The two levels (low and high) were set up at: time 5 (-) and 360 minutes (+); [B3B] 4.4 × 10-6(-) and 26.5 × 10-6 M (+); and water content in ethanol 40 (-) and 60% (+). The main parameter that determines the magnitude of the effects seems to be the charge component of B3B, which can be modulated by the pH. The results from the 23 fractional design indicated that the main variable inducing B3B aggregation is the water percentage in ethanol at each pH selected. The magnitude of this effect was pronounced at pH 4.1 where the carboxylic and nitrogen free base forms of B3B are maintained. The factors of time and [B3B], despite being small, are not insignificant. Finally, the effect of water content was investigated in a wide range of water percentage in these three pHs.

scholarly journals Cell Arrangement Method for Solving Systems of Linear Equations in Three Unknown

2019 ◽  
pp. 1-8
Author(s):  
A. Adu-Sackey ◽  
G. O. Lartey ◽  
F. T. Oduro ◽  
Stephen Eduafo
Keyword(s):  
Matrix Method ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Simultaneous Equation ◽  
Cell Arrangement ◽  
Alternative Approach ◽  
Daunting Task ◽  
Systems Of Linear Equations ◽  
Lengthy Process

In this paper, we develop an approach for finding the cofactor, ad joint, determinant and inverse of a three by three matrix under the Cell Arrangements method using the coefficient matrix of a given systems of linear equation in three unknowns. The method takes out completely the seemingly daunting task in evaluating such matrices associated to the standard matrix method in solving simultaneous equation in three variable. Unlike the standard matrix method that goes through a lengthy process to obtain separately all the matrices necessary for the determination of the unknowns, the structural frame of the Cell Arrangement method comes in handy and are consistent with the results from systems that have unique solutions. This alternative approach provides all the vital hybrid matrices of the coefficient matrix needed in the determination of the unknowns of the system of equations in three variables. It is our view that by far, the Cell arrangement method is easy to work with and less prone to errors that are often connected with other known methods.

Estimation of the performance stability of the newly developed topical haemostatic agents based on the chitosan/alginate fibrids

2016 ◽  
Vol 87 (7) ◽  
pp. 780-789 ◽  
Author(s):  
Marcin H Struszczyk ◽  
Bożena Wilbik-Hałgas ◽  
Michał Miklas ◽  
Magdalena Cichecka ◽  
Magdalena Kucharska ◽  
...  
Keyword(s):  
Medical Devices ◽  
Raw Materials ◽  
Testing Methods ◽  
Testing Method ◽  
Haemostatic Agents ◽  
Wide Range ◽  
The Stability ◽  
Preclinical And Clinical Studies ◽  
Selection Of

Designing medical devices requires a wide range of verification steps for estimation of the performance and safety. Designing the research program needs a rational selection of appropriate testing methods (in preclinical and clinical studies) for determination of the risk of potential incompatibilities resulting in adverse events. The significance of the appropriate selection of the testing method is increased in advanced medical devices. The presented research considers the verification of the functional properties of recently developed topical haemostatic agents with the use of the chitosan/alginate fibrids, based on the previously elaborated risk analysis made according to the guidelines of the PN-EN-ISO 14971:2012 and PN-EN ISO 22442-1:2008 standards. The aim of this research was to verify the stability of the performance of the newly developed haemostatic agents during storage. The defined aim of the study arose from the thesis that the appropriate selection of raw materials and a new manner of reprocessing them enabled keeping the usability of the final product for at least two years.

Stability of Squeeze-Film-Damper Supported Flexible Rotors

1977 ◽  
Vol 99 (4) ◽  
pp. 545-551 ◽  
Author(s):  
M. D. Rabinowitz ◽  
E. J. Hahn
Keyword(s):  
Steady State ◽  
System Stability ◽  
Squeeze Film ◽  
Design Data ◽  
Flexible Rotors ◽  
Wide Range ◽  
Single Mass ◽  
The Stability ◽  
Rotor Mass

Assuming the short bearing approximation and symmetric motions, the stability of the steady-state synchronous operation of centrally preloaded single-mass flexible rotors supported in squeeze-film bearing dampers is theoretically investigated. The stability regions are depicted over a wide range of system parameters and allow for easy determination of the stability of existing steady-state design data. The influence of rotor flexibility, rotor speed, bearing dimensions, lubricant viscosity, rotor mass distribution, and rotor unbalance on rotor-bearing system stability may be readily seen. In the absence of pressurization, instability regions were possible even with relatively high support damping, though no instability was indicated for speeds below the support natural frequency, or for bearing eccentricity ratio <0.4 at any speed. Pressurization of the lubricant supply was found to stabilize the system over the whole range of parameters investigated, regardless of unbalance, which would then be limited only by the bearing clearance. Data are presented which enable the minimum supply pressure to ensure full film lubrication to be conveniently determined.

scholarly journals Combined Application of Optical Fibers and CRLD Bolts to Monitor Deformation of a Pit-in-Pit Foundation

2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Chun Zhu ◽  
Kai Zhang ◽  
Huan Cai ◽  
Zhigang Tao ◽  
Bo An ◽  
...  
Keyword(s):  
Optical Fibers ◽  
Slip Surface ◽  
Deep Foundation ◽  
Foundation Pit ◽  
Deep Foundation Pit ◽  
Combined Application ◽  
Wide Range ◽  
Constant Resistance ◽  
The Stability ◽  
The Many

“Pit-in-pit” foundations, where the overall pit is divided into inner and outer pits, present a wide range of engineering problems and yet have received little detailed study. Among the many factors that affect the stability of a deep foundation pit, loading and rainfall are the two most important. Therefore, in this study, physical model experiments are carried out in the laboratory based on a pit-in-pit foundation that is typical of engineering applications in China, simulating the deformation of the system under different loading and rainfall flow conditions. Optical fibers along with constant resistance and large deformation (CRLD) bolts are adopted to collectively monitor the stress and strain inside the pit-in-pit foundation, assisted by fiber Bragg grating (FBG) displacement meters. The results of the monitoring show that the position of the inner pit relative to the outer pit has a strong influence on the stability of the outer pit. The side on which the inner pit is closest to the outer pit wall is the most prone to instability and should thus be reinforced. Comparison and analysis of monitoring results obtained with optical fibers and CRLD bolts allow a potentially dangerous slip surface to be identified, indicating the value of using this type of collective monitoring in deep foundation pits.

scholarly journals A new method for quantitative and qualitative representation of the noises type in Allan (and related) variances

2020 ◽  
Vol 72 (1) ◽  
Author(s):  
Kamil Maciuk ◽  
Jacek Kudrys ◽  
Mohammad Bagherbandi ◽  
Igor V. Bezmenov
Keyword(s):  
Sampling Interval ◽  
Satellite Clock ◽  
Qualitative And Quantitative ◽  
Quantitative Expression ◽  
Noise Type ◽  
Wide Range ◽  
Averaging Time ◽  
The Stability ◽  
The Time Domain

AbstractAllan variances and its related methods are commonly used to analyse a sequence of data in the time domain to measure frequency stability of oscillators. It allows for a determination of noise type as a function of the averaging time. This method is one of the most popular for identifying different noise types in the sensors data, and it is usually used for a wide range of studies on the stability of oscillators or atomic clocks. In this paper, the authors propose their own algorithm for a qualitative and quantitative expression of noise type using Allan and related variation. The methods currently used allow for the determination of the noise type graphically only, without quantifying the type and percentages for each of the integration steps. Our study allows for a numerical interpretation of the Allan (and related) variances data. A numerical example of the described method is based on GPS satellite clock corrections for 1825–2086 GPS Week (5 years) based on daily 30-s sampling interval products.

Symmetric Multistep Methods Revisited: II. Numerical Experiments

1999 ◽  
Vol 173 ◽  
pp. 309-314 ◽  
Author(s):  
T. Fukushima
Keyword(s):  
Multistep Methods ◽  
Computational Time ◽  
Integration Time ◽  
Implicit Methods ◽  
Symmetric Methods ◽  
Celestial Bodies ◽  
The Stability ◽  
Predictor Corrector ◽  
Symmetric Multistep Methods ◽  
Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

The many faces of STEM in materials science

1991 ◽  
Vol 49 ◽  
pp. 440-441
Author(s):  
John Silcox
Keyword(s):  
Materials Science ◽  
Auger Spectroscopy ◽  
Dark Field ◽  
High Tc Superconductors ◽  
High Tc ◽  
Acoustic Environment ◽  
Electromagnetic Vibration ◽  
The Many ◽  
Serial Mode

Determination of the microstructure and microchemistry of small features often provides the insight needed for the understanding of processes in real materials. In many cases, it is not adequate to use microscopy alone. Microdiffraction and microspectroscopic information such as EELS, X-ray microprobe analysis and Auger spectroscopy can all contribute vital parts of the picture. For a number of reasons, dedicated STEM offers considerable promise as a quantitative instrument. In this paper, we review progress towards effective quantitative use of STEM with illustrations drawn from studies of high Tc superconductors, compound semiconductors and metallization of H-terminated silicon.Intrinsically, STEM is a quantitative instrument. Images are acquired directly by detectors in serial mode which is particularly convenient for digital image acquisition, control and display. The VG HB501A at Cornell has been installed in a particularly stable electromagnetic, vibration and acoustic environment. Care has been paid to achieving UHV conditions (i.e., 10-10 Torr). Finally, it has been interfaced with a VAX 3200 work station by Kirkland. This permits, for example, the acquisition of bright field (or energy loss) images and dark field images simultaneously as quantitative arrays in perfect registration.

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