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Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 3rd...
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Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 3rd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: 31 May 2025 | Viewed by 5009

Special Issue Editors

Prof. Dr. Maria Luminița Scutaru

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Guest Editor
Department of Mechanical Engineering, Transilvania University of Brașov, B-dul Eroilor 20, 500036 Brașov, Romania
Interests: dynamic systems; multibody systems; analytical mechanics; mechanics of composite materials
Special Issues, Collections and Topics in MDPI journals
Dr. Catalin I. Pruncu

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Guest Editor
Departimento di Meccanica, Matematica e Management, Politecnico di Bari, 70125 Bari, Italy
Interests: numerical simulation; contact mechanics; engineering systems
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Luciano Lamberti

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Guest Editor
Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Viale Orabona 4, 70126 Bari, Italy
Interests: bioengineering and cell mechanics; nanosciences and nanotechnology; optical methods; materials science and characterization; structural optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Although it is considered that it is difficult to make further contributions in the field of mechanics, the spectacular evolution of technology and numerical calculation techniques have led to a reconsideration of these opinions and the development of increasingly sophisticated models that can predict, as accurately as possible, the phenomena that take place in dynamic systems. Therefore, researchers are studying mechanical systems with complicated behavior, observed in experiments and in computer models. The key requirement is that the system involves a nonlinearity. The impetus in mechanics and dynamical systems has come from many sources: computer simulation, experimental science, mathematics, and modeling. There are a wide range of influences. Computer experiments change the way in which we analyze these systems.

Topics of interest include, but are not limited to:

  • modeling mechanical systems
  • new methods in dynamic systems
  • behavior simulation of mechanical systems
  • nonlinear systems
  • multibody systems with elastic elements
  • multiple degrees of freedom
  • mechanical systems
  • experimental modal analysis
  • mechanics of materials

Prof. Dr. Maria Luminița Scutaru
Dr. Catalin I. Pruncu
Prof. Dr. Luciano Lamberti
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • dynamic systems
  • modelling of nonlinearities
  • algorithm
  • computer simulation
  • finite elements method

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Related Special Issues

Published Papers (4 papers)

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Research

19 pages, 5769 KiB  
Article
A Novel Method for Predicting the Behavior of a Sucker Rod Pumping Unit Based on the Polished Rod Velocity
by Jiaojian Yin and Hongzhang Ma
Mathematics 2024, 12(9), 1318; https://doi.org/10.3390/math12091318 - 25 Apr 2024
Cited by 1 | Viewed by 1159
Abstract
Fault dynamometer cards are the basis of the diagnosis technique for sucker rod pumping systems. Predicting fault cards with a pumping condition model is an economical and effective method. The usual model is described by a mixed function of the pump displacement and [...] Read more.
Fault dynamometer cards are the basis of the diagnosis technique for sucker rod pumping systems. Predicting fault cards with a pumping condition model is an economical and effective method. The usual model is described by a mixed function of the pump displacement and pump load, and it is difficult to use in the prediction method based on the analytical solution of the sucker rod string wave equation. In this paper, a normal pumping condition model described by a function of polished rod velocity is proposed. For the analytical solution of the sucker rod wave equation, an iterative prediction algorithm with pumping condition models is proposed, its convergence is analyzed, and then it is validated by classical finite difference method simulated cards and measured surface dynamometer cards. The results show that the proposed algorithm is accurate. The algorithm has a maximum relative error of 0.10% for the classical method simulated card area and 1.45% for the measured card area. The research of this paper provides an effective scheme for the design, prediction, and fault diagnosis of a sucker rod pumping system with an analytical solution. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 3rd Edition)
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16 pages, 7963 KiB  
Article
Investigating Behavior of Slider–Crank Mechanisms with Bearing Failures Using Vibration Analysis Techniques
by Mofareh Hassan Ghazwani and Van Vinh Pham
Mathematics 2024, 12(4), 544; https://doi.org/10.3390/math12040544 - 9 Feb 2024
Cited by 1 | Viewed by 1279
Abstract
This study focuses on investigating the behavior of slider–crank mechanisms with different bearing failures using a vibration analysis technique. The reliability and lifespan of bearings are crucial for such mechanisms, which convert rotary motion to reciprocating motion. Previous research primarily addressed ball-bearing failures, [...] Read more.
This study focuses on investigating the behavior of slider–crank mechanisms with different bearing failures using a vibration analysis technique. The reliability and lifespan of bearings are crucial for such mechanisms, which convert rotary motion to reciprocating motion. Previous research primarily addressed ball-bearing failures, neglecting needle bearings due to their specific applications. To bridge this gap, our experimental setup integrated both roller and ball bearings within a slider–crank mechanism. Vibration data were collected during normal operation, as well as under failure conditions of the ball and roller bearings. By analyzing the vibration signatures during simultaneous multiple failures, we gained insights into the nature of vibrations in the system. Furthermore, a mathematical model based on Hertzian contact was employed to calculate the theoretical frequency of ball bearings; however, due to the variable motion of the needle bearing, a novel mathematical model was proposed to estimate the defective impulse frequency, considering the inter-impact time between two impacts. The experimental results were compared with the healthy crank mechanism setup to draw meaningful conclusions. This research contributes to a comprehensive understanding of bearing failures in slider–crank mechanisms and provides valuable insights for designing reliable and long-lasting systems. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 3rd Edition)
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17 pages, 7153 KiB  
Article
Gibbs–Appell Equations in Finite Element Analysis of Mechanical Systems with Elements Having Micro-Structure and Voids
by Sorin Vlase, Marin Marin and Calin Itu
Mathematics 2024, 12(2), 178; https://doi.org/10.3390/math12020178 - 5 Jan 2024
Viewed by 945
Abstract
In this paper, the authors propose the application of the Gibbs–Appell equations to obtain the equations of motion in the case of a mechanical system that has elements with a micro-polar structure, containing voids. Voids can appear as a result of the processing [...] Read more.
In this paper, the authors propose the application of the Gibbs–Appell equations to obtain the equations of motion in the case of a mechanical system that has elements with a micro-polar structure, containing voids. Voids can appear as a result of the processing or manufacturing of the parts, or can be intentionally introduced. This research involves a model of the considered solid material containing voids. To determine the dynamic behavior of such a system, the Gibbs–Appell (GA) method is used to obtain the evolution equations, as an alternative to Lagrange’s classical description. The proposed method can be applied to any mechanical system consisting of materials with a micro-polar structure and voids. The study of such systems is interesting because the literature shows that even a reduce number of small voids can produce significant variations in physical behavior. The proposed method requires a smaller number of mathematical operations. To apply this method, the acceleration energy is calculated, which is then used to derive the equations. The method comes with advantages in the application to multibody systems having the mentioned properties and, in particular, in the study of robots and manipulators. Using the GA method, it is necessary to do a fewer differentiation operations than applying the Lagrange’s equations. This leads to a reduced amount of computation for obtaining the evolution equations. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 3rd Edition)
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12 pages, 2499 KiB  
Article
An Isogeometric Over-Deterministic Method (IG-ODM) to Determine Elastic Stress Intensity Factor (SIF) and T-Stress
by Khadija Yakoubi, Ahmed Elkhalfi, Hassane Moustabchir, Abdeslam El Akkad, Maria Luminita Scutaru and Sorin Vlase
Mathematics 2023, 11(20), 4293; https://doi.org/10.3390/math11204293 - 15 Oct 2023
Viewed by 999
Abstract
In order to examine the significance of Stress Intensity Factor and T-stress (K-T parameters) in modeling pressure-cracked structures, we propose a novel method known as the Isogeometric Over-Deterministic Method IG-ODM. IG-ODM utilizes the computation of stress and displacement fields through Extended Isogeometric Analysis [...] Read more.
In order to examine the significance of Stress Intensity Factor and T-stress (K-T parameters) in modeling pressure-cracked structures, we propose a novel method known as the Isogeometric Over-Deterministic Method IG-ODM. IG-ODM utilizes the computation of stress and displacement fields through Extended Isogeometric Analysis to improve the geometry and enhance the crack. Subsequently, these results are incorporated into the Williams expression, resulting in a set of deterministic equations that can be solved using a common solving method; this particular combination has never been attempted before. IG-ODM enables the computation of stress intensity factor SIF, T-stress, and higher-order parameters in the Williams expansion. To validate the effectiveness of this method, we conducted tests on a single-edge uniaxial-stress-cracked plate and a central uniaxial-stress-cracked plate. The results showed an error ranging from 0.06% to 2%. The obtained results demonstrate accuracy and satisfaction when compared to existing findings. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 3rd Edition)
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