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Nonlinear Analysis of Static and Dynamic Problems in Mechanical Engineering

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A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Mechanical Engineering".

Deadline for manuscript submissions: closed (28 February 2022) | Viewed by 21185

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Special Issue Editors

Prof. Dr. Ji Wang

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Guest Editor

Piezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, Ningbo 315211, China
Interests: nonlinear vibration; wave propagation; plate theory; structural analysis; ruspec; acoustic wave resonators
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Weiqiu Chen

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Guest Editor

Department of Engineering Mechanics, School of Aeronautics and Astronautics, Zhejiang University, No. 38, Zheda Road, Hangzhou, China
Interests: mechanics of advanced materials and structures; waves and vibrations in structures; mechanics of three-dimensional contact and crack problems; metamaterials and their mechanical responses; analytical methods in applied mathematics and mechanics
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Bin Huang

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Guest Editor

Piezoelectric Device Laboratory, School of Mechanical Engineering and Mechanics, Ningbo University, Ningbo 315211, China
Interests: mechanics of composite materials; structural vibration; pizeoelectricity; electromechanical coupling; smart materials and strucutres

Special Issue Information

Dear Colleagues,

It is our pleasure to announce that we will be editing a Special Issue on “Nonlinear Analyses and Methods of Static and Dynamic Problems in Mechanical Engineering” in Applied Sciences: Mechanical Engineering (SI:NAM/AS:ME), covering applications on the following subjects:

Stress analysis
Large deformation
Vibrations
Thermal stresses
Acoustics
Sensors and measurements
Wave propagation
Nanomaterials and nanostructures
Soft materials
Friction
Corrosion
Fluids
Heat transfer
Energy
Transportation
Infrastructure
Aerospace

Technical papers on analyses, methods, designs, modeling, properties, behavior, performance, characterization, and other aspects of theory, method, materials, structures, and applications in mechanical engineering with the consideration of nonlinear features are welcome. An expedited review process and expert evaluation will guarantee the timely publication of high-quality papers for the mechanical engineering community.

The announcement is to be released before 1 September 2021, and contributions will be finished by the end of February 2022. The target of the SI:NAM/AS:ME is 20+ high quality papers.

Prof. Dr. Ji Wang
Prof. Dr. Weiqiu Chen
Prof. Dr. Bin Huang
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. Applied Sciences 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 2400 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

stress analysis
large deformation
vibrations
thermal stresses
acoustics
sensors and measurements
wave propagation
nanomaterials and nanostructures
soft materials
friction
corrosion
fluids
heat transfer
energy
transportation
infrastructure
aerospace

Published Papers (13 papers)

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Research

12 pages, 4983 KiB

Open AccessArticle

Nonlinear Impact Force Reduction of Layered Polymers with the Damage-Trap Interface

by Md Shariful Islam and Luoyu Roy Xu

Appl. Sci. 2022, 12(14), 7078; https://doi.org/10.3390/app12147078 - 13 Jul 2022

Viewed by 1116

Abstract

In this paper, a damage-trap material interface design of polymeric materials was proposed. Towards that, baseline and layered Polymethyl methacrylate (PMMA) and Polycarbonate specimens were fabricated with a Loctite 5083 adhesive layer between the interfaces. Out-of-plane impact experiments were conducted and found that the maximum impact force was reduced in layered polymers with so-called “damage-trap material interfaces”. At the impact energy of 20 J, the maximum impact force of the layered PMMA specimens with the 5083 adhesive was reduced by 60% compared to the identical specimens without any adhesive bonding. For the layered Polycarbonate specimens with the 5083 adhesive bonding, the maximum impact force was reduced by 20% and energy absorption was increased by 130%. Simplified contact mechanics analysis showed that the low Young’s modulus of the 5083 adhesive layers was a key parameter in reducing impact force and damage. Therefore, a simple and effective way to design layered materials with improved impact resistance was proposed. Full article

(This article belongs to the Special Issue Nonlinear Analysis of Static and Dynamic Problems in Mechanical Engineering)

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11 pages, 803 KiB

Open AccessArticle

The Approximate Solution of Nonlinear Flexure of a Cantilever Beam with the Galerkin Method

by Jun Zhang, Rongxing Wu, Ji Wang, Tingfeng Ma and Lihong Wang

Appl. Sci. 2022, 12(13), 6720; https://doi.org/10.3390/app12136720 - 02 Jul 2022

Cited by 6 | Viewed by 1436

Abstract

For the optimal design and accurate prediction of structural behavior, the nonlinear analysis of large deformation of elastic beams has broad applications in various engineering fields. In this study, the nonlinear equation of flexure of an elastic beam, also known as an elastica, was solved by the Galerkin method for a highly accurate solution. The numerical results showed that the third-order solution of the rotation angle at the free end of the beam is more accurate and efficient in comparison with results of other approximate methods, and is perfectly consistent with the exact solution in elliptic functions. A general procedure with the Galerkin method is demonstrated for efficient solutions of nonlinear differential equations with the potential for adoption and implementation in more applications. Full article

(This article belongs to the Special Issue Nonlinear Analysis of Static and Dynamic Problems in Mechanical Engineering)

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15 pages, 3134 KiB

Open AccessArticle

Vibration and Wave Analyses in the Functionally Graded Graphene-Reinforced Composite Plates Based on the First-Order Shear Deformation Plate Theory

by Yunying Zhou, Dongying Liu and Jun Zhu

Appl. Sci. 2022, 12(6), 3140; https://doi.org/10.3390/app12063140 - 18 Mar 2022

Cited by 4 | Viewed by 1531

Abstract

Graphene platelets (GPLs) can be used to enhance the mechanical and electrical properties of the matrix material, which efficiently determines and improves the dynamic behavior in composite structures. Based on the first-order shear deformation theory, this paper investigates the vibration and wave problems in a functionally graded graphene-reinforced composite plate. The composite plate is composed of the polymer matrix reinforced with GPLs that are dispersed along the thickness direction, following four kinds of functionally graded patterns. The governing equation of dynamic problems in the composite plate can be described in the state space formulation, and be solved using the method of reverberation-ray matrix (MRRM). Unlike the traditional state space method, this method is unconditionally stable due to introducing the dual coordinates, which can inherently avoid the numerical instability. After a validation study to verify the present analysis, a parametric study is conducted to analyze the effect of weight fraction, size and distribution patterns of the reinforments, as well as the boundary conditions and aspect ratios on the dynamic behaviors of the composite plate, hence providing a better way to achieve improved dynamic resistances of the GPLs composite plates. Full article

(This article belongs to the Special Issue Nonlinear Analysis of Static and Dynamic Problems in Mechanical Engineering)

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8 pages, 255 KiB

Open AccessArticle

The Extended Galerkin Method for Approximate Solutions of Nonlinear Vibration Equations

by Ji Wang and Rongxing Wu

Appl. Sci. 2022, 12(6), 2979; https://doi.org/10.3390/app12062979 - 15 Mar 2022

Cited by 15 | Viewed by 2243

Abstract

An extension has been made to the popular Galerkin method by integrating the weighted equation of motion over the time of one period of vibrations to eliminate the harmonics from thee deformation function. A set of successive equations of coupled higher-order vibration amplitudes is resulted, and a nonlinear eigenvalue problem is obtained for the frequency-amplitude dependence of nonlinear vibrations with successive displacements. The subsequent solutions of vibration frequencies and deformation are consistent with other successive approximate methods, such as the harmonics balance method. This is an extension of the Galerkin method which has broad applications for asymptotic solutions, particularly for problems in solid mechanics. This extended Galerkin method can also be utilized for the analysis of free and forced nonlinear vibrations of structures as a new technique with significant advantages in calculations. Full article

(This article belongs to the Special Issue Nonlinear Analysis of Static and Dynamic Problems in Mechanical Engineering)

10 pages, 661 KiB

Open AccessArticle

Thickness-Stretch Vibration of an Infinite Piezoelectric Plate with Flexoelectricity

by Yan Guo, Bin Huang and Ji Wang

Appl. Sci. 2022, 12(5), 2436; https://doi.org/10.3390/app12052436 - 25 Feb 2022

Cited by 2 | Viewed by 1108

Abstract

In this paper, the thickness-stretch vibration of an infinite piezoelectric plate is studied, with consideration of the flexoelectric effect. The theoretical model developed herein is based on a one-dimensional formulation, with the assumption that the displacement and electric potential vary through the thickness. The Gibbs energy density function and variational principle are adopted to derive the constitutive equation with flexoelectricity, governing equations, and boundary conditions. For the effect of flexoelectricity, the coupling between the strain gradient through the thickness and the electric field is considered. Two electric boundary conditions are used in this work and the corresponding frequency shift due to the flexoelectricity is calculated. The present results demonstrate that the flexoelectric effect decreases the fundamental frequency of the thickness-stretch vibration and has a significant effect on the vibrational frequencies of the thickness-stretch mode of a thin piezoelectric plate. The results also show that the flexoelectric effect has a significant size dependency, and should be taken into consideration for the design and development of next-generation high-precision and high-frequency piezoelectric transducers and resonators in the future. Full article

(This article belongs to the Special Issue Nonlinear Analysis of Static and Dynamic Problems in Mechanical Engineering)

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10 pages, 542 KiB

Open AccessArticle

Static Bending and Vibration Analysis of a Rectangular Functionally Gradient Piezoelectric Plate on an Elastic Foundation

by Wei Wang, Haonan Li and Linquan Yao

Appl. Sci. 2022, 12(3), 1517; https://doi.org/10.3390/app12031517 - 30 Jan 2022

Cited by 2 | Viewed by 1666

Abstract

In this paper, a functionally graded piezoelectric plate on an elastic foundation composed of two different piezoelectric materials bonded together in the form of plate is studied, and its static bending and fundamental frequencies are analyzed. First, based on Kirchhoff plate theory and the Hamilton principle, the governing equations and corresponding boundary conditions of the model are derived, and then the equations are discretized and solved by the differential quadrature method (DQM). Finally, the effects of physical parameters such as length-to-height ratio, length-to-width ratio, material graded index, foundation stiffness coefficient, temperature change value and external voltage value on static bending deflection, and fundamental frequency value of the functionally graded piezoelectric plate with four sides simply supported are discussed. The calculated results are in good agreement with those in the literature. The data results show that the increase in the elastic foundation stiffness coefficient will increase the equivalent stiffness of the plate. In the process of work, due to the equivalent pressure value generated by the influence of the external voltage, it will lead to unstable phenomena. Full article

(This article belongs to the Special Issue Nonlinear Analysis of Static and Dynamic Problems in Mechanical Engineering)

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11 pages, 1964 KiB

Open AccessArticle

Influence of Dry Friction on the Dynamics of Cantilevered Pipes Conveying Fluid

by Zilong Guo, Qiao Ni, Lin Wang, Kun Zhou and Xiangkai Meng

Appl. Sci. 2022, 12(2), 724; https://doi.org/10.3390/app12020724 - 12 Jan 2022

Cited by 2 | Viewed by 1116

Abstract

A cantilevered pipe conveying fluid can lose stability via flutter when the flow velocity becomes sufficiently high. In this paper, a dry friction restraint is introduced for the first time, to evaluate the possibility of improving the stability of cantilevered pipes conveying fluid. First, a dynamical model of the cantilevered pipe system with dry friction is established based on the generalized Hamilton’s principle. Then the Galerkin method is utilized to discretize the model of the pipe and to obtain the nonlinear dynamic responses of the pipe. Finally, by changing the values of the friction force and the installation position of the dry friction restraint, the effect of dry friction parameters on the flutter instability of the pipe is evaluated. The results show that the critical flow velocity of the pipe increases with the increment of the friction force. Installing a dry friction restraint near the middle of the pipe can significantly improve the stability of the pipe system. The vibration of the pipe can also be suppressed to some extent by setting reasonable dry friction parameters. Full article

(This article belongs to the Special Issue Nonlinear Analysis of Static and Dynamic Problems in Mechanical Engineering)

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19 pages, 1087 KiB

Open AccessArticle

Effect of the Planetesimal Belt on the Dynamics of the Restricted Problem of 2 + 2 Bodies

by Govind Mahato, Ashok Kumar Pal, Sawsan Alhowaity, Elbaz I. Abouelmagd and Badam Singh Kushvah

Appl. Sci. 2022, 12(1), 424; https://doi.org/10.3390/app12010424 - 02 Jan 2022

Cited by 7 | Viewed by 1388

Abstract

In this paper, we study the existence and stability of collinear and noncollinear equilibrium points within the frame of the perturbed restricted problem of 2 + 2 bodies by a planetesimal belt. We compare and investigate the corresponding results of the perturbed and unperturbed models. The impact of the planetesimal belt is observed on collinear and noncollinear equilibrium points. We demonstrate that all equilibrium points are unstable, and we numerically investigate the noncollinear equilibrium points. Finally, we emphasize that the proposed problem is a credible model for describing the capture of small bodies by a planet. Full article

(This article belongs to the Special Issue Nonlinear Analysis of Static and Dynamic Problems in Mechanical Engineering)

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20 pages, 5976 KiB

Open AccessArticle

Dynamics Investigation on Axial-Groove Gas Bearing-Rotor System with Rod-Fastened Structure

by Sha Li, Yanjun Lu, Yongfang Zhang, Di Hei and Xiaowei Zhao

Appl. Sci. 2022, 12(1), 250; https://doi.org/10.3390/app12010250 - 28 Dec 2021

Viewed by 1437

Abstract

This research report discusses the dynamic behaviors of an axial-groove gas bearings-rotor system with rod-fastened structure. The time-based dependency-compressible Reynolds equation in the gas bearing nonlinear system is solved by the differential transformation method, and the continuous gas film forces of a three-axial-groove gas bearing are obtained. A dynamic mathematical model of the rotor system with rod-fastened structure supported in two- and three-axial-groove gas bearings with eight degrees of freedom is established. The dynamic motion equation of the rod-fastened rotor system is solved by the modified Newmark-β method based on disturbance compensation, which can reduce the computing error and improve computing stability. The dynamic characteristics of the rod-fastened rotor-gas bearing system are analyzed efficiently by the diversiform unbalance responses. The influence of the position angle of the pad on the nonlinear characteristics of the rod-fastened rotor system is also studied. Full article

(This article belongs to the Special Issue Nonlinear Analysis of Static and Dynamic Problems in Mechanical Engineering)

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18 pages, 54915 KiB

Open AccessArticle

Analysis of the Vibration Behaviors of Rotating Composite Nano-Annular Plates Based on Nonlocal Theory and Different Plate Theories

by Haonan Li, Wei Wang and Linquan Yao

Appl. Sci. 2022, 12(1), 230; https://doi.org/10.3390/app12010230 - 27 Dec 2021

Cited by 6 | Viewed by 1949

Abstract

Rotating machinery has significant applications in the fields of micro and nano meters, such as nano-turbines, nano-motors, and biomolecular motors, etc. This paper takes rotating nano-annular plates as the research object to analyze their free vibration behaviors. Firstly, based on Kirchhoff plate theory, Mindlin plate theory, and Reddy plate theory, combined with nonlocal constitutive relations, the differential motion equations of rotating functionally graded nano-annular plates in a thermal environment are derived. Subsequently, the numerical method is used to discretize and solve the motion equations. The effects of nonlocal parameter, temperature change, inner and outer radius ratio, and rotational velocity on the vibration frequencies of the nano-annular plates are analyzed through numerical examples. Finally, the relationship between the fundamental frequencies and the thickness-to-radius ratio of the nano-annular plates of clamped inner and outer rings is discussed, and the differences in the calculation results among the three plate theories are compared. Full article

(This article belongs to the Special Issue Nonlinear Analysis of Static and Dynamic Problems in Mechanical Engineering)

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11 pages, 27529 KiB

Open AccessArticle

Dynamic Response of Electro-Mechanical Properties of Cement-Based Piezoelectric Composites

by Yi Li, Youwei Zhang, Haiwei Dong, Wenjie Cheng, Chaoming Shi and Jiangying Chen

Appl. Sci. 2021, 11(24), 11925; https://doi.org/10.3390/app112411925 - 15 Dec 2021

Viewed by 1192

Abstract

By employing ordinary Portland cement as a matrix and PZT-5H piezoelectric ceramic as the functional body, 1-3 and 2-2 cement-based piezoelectric composites were prepared. Quasi-static compression tests were performed along with dynamic impact loading tests to study the electro-mechanical response characteristics of 1-3 and 2-2 cement-based piezoelectric composites. The research results show that both composites exhibit strain rate effects under quasi-static compression and dynamic impact loading since they are strain-rate sensitive materials. The sensitivity of the two composites has a non-linear mutation point: in the quasi-static state, the sensitivity of 1-3 and 2-2 composites is 157 and 169 pC/N, respectively; in the dynamic state, the respective sensitivity is 323 and 296 pC/N. Although the sensitivity difference is not significant, the linear range of the 2-2 composite is 24.8% and 61.3% larger than that of the 1-3 composite under quasi-static compression and dynamic impact loading, respectively. Accordingly, the 2-2 composite exhibits certain advantages as a sensor material, irrespective of whether it is subjected to quasi-static or dynamic loading. Full article

(This article belongs to the Special Issue Nonlinear Analysis of Static and Dynamic Problems in Mechanical Engineering)

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17 pages, 13625 KiB

Open AccessArticle

Development of Dynamics for Design Procedure of Novel Grating Tiling Device with Experimental Validation

by Qingshun Bai, Mohamed Shehata, Ayman Nada and Zhongxi Shao

Appl. Sci. 2021, 11(24), 11716; https://doi.org/10.3390/app112411716 - 09 Dec 2021

Cited by 2 | Viewed by 1781

Abstract

The article proposes a dynamic for design (DFD) procedure for a novel aperture grating tiling device using the multibody system (MBS) approach. The grating device is considered as a rigid-flexible MBS that is built primarily based totally at the load assumptions because of grating movement. This movement is utilized in many industrial applications, such as the compression of laser pulse, precision measuring instruments, and optical communication. A new design procedure of tiling grating device frame is introduced in order to optimize its design parameters and enhance the system stability. The dynamic loads are estimated based on the Lagrange multipliers that are obtained from the solution of the MBS model. This model is fully non-linear and moves in the three-dimensional space, and the relative movement of its bodies is restricted by the description of the constraints function in the motion manifold. The mechanism of the grating device is structurally analyzed in keeping with the dynamic conduct and therefore the generated forces. The symbolic manipulation as well as the computational work of solving the obtained differential-algebraic equations (DAEs) is carried out using MATLAB Symbolic Toolbox. Once the preliminary design has been attained, the stress behavior of the grating device is examined using the MATLAB FEATool Multiphysics toolkit, regarding system stability and design aspects. Moreover, the design was constructed in real life, and the movement has been verified experimentally, which confirms the effectiveness of the proposed procedure. In conclusion, the DFD procedure with trade-off optimization is utilized successfully to design the grating unit for maximum ranges of grating movements. Full article

(This article belongs to the Special Issue Nonlinear Analysis of Static and Dynamic Problems in Mechanical Engineering)

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17 pages, 2294 KiB

Open AccessArticle

Effect of Thickness Stretching on Bending and Free Vibration Behaviors of Functionally Graded Graphene Reinforced Composite Plates

by Zhuangzhuang Wang and Liansheng Ma

Appl. Sci. 2021, 11(23), 11362; https://doi.org/10.3390/app112311362 - 01 Dec 2021

Cited by 16 | Viewed by 1780

Abstract

The focus of this paper is the effect of thickness stretching on the static and dynamic behaviors of functionally graded graphene reinforced composite (FG-GRC) plates. The bending and free vibration behaviors of FG-GRC plates under simply supported conditions are studied based on two plate theories, with or without taking into account the thickness stretching effect, respectively, and the effect of thickness stretching on FG-GRC plates is analyzed by comparing the calculated results of the two types of plate theories. The properties of composite materials are estimated by the modified Halpin-Tsai model and rule of mixture, Hamilton’s principle is used to construct its governing equation, and the Navier solution method is used to find the closed solution. The numerical results show that the effect of thickness stretching depends mainly on the transverse anisotropy of the FG-GRC plates, and the FG-GRC plates are most significantly affected by the thickness stretching when the graphene nanoplatelets (GPLs) are asymmetrically distributed, and the effect of thickness stretching tends to increase as the total number of layers and the weight fraction of GPLs increase. Full article

(This article belongs to the Special Issue Nonlinear Analysis of Static and Dynamic Problems in Mechanical Engineering)

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