Noniterative Integration Algorithms with Controllable Numerical Dissipations for Structural Dynamics

2019 ◽  
Vol 16 (07) ◽  
pp. 1850111 ◽  
Author(s):  
Jinze Li ◽  
Kaiping Yu
Keyword(s):  
Structural Dynamics ◽  
Low Frequency ◽  
Conditional Stability ◽  
Linear Elastic ◽  
New Family ◽  
Special Cases ◽  
Frequency Domains ◽  
Stability And Accuracy ◽  
Stiffness Softening ◽  
New Algorithms

A new family of noniterative algorithms with controllable numerical dissipations for structural dynamics is studied. Particularly, this paper provides nine members of the proposed algorithms and two existing methods are included as two special cases. The proposed algorithms achieve unconditional stability and are second-order accurate for linear elastic systems. The explicit expressions of stability conditions for nonlinear stiffness systems are completely presented, which shows that new algorithms possess unconditional and conditional stability for stiffness softening and hardening systems, respectively. A comprehensive stability and accuracy analysis, including numerical energy dissipations and dispersions, are studied in order to gain insight into spectral properties of new algorithms. Due to the existence of the nonzero spurious root, this paper also pays attention to the influence of the spurious root, which shows that the spurious root does not influence numerical accuracy at low-frequency domains. Although the proposed algorithms exhibit the unusual overshoot behaviors in either displacement or velocity, numerical damping ratios in new algorithms can significantly eliminate this overshoot at a few steps. The new dissipative algorithms are appropriate to solve numerical transient responses of the structure. Numerical examples are also presented to demonstrate the analytical results.

A Generalized Structure-Dependent Semi-Explicit Method for Structural Dynamics

2018 ◽  
Vol 13 (11) ◽  
Author(s):  
Jinze Li ◽  
Kaiping Yu ◽  
Xiangyang Li
Keyword(s):  
Second Order ◽  
Numerical Dispersion ◽  
The Novel ◽  
Explicit Method ◽  
Dispersion Energy ◽  
Time Step ◽  
Linear Elastic ◽  
Special Cases ◽  
Stability And Accuracy ◽  
Stiffness Softening

In this paper, a novel generalized structure-dependent semi-explicit method is presented for solving dynamical problems. Some existing algorithms with the same displacement and velocity update formulas are included as the special cases, such as three Chang algorithms. In general, the proposed method is shown to be second-order accurate and unconditionally stable for linear elastic and stiffness softening systems. The comprehensive stability and accuracy analysis, including numerical dispersion, energy dissipation, and the overshoot behavior, are carried out in order to gain insight into the numerical characteristics of the proposed method. Some numerical examples are presented to show the suitable capability and efficiency of the proposed method by comparing with other existing algorithms, including three Chang algorithms and Newmark explicit method (NEM). The unconditional stability and second-order accuracy make the novel methods take a larger time-step, and the explicitness of displacement at each time-step succeeds in avoiding nonlinear iterations for solving nonlinear stiffness systems.

An Improved Structure-Dependent Explicit Method for Structural Dynamics

2008 ◽  
Author(s):  
Shuenn-Yih Chang ◽  
Chiu-Li Huang
Keyword(s):  
Low Frequency ◽  
Conditional Stability ◽  
Explicit Method ◽  
Time Step ◽  
Structural Dynamic ◽  
Linear Elastic ◽  
Acceleration Method ◽  
The Stability ◽  
Stiffness Softening ◽  
Hardening System

An explicit method is presented herein whose coefficients are determined from the initial structural properties of the analyzed system. Thus, it is structure-dependent. This method has a great stability property when compared to the previously published method [6], which is unconditionally stable for linear elastic and any instantaneous stiffness softening systems while it only has conditional stability for an instantaneous stiffness hardening system. The most important improvement of this method is that it has unconditional stability for general instantaneous stiffness hardening systems in addition to linear elastic and instantaneous stiffness softening systems. This implies that a time step may be selected base on accuracy consideration only and the stability problem might be neglected. Hence, many computational efforts can be saved in the step-by-step solution of a general structural dynamic problem, where the response is dominated by the low frequency modes and the high frequency responses are of no great interest, when compared to an explicit method, such as the Newmark explicit method, and an implicit method, such as the constant average acceleration method.

A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method

1993 ◽  
Vol 60 (2) ◽  
pp. 371-375 ◽  
Author(s):  
J. Chung ◽  
G. M. Hulbert
Keyword(s):  
Structural Dynamics ◽  
Time Integration ◽  
Low Frequency ◽  
Numerical Dissipation ◽  
Integration Algorithm ◽  
Integration Methods ◽  
New Family ◽  
Time Integration Methods ◽  
Improved Performance ◽  
Dynamics Problems

A new family of time integration algorithms is presented for solving structural dynamics problems. The new method, denoted as the generalized-α method, possesses numerical dissipation that can be controlled by the user. In particular, it is shown that the generalized-α method achieves high-frequency dissipation while minimizing unwanted low-frequency dissipation. Comparisons are given of the generalized-α method with other numerically dissipative time integration methods; these results highlight the improved performance of the new algorithm. The new algorithm can be easily implemented into programs that already include the Newmark and Hilber-Hughes-Taylor-α time integration methods.

Singular Mode Characteristics of Fluid-Structure Interaction Modal Formulations

2012 ◽  
Author(s):  
Jeffrey L. Cipolla
Keyword(s):  
Low Frequency ◽  
Order Reduction ◽  
Coupled System ◽  
Forced Response ◽  
Coupled Modes ◽  
Model Order ◽  
Linear Elastic ◽  
Frequency Domains ◽  
Rigid Body Modes ◽  
Mode Characteristics

Modal formulations for linear acoustic and vibration problems are important for model order reduction as well as physical interpretation and insight. In the case of structural acoustic systems, a number of formulations exist for the computation of the modes of the coupled system: these may be referred to as ‘coupled modes’, ‘in-water modes’, etc. These modes have the desirable property that they diagonalize the undamped structural-acoustic problem, making forced-response computations in the time- and frequency-domains trivial. In this paper, we review a number of alternative formulations for the undamped FSI mode problem, and concentrate on a particular aspect: the existence and nature of the singular modes of the systems, i.e. the modes at zero frequency. Corresponding to rigid-body modes in linear elastic systems, these modes are essential for accurate low-frequency performance of reduced-order models. It is found that the original, nonsymmetric system of Zienkiewicz and Newton [53] maintains physically reasonable singular mode properties, while many other formulations do not.

New family of Whitney numbers

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 309-320 ◽  
Author(s):  
B.S. El-Desouky ◽  
Nenad Cakic ◽  
F.A. Shiha
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Explicit Formulas ◽  
Basic Properties ◽  
New Family ◽  
Whitney Numbers ◽  
Special Cases

In this paper we give a new family of numbers, called ??-Whitney numbers, which gives generalization of many types of Whitney numbers and Stirling numbers. Some basic properties of these numbers such as recurrence relations, explicit formulas and generating functions are given. Finally many interesting special cases are derived.

scholarly journals Survival and Reliability Analysis with an Epsilon-Positive Family of Distributions with Applications

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 908
Author(s):  
Perla Celis ◽  
Rolando de la Cruz ◽  
Claudio Fuentes ◽  
Héctor W. Gómez
Keyword(s):  
Survival Data ◽  
Maximum Likelihood Estimates ◽  
New Class ◽  
New Family ◽  
Gamma Distributions ◽  
Special Cases ◽  
Log Normal ◽  
Positive Support ◽  
Positive Distributions ◽  
Family Of Distributions

We introduce a new class of distributions called the epsilon–positive family, which can be viewed as generalization of the distributions with positive support. The construction of the epsilon–positive family is motivated by the ideas behind the generation of skew distributions using symmetric kernels. This new class of distributions has as special cases the exponential, Weibull, log–normal, log–logistic and gamma distributions, and it provides an alternative for analyzing reliability and survival data. An interesting feature of the epsilon–positive family is that it can viewed as a finite scale mixture of positive distributions, facilitating the derivation and implementation of EM–type algorithms to obtain maximum likelihood estimates (MLE) with (un)censored data. We illustrate the flexibility of this family to analyze censored and uncensored data using two real examples. One of them was previously discussed in the literature; the second one consists of a new application to model recidivism data of a group of inmates released from the Chilean prisons during 2007. The results show that this new family of distributions has a better performance fitting the data than some common alternatives such as the exponential distribution.

scholarly journals A New Family of High-Order Ehrlich-Type Iterative Methods

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1855 ◽  
Author(s):  
Petko D. Proinov ◽  
Maria T. Vasileva
Keyword(s):  
Iterative Methods ◽  
Local Convergence ◽  
Semilocal Convergence ◽  
High Order ◽  
Convergence Theorems ◽  
New Family ◽  
Special Cases ◽  
Iteration Functions ◽  
Iteration Function ◽  
Local Convergence Analysis

One of the famous third-order iterative methods for finding simultaneously all the zeros of a polynomial was introduced by Ehrlich in 1967. In this paper, we construct a new family of high-order iterative methods as a combination of Ehrlich’s iteration function and an arbitrary iteration function. We call these methods Ehrlich’s methods with correction. The paper provides a detailed local convergence analysis of presented iterative methods for a large class of iteration functions. As a consequence, we obtain two types of local convergence theorems as well as semilocal convergence theorems (with computer verifiable initial condition). As special cases of the main results, we study the convergence of several particular iterative methods. The paper ends with some experiments that show the applicability of our semilocal convergence theorems.

scholarly journals Analysis of heart rate variability in corn snakes (Pantherophis guttatus)

2021 ◽  
Vol 10 (11) ◽  
pp. e294101119781
Author(s):  
Antonio Gomes da Silva Neto ◽  
Daniel Souza Ferreira Magalhães ◽  
Raduan Hage ◽  
Laurita dos Santos ◽  
José Carlos Cogo
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Nervous System ◽  
Autonomic Nervous System ◽  
Low Frequency ◽  
Autonomic Nervous ◽  
Rr Interval ◽  
Diagnosis And Prognosis ◽  
Frequency Domains ◽  
The Time Domain

The assessment of heart rate variability (HRV) by linear methods in conjunction with Poincaré plots can be useful for evaluating cardiac regulation by the autonomic nervous system and for the diagnosis and prognosis of heart disease in snakes. In this report, we describe an analysis of HRV in conscious adult corn snakes Pantherophis guttatus (P. guttatus).  The electrocardiogram (ECG) parameters were determined in adult corn snakes (8 females, 13 males) and used for HRV analysis, and the RR interval was analyzed by linear methods in the time and frequency domains. There was no sex-related difference in heart rate. However, significant differences were seen in the duration of the P, PR, and T waves and QRS complex; there was no difference in the QT interval. The values for the RR interval varied by 15.3% and 18.8% in male and female snakes, respectively, and there was considerable variation in the values for the high and low frequency domains. The changes in the time domain were attributed to regulation by the parasympathetic branch of the autonomic nervous system, in agreement with variations in the high and low frequency domains. The values for standard deviations 1 and 2 in Poincaré plots, as well as the values of the frequency domain, provide useful parameters for future studies of cardiac function in P. guttatus.

scholarly journals The modified beta transmuted family of distributions with applications using the exponential distribution

PLoS ONE ◽  
2021 ◽  
Vol 16 (11) ◽  
pp. e0258512
Author(s):  
Phillip Oluwatobi Awodutire ◽  
Oluwafemi Samson Balogun ◽  
Akintayo Kehinde Olapade ◽  
Ethelbert Chinaka Nduka
Keyword(s):  
Exponential Distribution ◽  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Life Time ◽  
Time Data ◽  
New Family ◽  
Special Cases ◽  
The Family ◽  
Family Of Distributions

In this work, a new family of distributions, which extends the Beta transmuted family, was obtained, called the Modified Beta Transmuted Family of distribution. This derived family has the Beta Family of Distribution and the Transmuted family of distribution as subfamilies. The Modified beta transmuted frechet, modified beta transmuted exponential, modified beta transmuted gompertz and modified beta transmuted lindley were obtained as special cases. The analytical expressions were studied for some statistical properties of the derived family of distribution which includes the moments, moments generating function and order statistics. The estimates of the parameters of the family were obtained using the maximum likelihood estimation method. Using the exponential distribution as a baseline for the family distribution, the resulting distribution (modified beta transmuted exponential distribution) was studied and its properties. The modified beta transmuted exponential distribution was applied to a real life time data to assess its flexibility in which the results shows a better fit when compared to some competitive models.

scholarly journals CROSS-MOMENTS COMPUTATION FOR STOCHASTIC CONTEXT-FREE GRAMMARS

2018 ◽  
Vol 33 (1) ◽  
pp. 041
Author(s):  
Velimir M. Ilić ◽  
Miroslav D. Ćirić ◽  
Miomir S. Stanković
Keyword(s):  
Random Variable ◽  
Sample Space ◽  
Efficient Computation ◽  
Context Free Grammar ◽  
Special Cases ◽  
The Cross ◽  
Stochastic Context Free Grammars ◽  
Context Free ◽  
New Algorithms ◽  
Vector Random Variable

In this paper we consider the problem of efficient computation of cross-moments of a vector random variable represented by a stochastic context-free grammar. Two types of cross-moments are discussed. The sample space for the first one is the set of all derivations of the context-free grammar, and the sample space for the second one is the set of all derivations which generate a string belonging to the language of the grammar. In the past, this problem was widely studied, but mainly for the cross-moments of scalar variables and up to the second order. This paper presents new algorithms for computing the cross-moments of an arbitrary order, while the previously developed ones are derived as special cases.

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