Pub Date : 2022-12-30DOI: 10.15625/0866-7136/17936
T. I. Thinh, P. N. Thanh
This paper is a study of the vibroacoustic behavior of orthotropic laminated composite rectangular plate under a sound wave excitation in thermal environments. An improved analytical procedure has been developed that allows for an efficient solution of the finite composite plate sound transmission problem. A symmetrically orthotropic laminated composite plate is considered. The plate is modeled with classic thin-plate theory and is assumed to be clamped on all four sides. The incident acoustic pressure is modeled as a harmonic plane wave impinging on the plate at an arbitrary angle. The sound transmission loss is calculated from the ratio of incident to transmitted acoustic powers.
{"title":"Vibroacoustic behavior of a rectangular composite plate in thermal environment","authors":"T. I. Thinh, P. N. Thanh","doi":"10.15625/0866-7136/17936","DOIUrl":"https://doi.org/10.15625/0866-7136/17936","url":null,"abstract":"This paper is a study of the vibroacoustic behavior of orthotropic laminated composite rectangular plate under a sound wave excitation in thermal environments. An improved analytical procedure has been developed that allows for an efficient solution of the finite composite plate sound transmission problem. A symmetrically orthotropic laminated composite plate is considered. The plate is modeled with classic thin-plate theory and is assumed to be clamped on all four sides. The incident acoustic pressure is modeled as a harmonic plane wave impinging on the plate at an arbitrary angle. The sound transmission loss is calculated from the ratio of incident to transmitted acoustic powers.","PeriodicalId":239329,"journal":{"name":"Vietnam Journal of Mechanics","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132864783","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 : 2022-12-30DOI: 10.15625/0866-7136/17909
Cong Ich Le, D. Nguyen
In this paper, vibration of Timoshenko microbeams with an axial force in micro-electromechanical systems (MEMS) is studied for the first time by using a nonlinear finite element procedure. Based on the von Kármán geometric nonlinearity and the modified couple stress theory (MCST), a beam element is formulated by employing hierarchical functions to interpolate the displacement field. Using the derived element, the discretized equation of motion for the microbeam is constructed and then solved by the Newton-Raphson iterative procedure in conjunction with the Newmark method. The natural frequencies, pull-in voltages and dynamic deflections are computed for a clamped-clamped microbeam under electrostatic actuation of a given direct current (DC) voltage. The numerical result reveals that the axial force and the microsize effect have a significant influence on the vibration, and the fundamental frequency of the microbeams is underestimated by ignoring the size effect. The effects of the axial force, the applied voltage and the material length scale parameter on the vibration of the beam are studied in detail and highlighted.
{"title":"Vibration of electrically actuated MEMS Timoshenko microbeams based on a hierarchical beam element","authors":"Cong Ich Le, D. Nguyen","doi":"10.15625/0866-7136/17909","DOIUrl":"https://doi.org/10.15625/0866-7136/17909","url":null,"abstract":"In this paper, vibration of Timoshenko microbeams with an axial force in micro-electromechanical systems (MEMS) is studied for the first time by using a nonlinear finite element procedure. Based on the von Kármán geometric nonlinearity and the modified couple stress theory (MCST), a beam element is formulated by employing hierarchical functions to interpolate the displacement field. Using the derived element, the discretized equation of motion for the microbeam is constructed and then solved by the Newton-Raphson iterative procedure in conjunction with the Newmark method. The natural frequencies, pull-in voltages and dynamic deflections are computed for a clamped-clamped microbeam under electrostatic actuation of a given direct current (DC) voltage. The numerical result reveals that the axial force and the microsize effect have a significant influence on the vibration, and the fundamental frequency of the microbeams is underestimated by ignoring the size effect. The effects of the axial force, the applied voltage and the material length scale parameter on the vibration of the beam are studied in detail and highlighted.","PeriodicalId":239329,"journal":{"name":"Vietnam Journal of Mechanics","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128026069","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 : 2022-12-30DOI: 10.15625/0866-7136/17932
Bui Tien Tu, L. Ly, Nguyen Thi Hong Phuong
A new analytical approach for nonlinear thermal buckling of Functionally Graded Graphene Platelet Reinforced Composite (FG-GPLRC) circular plates and shallow spherical caps using the first-order shear deformation theory (FSDT) is presented in this paper. The circular plates and shallow spherical caps are assumed to be subjected to uniformly distributed thermal loads. By applying the Galerkin method, the relations between thermal load–deflection are achieved to determine the postbuckling behavior and critical buckling loads of the considered structures. Special effects on the nonlinear thermal behavior of circular plates and shallow spherical caps with five different material distribution laws, different Graphene platelet (GPL) mass fractions, and geometrical dimensions are explored and discussed in numerical examples.
{"title":"A new analytical approach of nonlinear thermal buckling of FG-GPLRC circular plates and shallow spherical caps using the FSDT and Galerkin method","authors":"Bui Tien Tu, L. Ly, Nguyen Thi Hong Phuong","doi":"10.15625/0866-7136/17932","DOIUrl":"https://doi.org/10.15625/0866-7136/17932","url":null,"abstract":"A new analytical approach for nonlinear thermal buckling of Functionally Graded Graphene Platelet Reinforced Composite (FG-GPLRC) circular plates and shallow spherical caps using the first-order shear deformation theory (FSDT) is presented in this paper. The circular plates and shallow spherical caps are assumed to be subjected to uniformly distributed thermal loads. By applying the Galerkin method, the relations between thermal load–deflection are achieved to determine the postbuckling behavior and critical buckling loads of the considered structures. Special effects on the nonlinear thermal behavior of circular plates and shallow spherical caps with five different material distribution laws, different Graphene platelet (GPL) mass fractions, and geometrical dimensions are explored and discussed in numerical examples.","PeriodicalId":239329,"journal":{"name":"Vietnam Journal of Mechanics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132143704","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 : 2022-09-30DOI: 10.15625/0866-7136/17230
T. T. Huan, H. Anh
A novel biped walking pattern combining robust zero-moment-point ZMP technique and pre-determined foot-lifting value is proposed in this paper. The implementation of suggested approach contains following stages. Initially, a one-step ZMP curve for a small-sized humanoid is created using the 3rd-order interpolating equation, with pre-determined velocity responding the ZMP concept. The next step, biped gait planning is modeled as a non-linear MIMO plant including ten degree-of-freedom DOF. Then, the installation of a biped walking pattern generator (WPG) based on the new hybrid Neural-NARX model is completed. Eventually, the novel Enhanced Differential Evolution (EDE) technique is applied to optimally identify the weights of the hybrid Neural-NARX structure, for ensuring robust robot walking in terms of desired ZMP trajectories and pre-determined foot-lifting value. All case studies confirm that it is surely provide a biped WPG satisfying both of the effectiveness and high robustness. The verification of the newly proposed WPG is adequately tested via both simulation and experiment results.
{"title":"Advanced biped gait generator using NARX-MLP neural model optimized by enhanced evolutionary algorithm","authors":"T. T. Huan, H. Anh","doi":"10.15625/0866-7136/17230","DOIUrl":"https://doi.org/10.15625/0866-7136/17230","url":null,"abstract":"A novel biped walking pattern combining robust zero-moment-point ZMP technique and pre-determined foot-lifting value is proposed in this paper. The implementation of suggested approach contains following stages. Initially, a one-step ZMP curve for a small-sized humanoid is created using the 3rd-order interpolating equation, with pre-determined velocity responding the ZMP concept. The next step, biped gait planning is modeled as a non-linear MIMO plant including ten degree-of-freedom DOF. Then, the installation of a biped walking pattern generator (WPG) based on the new hybrid Neural-NARX model is completed. Eventually, the novel Enhanced Differential Evolution (EDE) technique is applied to optimally identify the weights of the hybrid Neural-NARX structure, for ensuring robust robot walking in terms of desired ZMP trajectories and pre-determined foot-lifting value. All case studies confirm that it is surely provide a biped WPG satisfying both of the effectiveness and high robustness. The verification of the newly proposed WPG is adequately tested via both simulation and experiment results.","PeriodicalId":239329,"journal":{"name":"Vietnam Journal of Mechanics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125477956","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 : 2022-09-30DOI: 10.15625/0866-7136/17479
M. Aydogdu
First of all Sentilkumar has to be congratulated for his paper [1]. In the paper, the author presented the vibration of double walled carbon nanotubes. He claimed that the equations of motion given in [2] are incorrect. The aim of this communication is to clarify this issue.
{"title":"Comments on “Axial vibration of double-walled carbon nanotubes using double-nanorod model with van der Waals force under Pasternak medium and magnetic effects [Vietnam Journal of Mechanics, Vol.44, No.1 (2022), pp. 29-43]”","authors":"M. Aydogdu","doi":"10.15625/0866-7136/17479","DOIUrl":"https://doi.org/10.15625/0866-7136/17479","url":null,"abstract":"First of all Sentilkumar has to be congratulated for his paper [1]. In the paper, the author presented the vibration of double walled carbon nanotubes. He claimed that the equations of motion given in [2] are incorrect. The aim of this communication is to clarify this issue. ","PeriodicalId":239329,"journal":{"name":"Vietnam Journal of Mechanics","volume":"24 26","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120842106","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 : 2022-09-30DOI: 10.15625/0866-7136/17546
N. T. Khiem, P. T. Hang
In this paper, there is proposed a novel damage index extracted from frequency response of cracked Timoshenko beam under moving harmonic load using the so-called Modal Assurance Criterion (MAC) concept. First, frequency response of a cracked Timoshenko beam subjected to harmonic force moving on the beam with constant speed is obtained in an analytical expression. Then, a scalar characteristic like the coherence between the frequency responses of intact and cracked beams is determined and called herein Spectral Assurance Criterion (SAC). Such designed criterion is dependent upon crack parameters (location and depth), the load frequency and speed as well as position on beam where the responses have been measured. Numerical analysis shows that SAC is much more sensitive to crack than natural frequencies and can be used as a novel damage index for crack detection in beam using moving load. The effect of moving load frequency and speed has been also examined with the aim to have got an indicator most adequate for the crack detection problem.
{"title":"A novel damage index extracted from frequency response of cracked Timoshenko beam subjected to moving harmonic load","authors":"N. T. Khiem, P. T. Hang","doi":"10.15625/0866-7136/17546","DOIUrl":"https://doi.org/10.15625/0866-7136/17546","url":null,"abstract":"In this paper, there is proposed a novel damage index extracted from frequency response of cracked Timoshenko beam under moving harmonic load using the so-called Modal Assurance Criterion (MAC) concept. First, frequency response of a cracked Timoshenko beam subjected to harmonic force moving on the beam with constant speed is obtained in an analytical expression. Then, a scalar characteristic like the coherence between the frequency responses of intact and cracked beams is determined and called herein Spectral Assurance Criterion (SAC). Such designed criterion is dependent upon crack parameters (location and depth), the load frequency and speed as well as position on beam where the responses have been measured. Numerical analysis shows that SAC is much more sensitive to crack than natural frequencies and can be used as a novel damage index for crack detection in beam using moving load. The effect of moving load frequency and speed has been also examined with the aim to have got an indicator most adequate for the crack detection problem.","PeriodicalId":239329,"journal":{"name":"Vietnam Journal of Mechanics","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116403781","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 : 2022-09-10DOI: 10.15625/0866-7136/17180
Cong Ich Le, D. Nguyen
The size dependent large displacement behavior of planar microbeams and microframes is studied in this paper using a corotational beam element. To account for the size effect, the modified couple stress theory (MCST) is employed in conjunction with Euler-Bernoulli beam theory in deriving the internal force vector and the tangent stiffness matrix of the beam element. The Newton-Raphson based iterative procedure is used in combination with the arc-length method to solve the nonlinear equilibrium equation and to trace the equilibrium paths. Various microbeams and microframes are analyzed to show the influence of the size effect on the large deflection behavior of the microstructure. The obtained result reveals that the size effect plays an important role on the large deflection response, and the displacements of the structure are over estimated by ignoring the size effect. A parametric study is carried out to highlight the influence of the material length scale parameter on the large displacement behavior of the microbeams and microframes.
{"title":"Size dependent large displacements of microbeams and microframes","authors":"Cong Ich Le, D. Nguyen","doi":"10.15625/0866-7136/17180","DOIUrl":"https://doi.org/10.15625/0866-7136/17180","url":null,"abstract":"The size dependent large displacement behavior of planar microbeams and microframes is studied in this paper using a corotational beam element. To account for the size effect, the modified couple stress theory (MCST) is employed in conjunction with Euler-Bernoulli beam theory in deriving the internal force vector and the tangent stiffness matrix of the beam element. The Newton-Raphson based iterative procedure is used in combination with the arc-length method to solve the nonlinear equilibrium equation and to trace the equilibrium paths. Various microbeams and microframes are analyzed to show the influence of the size effect on the large deflection behavior of the microstructure. The obtained result reveals that the size effect plays an important role on the large deflection response, and the displacements of the structure are over estimated by ignoring the size effect. A parametric study is carried out to highlight the influence of the material length scale parameter on the large displacement behavior of the microbeams and microframes.","PeriodicalId":239329,"journal":{"name":"Vietnam Journal of Mechanics","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128450890","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 : 2022-09-10DOI: 10.15625/0866-7136/17331
M. Nguyen, T. Bui
This paper presents a hybrid approach for multiscale topology optimization of structures. The topological shape of both macro-structure and micro-structure are concurrently optimized, based on the solid isotropic material with penalization (SIMP) technique in combination with finite element method (FEM). The material is assumed to have periodically patterned micro-structures, such that the effective properties can be evaluated via energy-based homogenization method (EBHM). In every iteration, the effective properties of material are passed to the macroscopic problem, and the macroscopic behavior (e.g. strain energy) is transferred back to the micro-scale problem, where the unit cell representing the micro-structure of material is determined for the next iteration. It is found that the update process can be done separately, i.e., the sensitivity of macro-scale design variables is not required during the update of micro-scale design variables, and vice versa. Hence, the proposal is that the macro-structure is updated by the gradient-free Proportional Topology Optimization (PTO) algorithm to utilize the computational efficiency of PTO. The micro-structure is still updated by the common gradient-based algorithm, namely Optimality Criteria (OC). Three benchmark numerical examples are investigated, demonstrating the feasibility and efficiency of the proposed hybrid approach.
{"title":"Concurrent multiscale topology optimization: A hybrid approach","authors":"M. Nguyen, T. Bui","doi":"10.15625/0866-7136/17331","DOIUrl":"https://doi.org/10.15625/0866-7136/17331","url":null,"abstract":"This paper presents a hybrid approach for multiscale topology optimization of structures. The topological shape of both macro-structure and micro-structure are concurrently optimized, based on the solid isotropic material with penalization (SIMP) technique in combination with finite element method (FEM). The material is assumed to have periodically patterned micro-structures, such that the effective properties can be evaluated via energy-based homogenization method (EBHM). In every iteration, the effective properties of material are passed to the macroscopic problem, and the macroscopic behavior (e.g. strain energy) is transferred back to the micro-scale problem, where the unit cell representing the micro-structure of material is determined for the next iteration. It is found that the update process can be done separately, i.e., the sensitivity of macro-scale design variables is not required during the update of micro-scale design variables, and vice versa. Hence, the proposal is that the macro-structure is updated by the gradient-free Proportional Topology Optimization (PTO) algorithm to utilize the computational efficiency of PTO. The micro-structure is still updated by the common gradient-based algorithm, namely Optimality Criteria (OC). Three benchmark numerical examples are investigated, demonstrating the feasibility and efficiency of the proposed hybrid approach.","PeriodicalId":239329,"journal":{"name":"Vietnam Journal of Mechanics","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129171778","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 : 2022-07-30DOI: 10.15625/0866-7136/17027
T. T. Hà, Hoang Hong Son, N. H. Phong
This study promotes a new algorithm for estimating the water pollution propagation with the primary goal of providing more reliable and high quality estimates to decision makers. To date, the widely used variational method suffers from the large computational burden which limits its application in practice. Moreover, this method, considering the initial state as a control variable, is very sensitive in specifying initial error, especially for unstable dynamical systems. The adaptive filter (AF), proposed in this paper, is aimed at overcoming these two drawbacks in the variational method: by its nature, the AF is sequential (no large batch assimilation window used) and stable even for unstable dynamics, with the gain parameters as control variables. The AF, developed in this paper, is an adaptive version of the Singular Evolutive Interpolated Kalman Filter (SEIKF). One of the new versions of this AF is that it uses a time-varying structure of the gain of SEIKF. To deal with the uncertainty of the system parameters and of the noise covariance, the proposed adaptive SEIKF (ASEIKF) makes use of the covariance of reduced rank iterated during assimilation process and of some pertinent gain parameters tuned adaptively to yield the minimum prediction error for the system output. The computational burden in implementation of the ASEIKF is reduced drastically due to applying the optimization tool known as a simultaneous perturbation stochastic approximation algorithm, which requires only two integrations of the numerical model. No iterative loop is required at each assimilation instant as usually happens with the standard gradient descent optimization algorithms. Data assimilation experiment, carried out by the SEIKF and ASEIKF, is implemented for the Thanh Nhan Lake in Hanoi and the performance comparison between the ASEIKF and SEIKF is given to show the high effectiveness of the proposed ASEIKF.
{"title":"Adaptive Singular Evolutive Interpolated Kalman filter and its application to data assimilation in 2D Water pollution model","authors":"T. T. Hà, Hoang Hong Son, N. H. Phong","doi":"10.15625/0866-7136/17027","DOIUrl":"https://doi.org/10.15625/0866-7136/17027","url":null,"abstract":"This study promotes a new algorithm for estimating the water pollution propagation with the primary goal of providing more reliable and high quality estimates to decision makers. To date, the widely used variational method suffers from the large computational burden which limits its application in practice. Moreover, this method, considering the initial state as a control variable, is very sensitive in specifying initial error, especially for unstable dynamical systems. The adaptive filter (AF), proposed in this paper, is aimed at overcoming these two drawbacks in the variational method: by its nature, the AF is sequential (no large batch assimilation window used) and stable even for unstable dynamics, with the gain parameters as control variables. The AF, developed in this paper, is an adaptive version of the Singular Evolutive Interpolated Kalman Filter (SEIKF). One of the new versions of this AF is that it uses a time-varying structure of the gain of SEIKF. To deal with the uncertainty of the system parameters and of the noise covariance, the proposed adaptive SEIKF (ASEIKF) makes use of the covariance of reduced rank iterated during assimilation process and of some pertinent gain parameters tuned adaptively to yield the minimum prediction error for the system output. The computational burden in implementation of the ASEIKF is reduced drastically due to applying the optimization tool known as a simultaneous perturbation stochastic approximation algorithm, which requires only two integrations of the numerical model. No iterative loop is required at each assimilation instant as usually happens with the standard gradient descent optimization algorithms. Data assimilation experiment, carried out by the SEIKF and ASEIKF, is implemented for the Thanh Nhan Lake in Hanoi and the performance comparison between the ASEIKF and SEIKF is given to show the high effectiveness of the proposed ASEIKF.","PeriodicalId":239329,"journal":{"name":"Vietnam Journal of Mechanics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114886784","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 : 2022-07-16DOI: 10.15625/0866-7136/17054
V. Senthilkumar
The present investigation analyses the critical buckling studies of triple-walled carbon nanotube using the Euler─Bernoulli model. The present study deals with three different boundary conditions, namely, simply-simply, clamped-clamped, and clamped-simply supported carbon nanotube. Using Bubnov─Galerkin and Petrov─Galerkin methods, the continuum model estimates the critical buckling load. The main advantage of these two approximate methods is to obtain a quick and valid result. The first and second Euler critical buckling loads decrease with the increase of length to outer diameter ratio for boundary conditions like simply-simply, clamped-clamped, and clamped-simply supported. Interestingly, the increase in the length to outer diameter ratio results in the rise in third Euler critical buckling for all three different boundary conditions. These two approximate methods provide reliable buckling load estimation using suitable polynomials.
{"title":"Some approximate buckling solutions of triple-walled carbon nanotube","authors":"V. Senthilkumar","doi":"10.15625/0866-7136/17054","DOIUrl":"https://doi.org/10.15625/0866-7136/17054","url":null,"abstract":"The present investigation analyses the critical buckling studies of triple-walled carbon nanotube using the Euler─Bernoulli model. The present study deals with three different boundary conditions, namely, simply-simply, clamped-clamped, and clamped-simply supported carbon nanotube. Using Bubnov─Galerkin and Petrov─Galerkin methods, the continuum model estimates the critical buckling load. The main advantage of these two approximate methods is to obtain a quick and valid result. The first and second Euler critical buckling loads decrease with the increase of length to outer diameter ratio for boundary conditions like simply-simply, clamped-clamped, and clamped-simply supported. Interestingly, the increase in the length to outer diameter ratio results in the rise in third Euler critical buckling for all three different boundary conditions. These two approximate methods provide reliable buckling load estimation using suitable polynomials.","PeriodicalId":239329,"journal":{"name":"Vietnam Journal of Mechanics","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134226509","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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