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Mathematical Problems in Mechanical Engineering, 2nd Edition
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Mathematical Problems in Mechanical Engineering, 2nd Edition

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

Deadline for manuscript submissions: closed (30 September 2023) | Viewed by 8792

Special Issue Editor

Dr. Carlos Llopis-Albert

E-Mail Website
Guest Editor
Institute of Mechanical and Biomechanical Engineering, Universitat Politècnica de València–Camino de Vera s/n, 46022 Valencia, Spain
Interests: mathematical modeling of engineering problems; mechanical engineering; robotics; computational mechanics; vehicle dynamics; energy efficiency and sustainability; transportation; multibody dynamics; finite element modeling; biomechanics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is devoted to ‘‘Mathematical Problems in Mechanical Engineering’’, and focuses on areas that involve and enrich the application of mathematics and numerical methods to mechanical engineering problems. Areas covered include computational mechanics, robotics, fluid mechanics, material simulations, applications to biomechanics and mechanics in medicine, multiphysics, fracture mechanics, multiscale mechanics, finite element modeling, optimization techniques, designing efficient material-handling systems, logistics and distribution, manufacturing industries, mathematical applications in transportation, energy, environmental issues, fuzzy sets and systems, decision analysis, and business technologies related to mechanical engineering.

The main goals of this Special Issue are to (1) provide real-world mathematical applications in mechanical engineering, (2) report on the latest progress in utilizing these groundbreaking technologies, and (3) share gained insights.

We invite authors to contribute original research articles addressing significant issues and contributing to the development of new concepts, methodologies, applications, trends, and knowledge in the field. Review articles describing the current state-of-the-art are also welcome.

Prof. Dr. Carlos Llopis-Albert
Guest Editor

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

  • mechanical engineering
  • mathematical models
  • simulations
  • computational mechanics
  • robotics
  • finite element modeling
  • industrial engineering
  • uncertain decision-making

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Published Papers (4 papers)

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Research

19 pages, 4288 KiB  
Article
Analysis of the Influence of Calculation Parameters on the Design of the Gearbox of a High-Power Wind Turbine
by Francisco Rubio, Carlos Llopis-Albert and Ana M. Pedrosa
Mathematics 2023, 11(19), 4137; https://doi.org/10.3390/math11194137 - 30 Sep 2023
Cited by 5 | Viewed by 1625
Abstract
As wind turbine power requirements have evolved from the order of kilowatts (kWs) to the order of several megawatts (MWs), wind turbine components have been subjected to more demanding and critical operating conditions. The wind turbine must cope with higher wind loads due [...] Read more.
As wind turbine power requirements have evolved from the order of kilowatts (kWs) to the order of several megawatts (MWs), wind turbine components have been subjected to more demanding and critical operating conditions. The wind turbine must cope with higher wind loads due to larger blade sizes, which are also time-varying, and, ultimately, higher power levels. One of the challenges in the manufacture of high-power wind turbines lies in the gearbox and consists of achieving ever-greater power density without compromising efficiency, i.e., greater load capacity with lower weight (and production cost) and reduced power losses. Epicyclic geartrains are used to build the gearbox due to various advantages in relation to conventional gear systems, such as higher feasible gear ratios, higher efficiency, compactnesss, and lower weight. In this paper, several epicyclic geartrains with different structures will be analysed to reveal the influence that certain design parameters have on the size and weight of the gearbox components in the selected model and, therefore, of the gearbox itself. For this purpose, the theoretical model of the gearbox will be planned and the influence of the calculation parameters on the gearbox design will be analyzed following ISO 6336. Special emphasis is placed on the influence of the material used; the modulus and tooth width on the size and weight of the gearbox will be observed. Critical stresses are also calculated. The goal is to prepare the theoretical basis for an optimization process subject to geometric, kinematic, and dynamic constraints that will result in a gearbox as compact, energy-dense, and light as possible without compromising the service life of the components. Full article
(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering, 2nd Edition)
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20 pages, 5858 KiB  
Article
Adaptive Self-Organizing Map Using Optimal Control
by Ali Najem Alkawaz, Jeevan Kanesan, Irfan Anjum Badruddin, Sarfaraz Kamangar, Mohamed Hussien, Maughal Ahmed Ali Baig and N. Ameer Ahammad
Mathematics 2023, 11(9), 1995; https://doi.org/10.3390/math11091995 - 23 Apr 2023
Viewed by 1658
Abstract
The self-organizing map (SOM), which is a type of artificial neural network (ANN), was formulated as an optimal control problem. Its objective function is to minimize the mean quantization error, and the state equation is the weight updating equation of SOM. Based on [...] Read more.
The self-organizing map (SOM), which is a type of artificial neural network (ANN), was formulated as an optimal control problem. Its objective function is to minimize the mean quantization error, and the state equation is the weight updating equation of SOM. Based on the objective function and the state equations, the Hamiltonian equation based on Pontryagin’s minimum principle (PMP) was formed. This study presents two models of SOM formulated as an optimal control problem. In the first model, called SOMOC1, the design is based on the state equation representing the weight updating equation of the best matching units of the SOM nodes in each iteration, whereas in the second model, called SOMOC2, it considers the weight updating equation of all the nodes in the SOM as the state updating equation. The learning rate is treated as the control variable. Based on the solution of the switching function, a bang-bang control was applied with a high and low learning rate. The proposed SOMOC2 model performs better than the SOMOC1 model and conventional SOM as it considers all the nodes in the Hamiltonian equation, and the switching function obtained from it is influenced by all the states, which provides one costate variable for each. The costate determines the marginal cost of violating the constraint by the state equations, and the switching function is influenced by this, hence producing a greater improvement in terms of the mean quantization error at the final iteration. It was found that the solution leads to an infinite order singular arc. The possible solutions for the suitable learning rates during the singular arc period are discussed in this study. Full article
(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering, 2nd Edition)
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15 pages, 3774 KiB  
Article
Training Multilayer Neural Network Based on Optimal Control Theory for Limited Computational Resources
by Ali Najem Alkawaz, Jeevan Kanesan, Anis Salwa Mohd Khairuddin, Irfan Anjum Badruddin, Sarfaraz Kamangar, Mohamed Hussien, Maughal Ahmed Ali Baig and N. Ameer Ahammad
Mathematics 2023, 11(3), 778; https://doi.org/10.3390/math11030778 - 3 Feb 2023
Cited by 4 | Viewed by 2582
Abstract
Backpropagation (BP)-based gradient descent is the general approach to train a neural network with a multilayer perceptron. However, BP is inherently slow in learning, and it sometimes traps at local minima, mainly due to a constant learning rate. This pre-fixed learning rate regularly [...] Read more.
Backpropagation (BP)-based gradient descent is the general approach to train a neural network with a multilayer perceptron. However, BP is inherently slow in learning, and it sometimes traps at local minima, mainly due to a constant learning rate. This pre-fixed learning rate regularly leads the BP network towards an unsuccessful stochastic steepest descent. Therefore, to overcome the limitation of BP, this work addresses an improved method of training the neural network based on optimal control (OC) theory. State equations in optimal control represent the BP neural network’s weights and biases. Meanwhile, the learning rate is treated as the input control that adapts during the neural training process. The effectiveness of the proposed algorithm is evaluated on several logic gates models such as XOR, AND, and OR, as well as the full adder model. Simulation results demonstrate that the proposed algorithm outperforms the conventional method in terms of improved accuracy in output with a shorter time in training. The training via OC also reduces the local minima trap. The proposed algorithm is almost 40% faster than the steepest descent method, with a marginally improved accuracy of approximately 60%. Consequently, the proposed algorithm is suitable to be applied on devices with limited computation resources, since the proposed algorithm is less complex, thus lowering the circuit’s power consumption. Full article
(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering, 2nd Edition)
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19 pages, 5926 KiB  
Article
Analysis of Acoustic Emission Signals Processed with Wavelet Transform for Structural Damage Detection in Concrete Beams
by Jose M. Machorro-Lopez, Jorge A. Hernandez-Figueroa, Francisco J. Carrion-Viramontes, Juan P. Amezquita-Sanchez, Martin Valtierra-Rodriguez, Saul E. Crespo-Sanchez, Jesus J. Yanez-Borjas, Juan A. Quintana-Rodriguez and Luis A. Martinez-Trujano
Mathematics 2023, 11(3), 719; https://doi.org/10.3390/math11030719 - 31 Jan 2023
Cited by 10 | Viewed by 2178
Abstract
Concrete beams are elements used in many civil structures; unfortunately, they can contain cracks that lead to the collapse of the structures if those defects are not detected early enough. In this article, a new method to determine the structural condition of concrete [...] Read more.
Concrete beams are elements used in many civil structures; unfortunately, they can contain cracks that lead to the collapse of the structures if those defects are not detected early enough. In this article, a new method to determine the structural condition of concrete beams subjected to bending is proposed. In general, it is based on the processing of the acoustic emissions (AE) signals, which are generated during the application of a load, by using the mathematical tool called wavelet transform (WT). The sound of the internal energy/crack is recorded as a hit or AE signal event; then, those signals acquired as waveforms are post-processed with the continuous WT (CWT); then, the wavelet energy (WE) is calculated for each hit by using an adequate scale range and the most convenient mother wavelet. Thus, with this method, it is possible to determine the structural condition (healthy or damaged) of concrete beams subjected to bending just by calculating the WE of any hit at any time and, even more, it is possible to define more precisely the stage of the structural condition as a healthy condition, micro-cracks appearance, the manifestation of a principal crack (hit with the highest WE), propagation of the principal crack, and final rupture. This method is experimentally validated in the laboratory, and additionally, ultrasonic pulse velocity tests (UPVT) are performed for some specimens to confirm the change between healthy and damaged conditions. The results are promising in order to apply this effective method in concrete beams of real-life structures. Full article
(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering, 2nd Edition)
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