Pub Date : 2021-01-01DOI: 10.4236/wjm.2021.1112016
Juan Jose Mejia Briseno, Francisco Casanova-del-Angel
ASTM standards for A413 aluminum alloy specimen assays were used based on standard E399-05, with a minimum requirement of three specimens. Linear elastic fracture mechanic testing was carried out in plane strain conditions and fracture toughness of the tested aluminum, critical stress intensity factor was determined. Four specimens with the selected geometry were made, since in the pre-cracking process a non-acceptable propagation of crack may be present, i.e., the crack does not propagate in a parabolic manner. In like manner, the Type SE (B) specimen, that is, a beam subject to bending under a monotonic load, was used. Stress efforts were induced in the experiment, the load mode for such experiments is mode I, determining a temporary value of the K Q apparent stress intensity factor. When such value complies with the validity criteria of E-399 Standard, it becomes the stress intensity factor K IC of material.
{"title":"Fracture Mechanics on Aluminum Specimens","authors":"Juan Jose Mejia Briseno, Francisco Casanova-del-Angel","doi":"10.4236/wjm.2021.1112016","DOIUrl":"https://doi.org/10.4236/wjm.2021.1112016","url":null,"abstract":"ASTM standards for A413 aluminum alloy specimen assays were used based on standard E399-05, with a minimum requirement of three specimens. Linear elastic fracture mechanic testing was carried out in plane strain conditions and fracture toughness of the tested aluminum, critical stress intensity factor was determined. Four specimens with the selected geometry were made, since in the pre-cracking process a non-acceptable propagation of crack may be present, i.e., the crack does not propagate in a parabolic manner. In like manner, the Type SE (B) specimen, that is, a beam subject to bending under a monotonic load, was used. Stress efforts were induced in the experiment, the load mode for such experiments is mode I, determining a temporary value of the K Q apparent stress intensity factor. When such value complies with the validity criteria of E-399 Standard, it becomes the stress intensity factor K IC of material.","PeriodicalId":70106,"journal":{"name":"力学国际期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70874377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-10DOI: 10.4236/wjm.2020.1011014
Shuping Chen
The orientation of fractures with transpressional and transtensional wrenches in pre-existing faults has not been quantitatively determined. Based on Coulomb failure criterion and Byerlee’s frictional sliding criterion, this paper has indicated quantitative geometric relationships between the pre-existing fault and the local induced principal stress axes caused by the rejuvenation of the pre-existing fault. For a hidden pre-existing fault with some cohesion, the angles between the local induced principal stress axes and the pre-existing fault quantitatively vary with the applied stress and the cohesion coefficient, the ratio of the thickness of the cover layer to the thickness of the whole wrench body, whether transpressional or transtensional wrenches occur. For a surface pre-existing fault with zero cohesion, the angles between the pre-existing fault and the local induced principal stress axes are related to the rock inner frictional angle regardless of both the applied stress and the cohesion coefficient where transpressional wrenches occur, and the local induced maximum principal stress axis is identical with the applied maximum principal stress axis where transtensional wrenches occur. Therefore, the geometric relationships between the pre-existing faults and their related fractures are defined, because the local induced principal stress axes determine the directions of the related fractures. The results can be applied to pre-existing weak fabrics. They can help to understand and analyze wrench structures in outcrops or subsurface areas. They are of significance in petroleum exploration.
{"title":"On the Orientation of Fractures with Transpressional and Transtensional Wrenches in Pre-Existing Faults","authors":"Shuping Chen","doi":"10.4236/wjm.2020.1011014","DOIUrl":"https://doi.org/10.4236/wjm.2020.1011014","url":null,"abstract":"The orientation of fractures with transpressional and transtensional wrenches in pre-existing faults has not been quantitatively determined. Based on Coulomb failure criterion and Byerlee’s frictional sliding criterion, this paper has indicated quantitative geometric relationships between the pre-existing fault and the local induced principal stress axes caused by the rejuvenation of the pre-existing fault. For a hidden pre-existing fault with some cohesion, the angles between the local induced principal stress axes and the pre-existing fault quantitatively vary with the applied stress and the cohesion coefficient, the ratio of the thickness of the cover layer to the thickness of the whole wrench body, whether transpressional or transtensional wrenches occur. For a surface pre-existing fault with zero cohesion, the angles between the pre-existing fault and the local induced principal stress axes are related to the rock inner frictional angle regardless of both the applied stress and the cohesion coefficient where transpressional wrenches occur, and the local induced maximum principal stress axis is identical with the applied maximum principal stress axis where transtensional wrenches occur. Therefore, the geometric relationships between the pre-existing faults and their related fractures are defined, because the local induced principal stress axes determine the directions of the related fractures. The results can be applied to pre-existing weak fabrics. They can help to understand and analyze wrench structures in outcrops or subsurface areas. They are of significance in petroleum exploration.","PeriodicalId":70106,"journal":{"name":"力学国际期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43818087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-10DOI: 10.4236/wjm.2020.1011015
E. Eze, U. E. Obasi, R. N. Ujumadu, Grace Ihuoma Kalu
This paper investigates the maximum interval of stability and convergence of solution of a forced Mathieu’s equation, using a combination of Frobenius method and Eigenvalue approach. The results indicated that the equilibrium point was found to be unstable and maximum bounds were found on the derivative of the restoring force showing sharp condition for the existence of periodic solution. Furthermore, the solution to Mathieu’s equation converges which extends and improves some results in literature.
{"title":"Maximum Interval of Stability and Convergence of Solution of a Forced Mathieu’s Equation","authors":"E. Eze, U. E. Obasi, R. N. Ujumadu, Grace Ihuoma Kalu","doi":"10.4236/wjm.2020.1011015","DOIUrl":"https://doi.org/10.4236/wjm.2020.1011015","url":null,"abstract":"This paper investigates the maximum interval of stability and convergence of solution of a forced Mathieu’s equation, using a combination of Frobenius method and Eigenvalue approach. The results indicated that the equilibrium point was found to be unstable and maximum bounds were found on the derivative of the restoring force showing sharp condition for the existence of periodic solution. Furthermore, the solution to Mathieu’s equation converges which extends and improves some results in literature.","PeriodicalId":70106,"journal":{"name":"力学国际期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47240675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-12DOI: 10.4236/wjm.2020.1010011
A. Ogura
We present the usefulness of mass-momentum “vectors” to analyze the collision problems in classical mechanics for both one and two dimensions with Galilean transformations. The Galilean transformations connect the mass-momentum “vectors” in the center-of-mass and the laboratory systems. We show that just moving the two systems to and fro, we obtain the final states in the laboratory systems. This gives a simple way of obtaining them, in contrast with the usual way in which we have to solve the simultaneous equations. For one dimensional collision, the coefficient of restitution is introduced in the center-of-mass system. This clearly shows the meaning of the coefficient of restitution. For two dimensional collisions, we only discuss the elastic collision case. We also discuss the case of which the target particle is at rest before the collision. In addition to this, we discuss the case of which the two particles have the same masses.
{"title":"Collisions in Classical Mechanics in Terms of Mass-Momentum “Vectors” with Galilean Transformations","authors":"A. Ogura","doi":"10.4236/wjm.2020.1010011","DOIUrl":"https://doi.org/10.4236/wjm.2020.1010011","url":null,"abstract":"We present the usefulness of mass-momentum “vectors” to analyze the collision problems in classical mechanics for both one and two dimensions with Galilean transformations. The Galilean transformations connect the mass-momentum “vectors” in the center-of-mass and the laboratory systems. We show that just moving the two systems to and fro, we obtain the final states in the laboratory systems. This gives a simple way of obtaining them, in contrast with the usual way in which we have to solve the simultaneous equations. For one dimensional collision, the coefficient of restitution is introduced in the center-of-mass system. This clearly shows the meaning of the coefficient of restitution. For two dimensional collisions, we only discuss the elastic collision case. We also discuss the case of which the target particle is at rest before the collision. In addition to this, we discuss the case of which the two particles have the same masses.","PeriodicalId":70106,"journal":{"name":"力学国际期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44512864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-22DOI: 10.4236/wjm.2020.1010012
Ze-hua Qiu
Rotation is antisymmetric and therefore is not a coherent element of the classical elastic theory, which is characterized by symmetry. A new theory of linear elasticity is developed from the concept of asymmetric strain, which is defined as the transpose of the deformation gradient tensor to involve rotation as well as symmetric strain. The new theory basically differs from the prevailing micropolar theory or couple stress theory in that it maintains the same basis as the classical theory of linear elasticity and does not need extra concepts, such as “microrotation” and “couple stresses”. The constitutive relation of the new theory, the three-parameter Hooke’s law, comes from the theorem about isotropic asymmetric linear elastic materials. Concise differential equations of translational motion are derived consequently giving the same velocity formula for P-wave and a different one for S-wave. Differential equations of rotational motion are derived with the introduction of spin, which has an intrinsic connection with rotation. According to the new theory, S-wave essentially has rotation as large as deviatoric strain and should be referred to as “shear wave” in the context of asymmetric strain. There are nine partial differential equations for the deformation harmony condition in the new theory; these are given with the first spatial differentiations of asymmetric strain. Formulas for rotation energy, in addition to those for (symmetric) strain energy, are derived to form a complete set of formulas for the total mechanical energy.
{"title":"A Simple Theory of Asymmetric Linear Elasticity","authors":"Ze-hua Qiu","doi":"10.4236/wjm.2020.1010012","DOIUrl":"https://doi.org/10.4236/wjm.2020.1010012","url":null,"abstract":"Rotation is antisymmetric and therefore is not a coherent element of the classical elastic theory, which is characterized by symmetry. A new theory of linear elasticity is developed from the concept of asymmetric strain, which is defined as the transpose of the deformation gradient tensor to involve rotation as well as symmetric strain. The new theory basically differs from the prevailing micropolar theory or couple stress theory in that it maintains the same basis as the classical theory of linear elasticity and does not need extra concepts, such as “microrotation” and “couple stresses”. The constitutive relation of the new theory, the three-parameter Hooke’s law, comes from the theorem about isotropic asymmetric linear elastic materials. Concise differential equations of translational motion are derived consequently giving the same velocity formula for P-wave and a different one for S-wave. Differential equations of rotational motion are derived with the introduction of spin, which has an intrinsic connection with rotation. According to the new theory, S-wave essentially has rotation as large as deviatoric strain and should be referred to as “shear wave” in the context of asymmetric strain. There are nine partial differential equations for the deformation harmony condition in the new theory; these are given with the first spatial differentiations of asymmetric strain. Formulas for rotation energy, in addition to those for (symmetric) strain energy, are derived to form a complete set of formulas for the total mechanical energy.","PeriodicalId":70106,"journal":{"name":"力学国际期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48220665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-22DOI: 10.4236/wjm.2020.1010013
S. Olszewski
In the relativistic mechanics, we calculate a minimal distance between the time scale of a one-dimensional motion having a larger velocity and the time scale of a similar motion with a lower velocity. Concerning the quantum theory, we demonstrate that mechanical parameters entering the electron motion in the Bohr hydrogen atom can provide us with a correct size of the time interval entering the Joule-Lenz law for the emission energy between two neighbouring quantum levels of the atom.
{"title":"Two Problems of Time Entering Respectively the Relativistic Mechanics and Electron Transport in Quantum Theory","authors":"S. Olszewski","doi":"10.4236/wjm.2020.1010013","DOIUrl":"https://doi.org/10.4236/wjm.2020.1010013","url":null,"abstract":"In the relativistic mechanics, we calculate a minimal distance between the time scale of a one-dimensional motion having a larger velocity and the time scale of a similar motion with a lower velocity. Concerning the quantum theory, we demonstrate that mechanical parameters entering the electron motion in the Bohr hydrogen atom can provide us with a correct size of the time interval entering the Joule-Lenz law for the emission energy between two neighbouring quantum levels of the atom.","PeriodicalId":70106,"journal":{"name":"力学国际期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48599904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
K. Shimada, Ryo Kato, Ryo Ikeda, H. Kikura, H. Takahashi
For cases in which a robot with installed solar cells and a sensor operates in a nuclear reactor building or in space for extravehicular activity, we require elastic and extensible solar cells. More than two different types of sensing are also required, minimally with photovoltaics and built-in electricity. Magnetic compound fluid (MCF) rubber solar cells are made of rubber, so they are elastic and extensible as well as sensitive. To achieve flexibility and an effective photovoltaic effect, MCF rubber solar cells must include both soluble and insoluble rubbers, Fe3O4, TiO2, Na2WO4∙2H2O, etc. On the basis of this constitution, we propose a consummate fabrication process for MCF rubber solar cells. The characteristics of these cells result from the semiconductor-like role of the molecules of TiO2, Fe3O4, Ni, Na2WO4∙2H2O, polydimethylsiloxane (PDMS), natural rubber (NR), oleic acid, polyvinyl alcohol (PVA), water and magnetic cluster involved in the MCF rubber. Their tendencies can be deduced by synthesizing knowledge about the enhancement of the reverse-bias saturation current IS and the diode ideality factor N, with conventional knowledge about the semiconductor affected by γ-irradiation and the attenuation of the photon energy of γ-rays.
{"title":"γ-Ray Irradiation Effect on MCF Rubber Solar Cells with both Photovoltaics and Sensing Involving Semiconductors Fabricated under Magnetic and Electric Fields","authors":"K. Shimada, Ryo Kato, Ryo Ikeda, H. Kikura, H. Takahashi","doi":"10.4236/wjm.2020.108008","DOIUrl":"https://doi.org/10.4236/wjm.2020.108008","url":null,"abstract":"For cases in which a robot with installed solar cells and a sensor operates in a nuclear reactor building or in space for extravehicular activity, we require elastic and extensible solar cells. More than two different types of sensing are also required, minimally with photovoltaics and built-in electricity. Magnetic compound fluid (MCF) rubber solar cells are made of rubber, so they are elastic and extensible as well as sensitive. To achieve flexibility and an effective photovoltaic effect, MCF rubber solar cells must include both soluble and insoluble rubbers, Fe3O4, TiO2, Na2WO4∙2H2O, etc. On the basis of this constitution, we propose a consummate fabrication process for MCF rubber solar cells. The characteristics of these cells result from the semiconductor-like role of the molecules of TiO2, Fe3O4, Ni, Na2WO4∙2H2O, polydimethylsiloxane (PDMS), natural rubber (NR), oleic acid, polyvinyl alcohol (PVA), water and magnetic cluster involved in the MCF rubber. Their tendencies can be deduced by synthesizing knowledge about the enhancement of the reverse-bias saturation current IS and the diode ideality factor N, with conventional knowledge about the semiconductor affected by γ-irradiation and the attenuation of the photon energy of γ-rays.","PeriodicalId":70106,"journal":{"name":"力学国际期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42006403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Understanding how stars form in molecular clouds is one of the ongoing research areas in astrophysics. Star formation is the fundamental process to which our current understanding remains incomplete due to the complexity of the physics that drives their formation within molecular clouds. In this article theoretical modelling of the lowest possible mass of the cloud needed for collapse and the core accretion rate has been presented for the molecular cloud collapsing under its gravity. In many of previous studies the critical mass of star forming cloud under its gravity has been modelled using kinetic energy and gravitational potential energy. However, we test the effect of thermodynamic efficiency factor together with other physical processes in describing the critical mass, and controlling or triggering the rate of mass falling onto the central core. Assuming that, the ratio of radiation luminosity to gravitational energy released per unit time of the collapsing MC is less than unity. Following this conceptual framework we have formulated the critical mass and the core accretion rate of the self-gravitating molecular cloud.
{"title":"Star Formation in Self-Gravitating Molecular Cloud: The Critical Mass and the Core Accretion Rate","authors":"G. M. Kumssa, S. B. Tessema","doi":"10.4236/wjm.2020.105005","DOIUrl":"https://doi.org/10.4236/wjm.2020.105005","url":null,"abstract":"Understanding how stars form in molecular clouds is one of the ongoing research areas in astrophysics. Star formation is the fundamental process to which our current understanding remains incomplete due to the complexity of the physics that drives their formation within molecular clouds. In this article theoretical modelling of the lowest possible mass of the cloud needed for collapse and the core accretion rate has been presented for the molecular cloud collapsing under its gravity. In many of previous studies the critical mass of star forming cloud under its gravity has been modelled using kinetic energy and gravitational potential energy. However, we test the effect of thermodynamic efficiency factor together with other physical processes in describing the critical mass, and controlling or triggering the rate of mass falling onto the central core. Assuming that, the ratio of radiation luminosity to gravitational energy released per unit time of the collapsing MC is less than unity. Following this conceptual framework we have formulated the critical mass and the core accretion rate of the self-gravitating molecular cloud.","PeriodicalId":70106,"journal":{"name":"力学国际期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43274559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The purpose of this paper was to investigate the impact of residual stresses on fatigue damage of offshore wind turbine monopiles by numerical analysis approach using ABAQUS software, a finite element analysis (FEA) tool. Three monopile models with the same dimension (within standard range) have been developed in ABAQUS and partitioned circumferentially into equal rings. Longitudinal partitions have been rotated through 180° as obtainable in practice. Characteristic loads typical of a real life offshore wind turbine environment have been applied to all three models, with tensile and compressive residual stresses applied as additional loads at the critical weld region to the first and second models while the third model had no additional load. With zero boundary conditions applied in all six degrees of freedom, the simulation has been run for 107 cycles of wind and wave loads as recommended in standards in each case. Stress results obtained from the critical weld region in the three models showed that the presence of tensile residual stresses equal to the material yield stress contributed a maximum 0.05% to fatigue damage of the monopile when compared with results from the model with no residual stress while the presence of compressive residual stresses with the magnitude of the yield stress of the material caused a gain of 0.06% in fatigue life by similar comparison, indicating negligible contribution of residual stresses to the stress build up in the critical weld region, thus suggesting that the magnitude of the residual stress as high as the yield stress of the material of the monopile is not large enough to cause the monopile to open up in the axial direction.
{"title":"Residual Stress Consideration in Fatigue Damage of Offshore Wind Turbine Monopiles: To Be or Not to Be?","authors":"A. A. Oyeniran, D. S. Aziaka","doi":"10.4236/wjm.2020.104004","DOIUrl":"https://doi.org/10.4236/wjm.2020.104004","url":null,"abstract":"The purpose of this paper was to investigate the impact of residual stresses on fatigue damage of offshore wind turbine monopiles by numerical analysis approach using ABAQUS software, a finite element analysis (FEA) tool. Three monopile models with the same dimension (within standard range) have been developed in ABAQUS and partitioned circumferentially into equal rings. Longitudinal partitions have been rotated through 180° as obtainable in practice. Characteristic loads typical of a real life offshore wind turbine environment have been applied to all three models, with tensile and compressive residual stresses applied as additional loads at the critical weld region to the first and second models while the third model had no additional load. With zero boundary conditions applied in all six degrees of freedom, the simulation has been run for 107 cycles of wind and wave loads as recommended in standards in each case. Stress results obtained from the critical weld region in the three models showed that the presence of tensile residual stresses equal to the material yield stress contributed a maximum 0.05% to fatigue damage of the monopile when compared with results from the model with no residual stress while the presence of compressive residual stresses with the magnitude of the yield stress of the material caused a gain of 0.06% in fatigue life by similar comparison, indicating negligible contribution of residual stresses to the stress build up in the critical weld region, thus suggesting that the magnitude of the residual stress as high as the yield stress of the material of the monopile is not large enough to cause the monopile to open up in the axial direction.","PeriodicalId":70106,"journal":{"name":"力学国际期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43320094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pascal Kuate Nkounhawa, D. Ndapeu, B. Kenmeugne, T. Beda
In the realization of mechanical structures, achieving stability and balance is a problem commonly encountered by engineers in the field of civil engineering, mechanics, aeronautics, biomechanics and many others. The study of plate behavior is a very sensitive subject because it is part of the structural elements. The study of the dynamic behavior of free vibration structures is done by modal analysis in order to calculate natural frequencies and modal deformations. In this paper, we present the modal analysis of a thin rectangular plate simply supported. The analytical solution of the differential equation is obtained by applying the method of separating the variables. We are talking about the exact solution of the problem to the limit values. However, numerical methods such as the finite element method allow us to approximate these functions with greater accuracy. It is one of the most powerful computational methods for predicting dynamic response in a complex structure subject to arbitrary boundary conditions. The results obtained by MEF through Ansys 15.0 are then compared with those obtained by the analytical method.
{"title":"Analysis of the Behavior of a Square Plate in Free Vibration by FEM in Ansys","authors":"Pascal Kuate Nkounhawa, D. Ndapeu, B. Kenmeugne, T. Beda","doi":"10.4236/wjm.2020.102002","DOIUrl":"https://doi.org/10.4236/wjm.2020.102002","url":null,"abstract":"In the realization of mechanical structures, achieving stability and balance is a problem commonly encountered by engineers in the field of civil engineering, mechanics, aeronautics, biomechanics and many others. The study of plate behavior is a very sensitive subject because it is part of the structural elements. The study of the dynamic behavior of free vibration structures is done by modal analysis in order to calculate natural frequencies and modal deformations. In this paper, we present the modal analysis of a thin rectangular plate simply supported. The analytical solution of the differential equation is obtained by applying the method of separating the variables. We are talking about the exact solution of the problem to the limit values. However, numerical methods such as the finite element method allow us to approximate these functions with greater accuracy. It is one of the most powerful computational methods for predicting dynamic response in a complex structure subject to arbitrary boundary conditions. The results obtained by MEF through Ansys 15.0 are then compared with those obtained by the analytical method.","PeriodicalId":70106,"journal":{"name":"力学国际期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44996401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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