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Symmetry in Mechanical Engineering: Properties and Applications

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A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Engineering and Materials".

Deadline for manuscript submissions: 30 September 2025 | Viewed by 20228

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Prof. Dr. Yunqing Tang

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Guest Editor

School of Mechanical Engineering, Shandong University, Jinan 250061, China
Interests: material design; material machining; friction and wear; nanoscale heat transfer; computational materials science
Special Issues, Collections and Topics in MDPI journals

Dr. Kun Xu

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Guest Editor

College of Electrical Engineering, Henan University of Technology, Zhengzhou 450001, China
Interests: flexible electronics and sensors; thin film transistor; neuromorphic device; mechanical nondestructive testing technology

Dr. Bing Yang

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Guest Editor

Centre for Advanced Laser Manufacturing (CALM), School of Mechanical Engineering, Shandong University of Technology, Zibo 255000, China
Interests: nanoscale thermal transport; interfacial thermal conductance; computational materials; laser micro-/nano- processing
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Special Issue Information

Dear Colleagues,

Symmetry in mechanical engineering refers to the balanced arrangement of components and features in a system or design. Symmetrical properties, such as axial, radial, or planar symmetry, enable the uniform distribution of forces, vibrations, and loads, resulting in improved structural integrity and reduced wear. A symmetrical design often offers greater stability, ease of manufacturing, and cost-effectiveness, and it has diverse applications in mechanical engineering, e.g., in structural engineering, symmetrical shapes and arrangements enhance load-bearing capacity, minimizing stress concentrations; in fluid mechanics, symmetrical profiles reduce drag, enhance flow characteristics, and improve energy efficiency. On the other hand, asymmetry can offer unique advantages to mechanical systems in specific scenarios: e.g., by introducing asymmetry via variations in material properties, surface textures, or geometry, a specialized thermal behavior could be performed, such as localized heat spreading, directed thermal gradients, or controlled temperature differentials. Therefore, constructing or modifying symmetry could provide properties that enhance the reliability, functionality and efficiency of mechanical systems, which is an effective approach in mechanical engineering to satisfy the requirements of performance and functions for different applications and under different conditions.

Prof. Dr. Yunqing Tang
Dr. Kun Xu
Dr. Bing Yang
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. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

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Keywords

mechanical engineering
symmetric structure
asymmetric structure
mechanical design
machining
MEMS
structural reliability
thermal management
mass transfer
topology optimization

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Published Papers (11 papers)

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Research

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17 pages, 9908 KiB

Open AccessArticle

Effect of Laying Angle on the Stress Distribution and Stiffness Degradation of Symmetrically Cracked Laminates

by Zhicheng Huang, Biao Xiong, Xingguo Wang and Fulei Chu

Symmetry 2025, 17(4), 495; https://doi.org/10.3390/sym17040495 - 25 Mar 2025

Viewed by 184

Abstract

In this paper, the effects of laying angle on the stress distribution and stiffness degradation of glass epoxy laminates with symmetrical cracks are systematically studied by variational analysis and numerical simulation. Based on the principle of minimum complementary energy, the control equation was established and solved using MATLAB programming. The stress field and stiffness attenuation characteristics of 90°-layer crack density (CD = 0.5 cr/mm) and laminates with different angles

{[θ_{m} / 90_{n}]}_{s}

were analyzed. The results show that the crack significantly aggravates the stress concentration effect, and when the laying angle exceeds 45°, the crack growth rate and stiffness degradation rate are significantly improved. Specifically, when the laying angle is 30° and L₁/t₁ = 50, the stiffness degradation rate (E_x/E_x0) of the laminates only decreases to 0.987, while when the laying angle increases to 60° and L₁/t₁ = 3, the stiffness degradation rate suddenly decreases to 0.754 under the same conditions, indicating that small-angle laying (<45°) can effectively alleviate local stress concentration and delay stiffness degradation. By comparing the experimental data of existing references, the model error is verified to be less than 1%, and the reliability of the method is confirmed. It is further proposed that in the design of symmetrical laminated plates, the crack propagation resistance can be significantly optimized by controlling the laying angle of the main bearing layer in the range of 30°~45°, which provides a quantitative basis for crack suppression and structural life improvement in engineering. Full article

(This article belongs to the Special Issue Symmetry in Mechanical Engineering: Properties and Applications)

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19 pages, 2517 KiB

Open AccessArticle

Bending Analysis of Symmetrical Porous Functionally Graded Sandwich Panels

by Zhicheng Huang, Yingjie Chen, Xingguo Wang and Fulei Chu

Symmetry 2025, 17(3), 327; https://doi.org/10.3390/sym17030327 - 21 Feb 2025

Viewed by 330

Abstract

The study of the mechanical behavior of functionally graded material (FGM) sandwich plates under thermo-mechanical loading is of great significance for advanced structural design. This study systematically verifies the applicability of the shear strain functions proposed by Reddy and Touratier in the nonlinear bending analysis of porous FGM sandwich plates. Using the existing four-variable shear deformation theory framework, the governing equations are derived through the principle of minimum potential energy, and the Navier method is applied for a numerical solution. For the first time, the study systematically compared the effects of three different porosity distribution patterns on dimensionless deflection, and verified the reliability of the model by comparing it with literature data. The results demonstrate that the adopted shear strain functions can accurately predict the influence of key parameters, including layer thickness ratio, aspect ratio, side-to-thickness ratio, volume fraction index, and porosity, on the deflection performance of sandwich plates. This research provides an important verification basis for the theoretical analysis and engineering application of FGM sandwich plates, particularly offering quantitative evidence for assessing the influence of porosity effects on theoretical prediction accuracy. Full article

(This article belongs to the Special Issue Symmetry in Mechanical Engineering: Properties and Applications)

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34 pages, 13286 KiB

Open AccessArticle

Galerkin-Type Solution of the Föppl–von Kármán Equations for Square Plates

by Sergey Lychev, Alexander Digilov and Nikolay Djuzhev

Symmetry 2025, 17(1), 32; https://doi.org/10.3390/sym17010032 - 27 Dec 2024

Cited by 1 | Viewed by 923

Abstract

The solution of the non-linear Föppl–von Kármán equations for square plates in the form of expansion over a system of eigenfunctions, generated by a linear self-adjoint operator, is obtained. The coefficients of the expansion are determined via the reduction method from the infinite-dimensional system of cubic equations. This allows the proposed solution to be considered as a non-linear generalization of the classical Galerkin approach. The novelty of the study is in the strict formulation of the auxiliary boundary problem, which makes it possible to take into account a rigid fixation against any displacements along the boundary. To verify the proposed solution, it is compared with experimental data. The latter is obtained by the holographic interferometry of small deflection increments superimposed on the large deflection caused by initial pressure. Experiment and theory show a good agreement. Full article

(This article belongs to the Special Issue Symmetry in Mechanical Engineering: Properties and Applications)

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15 pages, 4450 KiB

Open AccessArticle

Enhancing the Proportion of Sub-5 μm Atomized Droplet Size in Medical Air-Compression Nebulizer

by Kun Xu, Zhongyou Lu, Li Wang and Yunqing Tang

Symmetry 2025, 17(1), 6; https://doi.org/10.3390/sym17010006 - 24 Dec 2024

Viewed by 4179

Abstract

Medical air-compression nebulizers deliver atomized medication to the lungs, providing rapid and painless treatment for respiratory diseases. However, the size of most atomized droplets is around 10 μm, limiting drug deposition in the lower airways and alveoli, with increasing the proportion of sub-5 μm droplets remaining challenging. In this work, finite element analysis was employed to model the effects of gas flow rate, liquid channel width, and broken baffle structure on droplet size distribution, aiming to optimize structure symmetrical parameters and operating conditions. A novel compression atomizer was developed and experimentally evaluated, incorporating an improved symmetrical structure for the crushing baffle. Following this modification, the proportion of sub-5 μm droplets increased from 54.6% to 59.25%, representing a 4.65% enhancement in the generation of sub-5 μm droplets. The effects of gas flow rate and liquid concentration on droplet size distribution were systematically investigated to further optimize the atomization performance. The results demonstrated a significant increase in the proportion of sub-5 μm droplets, thereby enhancing drug delivery efficiency to the lower respiratory tract and improving treatment efficacy for respiratory diseases. Full article

(This article belongs to the Special Issue Symmetry in Mechanical Engineering: Properties and Applications)

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19 pages, 1531 KiB

Open AccessArticle

Direct and Inverse Kinematics of a 3RRR Symmetric Planar Robot: An Alternative of Active Joints

by Jordy Josue Martinez Cardona, Manuel Cardona, Jorge I. Canales-Verdial and Jose Luis Ordoñez-Avila

Symmetry 2024, 16(5), 590; https://doi.org/10.3390/sym16050590 - 10 May 2024

Cited by 2 | Viewed by 2007

Abstract

Existing direct and inverse kinematic models of planar parallel robots assume that the robot’s active joints are all at the bases. However, this approach becomes excessively complex when modeling a planar parallel robot in which the active joints are within one single kinematic chain. To address this problem, our article unveils an alternative for a 3RRR symmetric planar robot modeling technique for the derivation of the robot workspace and the analysis of its direct and inverse kinematics. The workspace was defined using a system of inequalities, and the direct and inverse kinematics models were generated using vectorial analysis and an optimized geometrical approach, respectively. The resulting models are systematically presented and validated. Two final model renditions are delivered supplying a thorough equation analysis and an applicability discussion based on the importance of the robot’s mobile platform orientation. The advantages of this model are discussed in comparison to the traditional modeling approach: whereas conventional techniques require the solution of complex eighth-degree polynomials for the analysis of the active joint configuration of these robots, these models provide an efficient back-of-the-envelope analysis approach that requires the solution of a simple second-degree polynomial. Full article

(This article belongs to the Special Issue Symmetry in Mechanical Engineering: Properties and Applications)

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18 pages, 9551 KiB

Open AccessArticle

A Microstructural Study of Cu-10Al-7Ag Shape Memory Alloy in As-Cast and Quenched Conditions

by Lovro Liverić, Wojciech Sitek, Przemysław Snopiński, Wojciech Maziarz and Tamara Holjevac Grgurić

Symmetry 2024, 16(5), 545; https://doi.org/10.3390/sym16050545 - 2 May 2024

Cited by 1 | Viewed by 1320

Abstract

Shape memory alloys (SMAs) represent an exceptional class of smart materials as they are able to recover their shape after mechanical deformation, making them suitable for use in actuators, sensors and smart devices. These unique properties are due to the thermoelastic martensitic transformation that can occur during both thermal and mechanical deformation. Cu-based SMAs, especially those incorporating Al and Ag, are attracting much attention due to their facile production and cost-effectiveness. Among them, Cu-Al-Ag SMAs stand out due to their notably high temperature range for martensitic transformation. In this study, a Cu-based SMA with a new ternary composition of Cu-10Al-7Ag wt.% was prepared by arc melting and the samples cut from this casting alloy were quenched in water. Subsequently, the phase composition and the development of the microstructure were investigated. In addition, the morphology of the martensite was studied using advanced techniques such as electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM). The analyzes confirmed the presence of martensitic structures in both samples; mainly 18R (β_1′) martensite was present but a small volume fraction of (γ_1′) martensite also was noticed in the as-quenched sample. The observation of fine, twinned martensite plates in the SMA alloy with symmetrically occurring basal plane traces between the twin variants underlines the inherent correlation between microstructural symmetry and the properties of the material and provides valuable insights into its behavior. The hardness of the quenched sample was found to be lower than the as-cast counterpart, which can be linked to the solutioning of Ag particles during the heat treatment. Full article

(This article belongs to the Special Issue Symmetry in Mechanical Engineering: Properties and Applications)

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15 pages, 13929 KiB

Open AccessEditor’s ChoiceArticle

Effects of KoBo-Processing and Subsequent Annealing Treatment on Grain Boundary Network and Texture Development in Laser Powder Bed Fusion (LPBF) AlSi10Mg Alloy

by Przemysław Snopiński

Symmetry 2024, 16(1), 122; https://doi.org/10.3390/sym16010122 - 19 Jan 2024

Cited by 5 | Viewed by 1845

Abstract

It is well known that the properties of polycrystalline metals are related to grain boundaries (GBs), which are fundamental structural elements where crystallographic orientations change abruptly and often exhibit some degree of symmetry. Grain boundaries often exhibit unique structural, chemical, and electronic properties that differ from bulk crystalline domains. Their effects on material properties, including mechanical strength, corrosion resistance, and electrical conductivity, make grain boundaries a focus of intense scientific investigation. In this study, the microstructural transformation of an AlSi10Mg alloy subjected to KoBo extrusion and subsequent annealing is investigated. A notable discovery is the effectiveness of a strain-annealing method for grain boundary engineering (GBE) of the LPBF AlSi10Mg alloy. In particular, this study shows a significant increase in the population of coincidence site lattice boundaries (CSL), which embody the symmetry of the crystal lattice structure. These boundaries, which are characterised by a high degree of symmetry, contribute to their special properties compared to random grain boundaries. The experimental results emphasise the crucial role of strain-induced boundary migration (SIBM) in the development of a brass texture in the microstructure of the alloy after annealing. In addition, the presented results demonstrate the feasibility of applying GBE to materials with high stacking fault energy (SFE), which opens up new possibilities for optimizing their properties. Full article

(This article belongs to the Special Issue Symmetry in Mechanical Engineering: Properties and Applications)

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24 pages, 9481 KiB

Open AccessArticle

Distributed Rotational Inertia Load Excitation Model and Its Impact on High-Speed Jointed Rotor Dynamic Response

by Fayong Wu, Jie Hong and Xueqi Chen

Symmetry 2023, 15(11), 2009; https://doi.org/10.3390/sym15112009 - 1 Nov 2023

Viewed by 1607

Abstract

Contemporary aero-engines aim for enhanced efficiency and weight reduction. They are designed to increase rotor operational speed while reducing rotor bending stiffness. This may result in bending deformation in rotor systems within the operational speed range. Such deformation can change the relative positions of rotor components, potentially causing increased mass asymmetry or unbalance. Traditional rotor dynamic models typically assume a constant rotor state. They approximate unbalance using constant mass eccentricities at certain rotor cross-sections. However, this approach has its limitations. This paper focuses on a high-speed jointed rotor system. A distributed rotational inertia load excitation model is proposed. This model explicitly considers the rotor’s variable unbalance state at different operational speeds. The study involves both simulations and experimental investigations. The results show that at high speeds, bending deformation causes the unbalance and rotational inertia load to shift from a concentrated to a distributed state. Notably, the localized rotational inertia moment from thin-disk components like turbine disks becomes significant at high speeds. This results in a rapid increase in bearing load with rotational speed. It also profoundly affects the rotor’s joints, causing interfacial slip and sudden changes in rotor vibration characteristics. Full article

(This article belongs to the Special Issue Symmetry in Mechanical Engineering: Properties and Applications)

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22 pages, 7587 KiB

Open AccessArticle

Analysis of High-Speed Rotor Vibration Failure Due to Sudden Angular Deformation of Bolt Joints

by Fayong Wu, Jie Hong, Xueqi Chen and Yanhong Ma

Symmetry 2023, 15(10), 1937; https://doi.org/10.3390/sym15101937 - 19 Oct 2023

Cited by 3 | Viewed by 2362

Abstract

As the efficiency of advanced aero engines improves, the operational speed of their rotors increases. This heightened operational speed makes the rotor dynamics highly sensitive to changes in the rotor’s mass asymmetry state, or unbalance state. During the use of a dual-spool turbofan engine, when its supercritical high-pressure rotor (HPR) exceeds a certain operational speed, the rotor’s vibration spikes and continues to increase with the operational speed until it drops sharply near the maximum operational speed. Analysis of the bolt joints in the faulty rotor reveals various phenomena such as joint interface damage, changes in bolt loosening torque distribution, and alterations in rotor initial unbalance. This paper proposes that at high operational speeds, the bolt joint of the HPR undergoes sudden angular deformation, resulting in the slanting of the principal axis of inertia of the turbine disk. This slant leads to changes in the unbalanced state of the HPR. The additional unbalance causes a sudden rotational inertia load excitation, triggering the rotor vibration failure. Subsequently, a rotor dynamic model that incorporates the angular deformation of the joints is established to simulate how this joint deformation influences the dynamic response of the rotor. The simulation results align well with the observed failure phenomenon and validate the proposed failure mechanism. Finally, troubleshooting measures are proposed and implemented in the faulty engine, effectively mitigating the vibration fault. Full article

(This article belongs to the Special Issue Symmetry in Mechanical Engineering: Properties and Applications)

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34 pages, 12809 KiB

Open AccessArticle

System Modeling and Simulation for Investigating Dynamic Characteristics of Geared Symmetric System Based on Linear Analysis

by Joo-Mi Bahk, Sun-Hak Kim and Jong-Yun Yoon

Symmetry 2023, 15(10), 1904; https://doi.org/10.3390/sym15101904 - 11 Oct 2023

Viewed by 1828

Abstract

Complex vibrational phenomena, such as gear impacts and mesh stiffness excitations, often require a significant amount of effort to be revealed using nonlinear analytical methods. However, key parameters for addressing vibrational problems can often be identified through simplified approaches based on linear analysis models. In light of these considerations, this study aimed to propose linear analytical methods to investigate the influences of various key parameters within symmetric systems. To achieve the main goal of this study, system modeling and eigensolutions were first implemented, focusing on a specific manual transmission with a front-engine/front-wheel configuration. Second, analytical techniques to reduce the number of degrees of freedom from the original symmetric system were suggested, and the reduced model was validated. Third, the system responses in the time domain were examined, along with key system parameters, such as gear mesh stiffness and clutch dampers, using state–variable equations. As a result, the findings from the linear system model demonstrated the fundamental dynamic characteristics of the torsional system within specific frequency regimes relevant to noise and vibration problems. Furthermore, the reduced lumped linear model employing the state–variable formula established its reliability in determining key parameters for mitigating noise and vibration problems. Full article

(This article belongs to the Special Issue Symmetry in Mechanical Engineering: Properties and Applications)

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Review

Jump to: Research

21 pages, 6320 KiB

Open AccessReview

Research Progress on the Design of Surface Texture in Tribological Applications: A Mini-Review

by Keyang Chen and Yunqing Tang

Symmetry 2024, 16(11), 1523; https://doi.org/10.3390/sym16111523 - 14 Nov 2024

Cited by 2 | Viewed by 1502

Abstract

Surface texturing technology, as an advanced method to improve surface tribological properties of friction pairs, has been widely used in many fields. In this work, the influence of surface texture parameters on tribological properties of friction pair surfaces are reviewed. For the currently most developed surface textures with symmetry and simple geometries and distributions, it is found that they could help reduce friction mainly by enhancing their dynamic pressure lubrication capability, storing abrasive debris and lubricants for dynamic lubrication or promoting the formation of friction films on surfaces of friction pairs. The dominant design parameters of surface textures influencing their tribological performance are found to be shape, geometry and density, while working condition, including contact mode and lubrication situation, also has a significant influence on the performance of surface textures with specific features. Asymmetric textures and multi-scale composite textures also show great tribological performance, while the coupling mechanism across different factors is still unclear, which makes it a challenge to maximize the advantage of asymmetric or multi-scale composite textures. The development of machine learning provides promising approaches for the multi-parameter optimization of surface textures, which is expected to promote and accelerate the design of advanced surface textures. Full article

(This article belongs to the Special Issue Symmetry in Mechanical Engineering: Properties and Applications)

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