Characterization of Real Eigenvalues in Linear Viscoelastic Oscillators and the Nonviscous Set

2013 ◽  
Vol 81 (2) ◽  
Author(s):  
Mario Lázaro ◽  
José L. Pérez-Aparicio
Keyword(s):  
Time History ◽  
Negative Numbers ◽  
Closed Intervals ◽  
Convolution Integrals ◽  
History Of ◽  
Linear Viscoelastic ◽  
One Step ◽  
Damping Model ◽  
Theoretical Results

In structural dynamics, energy dissipative mechanisms with nonviscous damping are characterized by their dependence on the time-history of the response velocity, which is mathematically represented by convolution integrals involving hereditary functions. The widespread Biot damping model assumes that such functions are exponential kernels, which modify the eigenvalues' set so that as many real eigenvalues (named nonviscous eigenvalues) as kernels are added to the system. This paper is focused on the study of a mathematical characterization of the nonviscous eigenvalues. The theoretical results allow the bounding of a set belonging to the real negative numbers, called the nonviscous set, constructed as the union of closed intervals. Exact analytical solutions of the nonviscous set for one and two exponential kernels and approximated solutions for the general case of N kernels are developed. In addition, the nonviscous set is used to build closed-form expressions to compute the nonviscous eigenvalues. The results are validated with numerical examples covering single and multiple degree-of-freedom systems where the proposed method is compared with other existing one-step approaches available in the literature.

scholarly journals Four-dimensional impedance manometry derived from esophageal high-resolution impedance-manometry studies: a novel analysis paradigm

2020 ◽  
Vol 13 ◽  
pp. 175628482096905
Author(s):  
Wenjun Kou ◽  
Dustin A. Carlson ◽  
Neelesh A. Patankar ◽  
Peter J. Kahrilas ◽  
John E. Pandolfino
Keyword(s):  
High Resolution ◽  
Flow Rate ◽  
Time History ◽  
Type I ◽  
Bolus Transit ◽  
Time Flow ◽  
Biophysical Analysis ◽  
History Of ◽  
Emptying Time

Background: This study aimed to introduce a novel analysis paradigm, referred to as 4-dimensional (4D) manometry based on biophysical analysis; 4D manometry enables the visualization of luminal geometry of the esophagus and esophagogastric junction (EGJ) using high-resolution-impedance-manometry (HRIM) data. Methods: HRIM studies from two asymptomatic controls and one type-I achalasia patient were analyzed. Concomitant fluoroscopy images from one control subject were used to validate the calculated temporal-spatial luminal radius and time-history of intraluminal bolus volume and movement. EGJ analysis computed diameter threshold for emptying, emptying time, flow rate, and distensibility index (DI), which were compared with bolus flow time (BFT) analysis. Results: For normal control, calculated volumes for 5 ml swallows were 4.1 ml–6.7 ml; for 30 ml swallows 21.3 ml–21.8 ml. With type-I achalasia, >4 ml of intraesophageal bolus residual was present both pre- and post-swallow. The four phases of bolus transit were clearly illustrated on the time-history of bolus movement, correlating well with the fluoroscopic images. In the control subjects, the EGJ diameter threshold for emptying was 8 mm for 5 ml swallows and 10 mm for 30 ml swallows; emptying time was 1.2–2.2 s for 5 ml swallows (BFT was 0.3–3 s) and 3.25–3.75 s for 30 ml swallows; DI was 2.4–3.4 mm2/mmHg for 5 ml swallows and 4.2–4.6 mm2/mmHg for 30 ml swallows. Conclusions: The 4D manometry system facilitates a comprehensive characterization of dynamic esophageal bolus transit with concurrent luminal morphology and pressure from conventional HRIM measurements. Calculations of flow rate and wall distensibility provide novel measures of EGJ functionality.

Modal Analysis of Nonviscously Damped Beams

2006 ◽  
Vol 74 (5) ◽  
pp. 1026-1030 ◽  
Author(s):  
S. Adhikari ◽  
M. I. Friswell ◽  
Y. Lei
Keyword(s):  
Natural Frequencies ◽  
Past History ◽  
Kernel Functions ◽  
Mode Shapes ◽  
Damping Force ◽  
The Past ◽  
Convolution Integrals ◽  
Special Cases ◽  
History Of ◽  
Damping Model

Linear dynamics of Euler–Bernoulli beams with nonviscous nonlocal damping is considered. It is assumed that the damping force at a given point in the beam depends on the past history of velocities at different points via convolution integrals over exponentially decaying kernel functions. Conventional viscous and viscoelastic damping models can be obtained as special cases of this general damping model. The equation of motion of the beam with such a general damping model results in a linear partial integro-differential equation. Exact closed-form equations of the natural frequencies and mode shapes of the beam are derived. Numerical examples are provided to illustrate the new results.

scholarly journals Analysis of Nonviscous Oscillators Based on the Damping Model Perturbation

2016 ◽  
Vol 2016 ◽  
pp. 1-19
Author(s):  
Mario Lázaro ◽  
César F. Casanova ◽  
Ignacio Ferrer ◽  
Pedro Martín
Keyword(s):  
Fractional Derivatives ◽  
Numerical Approach ◽  
Kernel Functions ◽  
Series Expansions ◽  
Convolution Integrals ◽  
Taylor Series Expansions ◽  
Linear Viscoelastic ◽  
Motion Characteristic ◽  
Independent Variable ◽  
Damping Model

A novel numerical approach to compute the eigenvalues of linear viscoelastic oscillators is developed. The dissipative forces of these systems are characterized by convolution integrals with kernel functions, which in turn contain a set of damping parameters. The free-motion characteristic equation defines implicitly the eigenvalues as functions of such parameters. After choosing one of them as independent variable, the key idea of the current paper is to obtain a differential equation whose solution can be considered, under certain conditions, a good approximation. The method is validated with several numerical examples related to damping models based on exponential kernels, on fractional derivatives, and on the well-known viscous model. Taylor series expansions up to the second order are obtained and in addition analytical solutions for the viscous model are achieved. The numerical results are very close to the exact ones for light and medium levels of damping and also very good for high levels if the chosen parameter is close to initial values that are defined for every case.

Performance of cylindrical liquid storage tanks in Silakhor, Iran earthquake of March 31, 2006

2007 ◽  
Vol 40 (4) ◽  
pp. 173-182 ◽  
Author(s):  
Sassan Eshghi ◽  
Mehran S. Razzaghi
Keyword(s):  
Linear Time ◽  
Time History ◽  
Storage Tanks ◽  
Liquid Storage ◽  
History Analysis ◽  
History Of ◽  
Flexible Foundation ◽  
Theoretical Results ◽  
Strong Ground ◽  
Good Agreement

Several on-ground cylindrical liquid storage tanks experienced strong ground motion during the “Silakhor” earthquake of March 31, 2006 in western Iran, and some of the tanks suffered minor to moderate damage. In this study two of the affected tanks that were located close to the station of recording the time history of the earthquake were investigated. Responses of these tanks to the earthquake were estimated using published methods and also non-linear time history analysis, for both rigid foundation and flexible foundation assumptions. Theoretical results were compared and were generally in good agreement with the observed performance of tanks during the earthquake. For the broad tank uplift displacements observed from the earthquake matched quite closely the predictions of numerical analysis and some of the published methods, although there was a significant variation in the predictions of various methods. It was also shown that axial stresses in tank shells uplifting under earthquake are very dependent on the rigidity of the foundation.

scholarly journals Proposal of a Viscous Model for Nonviscously Damped Beams Based on Fractional Derivatives

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Mario Lázaro ◽  
Jose M. Molines-Cano ◽  
Ignacio Ferrer ◽  
Vicente Albero
Keyword(s):  
Fractional Derivatives ◽  
Viscoelastic Materials ◽  
One Dimensional ◽  
Damping Matrix ◽  
Convolution Integrals ◽  
Stiffness Matrices ◽  
History Of ◽  
Numerical Tools ◽  
Theoretical Results ◽  
Modal Space

Viscoelastic materials are widely used in structural dynamics for the control of the vibrations and energy dissipation. They are characterized by damping forces that depend on the history of the velocity response via hereditary functions involved in convolution integrals, leading to a frequency-dependent damping matrix. In this paper, one-dimensional beam structures with viscoelastic materials based on fractional derivatives are considered. In this work, the construction of a new equivalent viscous system with fictitious parameters but capable of reproducing the response of the viscoelastic original one with acceptable accuracy is proposed. This allows us to take advantage of the well-known available numerical tools for viscous systems and use them to find response of viscoelastic structures. The process requires the numerical computation of complex frequencies. The new fictitious viscous parameters are found to be matching the information provided by the frequency response functions. New mass, damping, and stiffness matrices are found, which in addition have the property of proportionality, so they become diagonal in the modal space. The theoretical results are contrasted with two different numerical examples.

Acoustic Impact Technique for Characterization of Defects in Laminated Composites

1993 ◽  
Author(s):  
A. Haque ◽  
Pollapragada K. Raju
Keyword(s):  
Time Domain ◽  
Laminated Composites ◽  
Time History ◽  
Region Of Interest ◽  
Experimental Configuration ◽  
History Of ◽  
Acoustic Impact ◽  
The Time Domain ◽  
Laminated Structures

Abstract The Acoustic Impact Technique (AIT) of nondestructive testing (NDT) has been investigated in detecting gross defects such as delamination in laminated composites. The use of Acoustic Impact Technique has shown encouraging results by previous investigators in identifying defects like delamination and disbonds in honeycomb structures. Very limited work has been reported in the literature about the utility of AIT as a NDT tool for testing in laminated structures. The present work investigates the sensitiveness of the AIT method in detecting delamination in laminated composites in terms of size, shape, position and degree of concentration. The significant advantage of AIT is that this technique is attractive for field applications. The method involves striking the structure with an instrumented impacter in the region of interest and recording the time history of the impulse. The response of the signals received from both good and defective zones of a specimen were analyzed in the time domain. The experimental configuration used by previous investigators was very restrictive. In this study a different approach to AIT is developed. The effectiveness of AIT was evaluated by making a comparative study with ultrasonic C-scan in detecting similar types of defects. The results indicate the sensitiveness of AIT in detecting delamination in laminated composites in terms of size, depth and degree of concentration.

Estimating settlements in dry sands during earthquakes

1976 ◽  
Vol 13 (4) ◽  
pp. 355-363 ◽  
Author(s):  
W. D. L. Finn ◽  
P. M. Byrne
Keyword(s):  
Empirical Relationship ◽  
Time History ◽  
Earthquake Excitation ◽  
Wide Range ◽  
History Of ◽  
Linear Viscoelastic ◽  
Earthquake Scaling ◽  
Shear Strains ◽  
Surface Settlements ◽  
Settlement Distribution

An analytical method for predicting the settlement of a horizontal stratum of dry sand subjected to earthquake excitation is presented. An equivalent linear viscoelastic dynamic analysis is used to determine the time-history of shear strains at various levels within the stratum. The vertical strains caused by these shear strains are calculated by an empirical relationship shown to be in close agreement with laboratory test data over a wide range of relative densities. This allows the settlement distribution with depth to be calculated as a function of time.The method was applied to a 50 ft (15 m) stratum of sand. A base acceleration corresponding to 0–10 s of the N–S component of El Centro earthquake was used. Settlement distribution vs. depth, as well as surface settlements for various relative densities and earthquake scaling factors are shown. The effect of surcharge loading on settlements is investigated in an approximate manner.The results may be used to estimate differential settlement of a structure due to an earthquake. The results show that while the compaction of the upper layers may be sufficient to reduce the settlements due to static loads to tolerable amounts, deep-seated settlements will still occur during an earthquake.

Subversive Mobilities

Transfers ◽  
2013 ◽  
Vol 3 (1) ◽  
pp. 7-25 ◽  
Author(s):  
Mikkel Thelle
Keyword(s):  
Public Space ◽  
Cultural History ◽  
Turn Of The Century ◽  
Public Action ◽  
History Of ◽  
Urban Conflict

The article approaches mobility through a cultural history of urban conflict. Using a case of “The Copenhagen Trouble,“ a series of riots in the Danish capital around 1900, a space of subversive mobilities is delineated. These turn-of-the-century riots points to a new pattern of mobile gathering, the swarm; to a new aspect of public action, the staging; and to new ways of configuring public space. These different components indicate an urban assemblage of subversion, and a new characterization of the “throwntogetherness“ of the modern public.

PROGRAM OF PREDICTION AND MANAGEMENT OF COINTEGED DYNAMIC ECONOMIC PROCESSES BASED ON THE CYBERNETIC APPROACH

2019 ◽  
Author(s):  
Olena Bundak ◽  
Nataliia Zubovetska
Keyword(s):  
Computer Program ◽  
Pair Correlation ◽  
Time History ◽  
Critical Area ◽  
Concrete Object ◽  
Graphic Arts ◽  
Ex Post ◽  
History Of ◽  
Successive Change ◽  
Rms Errors

A method and computer program ConRow, which prognostication of development of the dynamically CPLD economic transients is executed by, is described in the article. Such prognostication of economic processes is very important in the cases when their development can result in undesirable consequences, that to go out in the so-called critical area. Extrapolation in a critical area with the use of information about the conduct of the system at an area, near to it, allows to estimate to the lead through of experiment in the critical area of his consequence. For the imitation of conduct of object the function of review is set on entrance influence. For a concrete object this function can express, for example, dependence of change of level sale from time-history of charges on advertising and set as a numeral row. Statistics as a result of analysis of row are represented in a table, where the level of meaningfulness is set statistician, and also parameters of the handed over criteria. The graphic reflection of information is intended for visualization of analysis. Here represented on the points of graphic arts, the crooked smoothing which are calculated as полиномиальные regressions is added. The best approaching is controlled by sight on the proper graph, and also by minimization of their rms errors. Models of prognostication by sight and as formulas represented on graphic arts, the middle is here determined tailings and their chance is checked up on statistics of signs. After the got models determined also and prognosis values of influences and reviews. Establishing an order models of Сr(p) of co integrate regression is carried out separate custom controls. The coefficient of clay correlation of ruФ shows by itself pair correlation between lines with a successive change in relation to each other on a size to лагу of l = 1, 2, 3 . The program was tested on the example of ex-post prognosis at establishing an integration connection and possibility of prognostication of growth of nominal average monthly settlings on the basis of these statistical indexes of consumer inflation in Ukraine.

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