The paper aims to investigate combined bending-tension/compression deformation of a micro-bar. The strain-driven nonlocal differential model which involves information about long-range interactions between atoms is used to develop the mechanical model and theoretical formulations. Subsequently, effects of internal long-range scale parameter, length of micro-bar, external loads and bending rigidity on combined deformation are shown and discussed. In particular, the upper bound of internal longrange scale parameter and the buckling load are achieved during bending-compression analyses. It is demonstrated that the existence of internal scale parameter or axial tensile load decreases combined deformation. The deflection at the midpoint reduces with increasing bending rigidity, while it rises with increasing length of the microbar. Additionally, an effect of the acting position of transverse load on combined deformation is discussed and deflection at the symmetry point of transverse acting position is achieved. When the long-range interaction is taken into consideration, the equivalent stiffness of the micro-bar subjected to combined bending-tension is stiffer than that predicted by classical mechanics, and it validates the existing nonlocal hardening model. The combined bending-compression of the micro-bar reveals that the deflection may increase or decrease with an increase in the long-range scale or structural length, which verifies both the nonlocal softening and hardening models.
{"title":"Combined bending-tension/compression deformation of micro-bars accounting for strain-driven long-range interactions","authors":"N. Zhang, J. Yan, C. Li, J. Zhou","doi":"10.24423/AOM.3031","DOIUrl":"https://doi.org/10.24423/AOM.3031","url":null,"abstract":"The paper aims to investigate combined bending-tension/compression deformation of a micro-bar. The strain-driven nonlocal differential model which involves information about long-range interactions between atoms is used to develop the mechanical model and theoretical formulations. Subsequently, effects of internal long-range scale parameter, length of micro-bar, external loads and bending rigidity on combined deformation are shown and discussed. In particular, the upper bound of internal longrange scale parameter and the buckling load are achieved during bending-compression analyses. It is demonstrated that the existence of internal scale parameter or axial tensile load decreases combined deformation. The deflection at the midpoint reduces with increasing bending rigidity, while it rises with increasing length of the microbar. Additionally, an effect of the acting position of transverse load on combined deformation is discussed and deflection at the symmetry point of transverse acting position is achieved. When the long-range interaction is taken into consideration, the equivalent stiffness of the micro-bar subjected to combined bending-tension is stiffer than that predicted by classical mechanics, and it validates the existing nonlocal hardening model. The combined bending-compression of the micro-bar reveals that the deflection may increase or decrease with an increase in the long-range scale or structural length, which verifies both the nonlocal softening and hardening models.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68938892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The present work is devoted to the free convection flow occurring about a heated vertically stretching permeable surface placed in a porous medium under the influence of a temperature dependent internal heat generation or absorption. There are volume radiative heat sources in the fluid and the system is permeated by a uniform magnetic field. It is shown that the governing equations are reducible to a self-similar nonlinear ordinary differential equation of third order whose solutions are constructed analytically in the purely exponential series form. Under special circumstances, closed-form solutions are available which clearly indicate the existence of dual natural convection solutions. Otherwise, analytical solutions are still possible which are shown to be computed from an elegant algorithm without a need to invoke any numerical means. Exact solutions demonstrate, in physical insight that, in the presence of a heat sink absorbing the temperature from the porous medium increases the rate of heat transfer from the wall, whereas a heat source mechanism will surely overheat the system during the wall heating process, resulting in poor heat transfer rates. The presented exact solutions are beneficial for investigation of free convection phenomena in different geometries taking into account more complex physical features in higher dimensions.
{"title":"MHD natural convection in saturated porous media with heat generation/absorption and thermal radiation: closed-form solutions","authors":"M. Turkyilmazoglu","doi":"10.24423/AOM.3049","DOIUrl":"https://doi.org/10.24423/AOM.3049","url":null,"abstract":"The present work is devoted to the free convection flow occurring about a heated vertically stretching permeable surface placed in a porous medium under the influence of a temperature dependent internal heat generation or absorption. There are volume radiative heat sources in the fluid and the system is permeated by a uniform magnetic field. It is shown that the governing equations are reducible to a self-similar nonlinear ordinary differential equation of third order whose solutions are constructed analytically in the purely exponential series form. Under special circumstances, closed-form solutions are available which clearly indicate the existence of dual natural convection solutions. Otherwise, analytical solutions are still possible which are shown to be computed from an elegant algorithm without a need to invoke any numerical means. Exact solutions demonstrate, in physical insight that, in the presence of a heat sink absorbing the temperature from the porous medium increases the rate of heat transfer from the wall, whereas a heat source mechanism will surely overheat the system during the wall heating process, resulting in poor heat transfer rates. The presented exact solutions are beneficial for investigation of free convection phenomena in different geometries taking into account more complex physical features in higher dimensions.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68938430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The fractional plasticity was proposed to model the stress-strain behaviour of granular soils, but only within the scope of classical triaxial loading condition. In this study an attempt is made to develop a 3D fractional plasticity model for granular soils subjected to true triaxial loads by using characteristic stress, where all the fractional-order and integer-order derivatives can be easily obtained. Without using a plastic potential, the non-associated plastic flow rule is achieved by performing fractional derivatives of the yielding function in the characteristic stress space. The obtained plastic flow direction is found to be influenced by the fractional order, characteristic stress parameter and intermediate stress ratio. To further validate the proposed model, a series of true triaxial test results of different granular soils are simulated, from which good agreement between the model predictions and the corresponding test results is found.
{"title":"State-dependent fractional plasticity model for the true triaxial behaviour of granular soil","authors":"Y. Sun, W. Sumelka","doi":"10.24423/AOM.3084","DOIUrl":"https://doi.org/10.24423/AOM.3084","url":null,"abstract":"The fractional plasticity was proposed to model the stress-strain behaviour of granular soils, but only within the scope of classical triaxial loading condition. In this study an attempt is made to develop a 3D fractional plasticity model for granular soils subjected to true triaxial loads by using characteristic stress, where all the fractional-order and integer-order derivatives can be easily obtained. Without using a plastic potential, the non-associated plastic flow rule is achieved by performing fractional derivatives of the yielding function in the characteristic stress space. The obtained plastic flow direction is found to be influenced by the fractional order, characteristic stress parameter and intermediate stress ratio. To further validate the proposed model, a series of true triaxial test results of different granular soils are simulated, from which good agreement between the model predictions and the corresponding test results is found.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48428545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study complements a series of preliminary experimental studies of the destabilization of a granular stack immersed by fluidization, the particular case being the transient regime of homogeneous fluidization. The significant influence of the initial density (initial volume fraction) of the granular stack on the transient homogeneous fluidization regime is highlighted. An initially loose stack fluidizes turbulently and chaotically in a few seconds, from the injection zone to the top of the granular layer. Conversely, for the same material in an initially dense state, there is a mass takeoff of the stack, which is added to the propagation of porosity wave instability from the bottom to the top of the stack with fast kinetics that decompacts the medium. The results also showed that the velocity of this porosity wave seems almost constant regardless of the fluidization velocity.
{"title":"Influence of initial density of granular stack on transient regime of homogeneous fluidization","authors":"A. Drame, L. Wang, B. Diourte","doi":"10.24423/AOM.3057","DOIUrl":"https://doi.org/10.24423/AOM.3057","url":null,"abstract":"This study complements a series of preliminary experimental studies of the destabilization of a granular stack immersed by fluidization, the particular case being the transient regime of homogeneous fluidization. The significant influence of the initial density (initial volume fraction) of the granular stack on the transient homogeneous fluidization regime is highlighted. An initially loose stack fluidizes turbulently and chaotically in a few seconds, from the injection zone to the top of the granular layer. Conversely, for the same material in an initially dense state, there is a mass takeoff of the stack, which is added to the propagation of porosity wave instability from the bottom to the top of the stack with fast kinetics that decompacts the medium. The results also showed that the velocity of this porosity wave seems almost constant regardless of the fluidization velocity.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43330707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper analyzes stochastic vibrations of a viscoelastic nanobeam under axial loadings. Based on the higher-order nonlocal strain gradient theory and the Liapunov functional method, bounds of the almost sure asymptotic stability of a nanobeam are obtained as a function of retardation time, variance of the stochastic force, higher-order and lower-order scale coefficients, strain gradient length scale, and intensity of the deterministic component of axial loading. Analytical results from this study are first compared with those obtained from the Monte Carlo simulation. Numerical calculations are performed for the Gaussian and harmonic non-white processes as models of axial forces.
{"title":"Mathematical modeling and stochastic stability analysis of viscoelastic nanobeams using higher-order nonlocal strain gradient theory","authors":"I. Pavlović, R. Pavlović, G. Janevski","doi":"10.24423/AOM.3139","DOIUrl":"https://doi.org/10.24423/AOM.3139","url":null,"abstract":"This paper analyzes stochastic vibrations of a viscoelastic nanobeam under axial loadings. Based on the higher-order nonlocal strain gradient theory and the Liapunov functional method, bounds of the almost sure asymptotic stability of a nanobeam are obtained as a function of retardation time, variance of the stochastic force, higher-order and lower-order scale coefficients, strain gradient length scale, and intensity of the deterministic component of axial loading. Analytical results from this study are first compared with those obtained from the Monte Carlo simulation. Numerical calculations are performed for the Gaussian and harmonic non-white processes as models of axial forces.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47674418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In recent years, artificial neural networks have been proposed for engineering applications, such as predicting stresses and strains in structural elements. However, the question arises, how many complex influences can be included in an artificial neural network (ANN) and how accurate these predictions are in comparison to classical finite element solutions. A weakness of finite element predictions is that they can behave sensitive and unstable to changes in material parameters. An ANN does not need an underlying model with parameters and uses input variables, only. In the present study the stability of numerical results obtained by ANN and FEM are compared to each other for a problem in structural dynamics. The result gives new insight about the possibilities to predict accurately structural deformations by means of ANNs. As an example for highly complex geometrically and physically nonlinear structural deformations, the response of circular metal plates subjected to shock waves is investigated.
{"title":"Stability of feed forward artificial neural networks versus nonlinear structural models in high speed deformations: A critical comparison","authors":"M. Stoffel, F. Bamer, B. Markert","doi":"10.24423/AOM.3091","DOIUrl":"https://doi.org/10.24423/AOM.3091","url":null,"abstract":"In recent years, artificial neural networks have been proposed for engineering applications, such as predicting stresses and strains in structural elements. However, the question arises, how many complex influences can be included in an artificial neural network (ANN) and how accurate these predictions are in comparison to classical finite element solutions. A weakness of finite element predictions is that they can behave sensitive and unstable to changes in material parameters. An ANN does not need an underlying model with parameters and uses input variables, only. In the present study the stability of numerical results obtained by ANN and FEM are compared to each other for a problem in structural dynamics. The result gives new insight about the possibilities to predict accurately structural deformations by means of ANNs. As an example for highly complex geometrically and physically nonlinear structural deformations, the response of circular metal plates subjected to shock waves is investigated.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42710055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the present paper the linear theory of thermoelasticity for isotropic and homogeneous solids with macro-, meso- and microporosity is considered. In this theory the independent variables are the displacement vector field, the changes of the volume fractions of pore networks and the variation of temperature. The fundamental solution of the system of steady vibrations equations is constructed explicitly by means of elementary functions. The basic internal and external boundary value problems (BVPs) are formulated and the uniqueness theorems of these problems are proved. The basic properties of the surface (single-layer and double-layer) and volume potentials are established and finally, the existence theorems for regular (classical) solutions of the internal and external BVPs of steady vibrations are proved by using the potential method (boundary integral equation method) and the theory of singular integral equations.
{"title":"Potential method in the theory of thermoelasticity for materials with triple voids","authors":"M. Svanadze","doi":"10.24423/AOM.3118","DOIUrl":"https://doi.org/10.24423/AOM.3118","url":null,"abstract":"In the present paper the linear theory of thermoelasticity for isotropic and homogeneous solids with macro-, meso- and microporosity is considered. In this theory the independent variables are the displacement vector field, the changes of the volume fractions of pore networks and the variation of temperature. The fundamental solution of the system of steady vibrations equations is constructed explicitly by means of elementary functions. The basic internal and external boundary value problems (BVPs) are formulated and the uniqueness theorems of these problems are proved. The basic properties of the surface (single-layer and double-layer) and volume potentials are established and finally, the existence theorems for regular (classical) solutions of the internal and external BVPs of steady vibrations are proved by using the potential method (boundary integral equation method) and the theory of singular integral equations.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2019-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46041150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper presents a brief review of the observational facts related to plasma filamentation in astrophysics and the subtle structures of plasma in Transient Luminous Events (TLE’s) and an analysis of the physical mechanism that could contribute to formation of filaments in plasma inside streamers. The values of physical parameters are assumed such as to resemble the physical conditions in streamers of the TLE’s. Estimates of the typical spatial scales of these structures and temporal characteristics of filament formation are given. The analysis concerns a non-magnetic mechanism based on a form of non-relativistic dissipative instability and the electron-nitrogen collisional 2 Π g resonance. It is argued that the influence of the magnetic field is negligible at the leading order at least up to the altitudes of about 65–70 km. Under the conditions related to those in plasma inside the TLE’s, derived based on the current knowledge of physical parameters within the electric discharges, the identified dissipative-resonant instability is demonstrated to be the only/most vigorous linear instability developing in the system. It results in periodic plasma density distribution in the direction transverse to the electric field. The obtained time scales of the instability development are quick and proportional to the inverse of the ion-neutral collision frequency, 1/ ν i , whereas the proposed spatial scale of the density stripes/filaments is proportional to the electron temperature and inversely proportional to the speed of the discharge.
{"title":"Subtle structure of streamers under conditions resembling those of Transient Luminous Events","authors":"J. Blecki, K. Mizerski","doi":"10.24423/AOM.3009","DOIUrl":"https://doi.org/10.24423/AOM.3009","url":null,"abstract":"The paper presents a brief review of the observational facts related to plasma filamentation in astrophysics and the subtle structures of plasma in Transient Luminous Events (TLE’s) and an analysis of the physical mechanism that could contribute to formation of filaments in plasma inside streamers. The values of physical parameters are assumed such as to resemble the physical conditions in streamers of the TLE’s. Estimates of the typical spatial scales of these structures and temporal characteristics of filament formation are given. The analysis concerns a non-magnetic mechanism based on a form of non-relativistic dissipative instability and the electron-nitrogen collisional 2 Π g resonance. It is argued that the influence of the magnetic field is negligible at the leading order at least up to the altitudes of about 65–70 km. Under the conditions related to those in plasma inside the TLE’s, derived based on the current knowledge of physical parameters within the electric discharges, the identified dissipative-resonant instability is demonstrated to be the only/most vigorous linear instability developing in the system. It results in periodic plasma density distribution in the direction transverse to the electric field. The obtained time scales of the instability development are quick and proportional to the inverse of the ion-neutral collision frequency, 1/ ν i , whereas the proposed spatial scale of the density stripes/filaments is proportional to the electron temperature and inversely proportional to the speed of the discharge.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2018-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49469404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper presents large eddy simulation (LES) study aiming at investigations of an influence of flow conditions on a spark ignition process in a two-phase shear dominated flow. Implicit LES approach is applied for the combustion modelling and the spark is modelled using the energy deposition model of Lacaze et al. [20]. We examine an impact of turbulence intensities and randomness of initial distributions of velocity fluctuations on a flame development during the spark duration and shortly after it is switched off. It is found that for a strong spark, as used in IC engines, the turbulence intensity has little effect on the ignition and flame kernel growth and no significant differences are seen even if the turbulence intensities differ four times. It is observed that weak turbulent structures cannot affect fast flame propagation mechanism and its development is conditioned by evaporation and rapid thermal expansion. In such regimes, the turbulence seems to be too weak to significantly alter the flame dynamics. It is found that at the initial stage of the flame development it grows toward the fuel-rich region and spread over the fuel-lean side only after the evaporated fuel diffuses and mixes with the oxidizer stream. The flame size and its shape turn out to be equally dependent on the initial distribution of the turbulence fluctuations and turbulence intensity.
{"title":"LES study of turbulence intensity impact on spark ignition in a two-phase flow","authors":"J. Stempka, L. Kuban, A. Tyliszczak","doi":"10.24423/AOM.3018","DOIUrl":"https://doi.org/10.24423/AOM.3018","url":null,"abstract":"The paper presents large eddy simulation (LES) study aiming at investigations of an influence of flow conditions on a spark ignition process in a two-phase shear dominated flow. Implicit LES approach is applied for the combustion modelling and the spark is modelled using the energy deposition model of Lacaze et al. [20]. We examine an impact of turbulence intensities and randomness of initial distributions of velocity fluctuations on a flame development during the spark duration and shortly after it is switched off. It is found that for a strong spark, as used in IC engines, the turbulence intensity has little effect on the ignition and flame kernel growth and no significant differences are seen even if the turbulence intensities differ four times. It is observed that weak turbulent structures cannot affect fast flame propagation mechanism and its development is conditioned by evaporation and rapid thermal expansion. In such regimes, the turbulence seems to be too weak to significantly alter the flame dynamics. It is found that at the initial stage of the flame development it grows toward the fuel-rich region and spread over the fuel-lean side only after the evaporated fuel diffuses and mixes with the oxidizer stream. The flame size and its shape turn out to be equally dependent on the initial distribution of the turbulence fluctuations and turbulence intensity.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2018-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42564960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
I. Senjanović, I. Čatipović, N. Alujevic, D. Čakmak, N. Vladimir
In this paper rigorous formulae for natural frequencies of in-plane and out-of-plane free vibrations of a rotating ring are derived. An in-plane vibration mode of the ring is characterised by coupled flexural and extensional deformations, whereas an out-of-plane mode is distinguished by coupled flexural and torsional deformations. The expressions for natural frequencies are derived from a generalised toroidal shell theory. For the in-plane vibrations, the ring is considered to be a short top segment of a toroidal shell. For the out-of-plane vibrations, the ring is considered to be a side segment of the shell. Natural vibrations are analysed by the energy approach. The expressions for the ring strain and kinetic energies are deduced from the corresponding expressions for the torus. It is shown that the ring rotation causes bifurcation of natural frequencies of the in-plane vibrations only. Bifurcation of natural frequencies of the out-of-plane vibrations does not occur. Otherwise, for non-rotating rings, the derived formulae for the natural frequencies of the in-plane and the out-of-plane flexural vibrations are very similar. The derived analytical results are validated by a comparison with FEM and FSM (Finite Strip Method) results, as well as with experimental results available in the literature.
{"title":"Free in-plane and out-of-plane vibrations of rotating thin ring based on the toroidal shell theory","authors":"I. Senjanović, I. Čatipović, N. Alujevic, D. Čakmak, N. Vladimir","doi":"10.24423/aom.3013","DOIUrl":"https://doi.org/10.24423/aom.3013","url":null,"abstract":"In this paper rigorous formulae for natural frequencies of in-plane and out-of-plane free vibrations of a rotating ring are derived. An in-plane vibration mode of the ring is characterised by coupled flexural and extensional deformations, whereas an out-of-plane mode is distinguished by coupled flexural and torsional deformations. The expressions for natural frequencies are derived from a generalised toroidal shell theory. For the in-plane vibrations, the ring is considered to be a short top segment of a toroidal shell. For the out-of-plane vibrations, the ring is considered to be a side segment of the shell. Natural vibrations are analysed by the energy approach. The expressions for the ring strain and kinetic energies are deduced from the corresponding expressions for the torus. It is shown that the ring rotation causes bifurcation of natural frequencies of the in-plane vibrations only. Bifurcation of natural frequencies of the out-of-plane vibrations does not occur. Otherwise, for non-rotating rings, the derived formulae for the natural frequencies of the in-plane and the out-of-plane flexural vibrations are very similar. The derived analytical results are validated by a comparison with FEM and FSM (Finite Strip Method) results, as well as with experimental results available in the literature.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2018-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42287626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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