Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved ...Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method(ICCM).The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate.The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method.From the continuity condition of the vibration displacement function at the cutout,the transition matrix between the two coordinate systems is constructed,and the mass and stiffness matrices are completely obtained.As a result,the calculation is simplified and the computational efficiency of the solution is improved.In this paper,numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods,and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics.展开更多
Moving-load induced vibrations can,in certain instances,exceed those caused by equivalent static loads,especially at the critical velocity of moving loads.Suppressing these vibrations is of critical practical importan...Moving-load induced vibrations can,in certain instances,exceed those caused by equivalent static loads,especially at the critical velocity of moving loads.Suppressing these vibrations is of critical practical importance in various engineering fields,including the design of precision robotics and advanced aerospace structures where components are subject to moving loads.In this paper,an inertial nonlinear energy sink(NES)is used for the first time to reduce the vibration response of graphene platelet(GPL)-reinforced nanocomposite beams with elastic boundaries under moving loads.Based on the von Kármán nonlinear theory,the governing equations of the beam-NES system are derived using the Lagrange equation.The Newmark-Newton method,in conjunction with the Heaviside step function,is used to obtain the nonlinear responses of the beam under moving loads.The effects of the boundary spring stiffness,the GPL parameters,as well as the velocity and frequency of the moving loads on the beam response and the performance of the NES are thoroughly studied.The results of this work provide insights into applying NESs to suppress the nonlinear vibrations induced by moving loads in composite structures with elastic boundaries.展开更多
In this paper,an efficient,convenient and explicit method based on the Haar wavelet discretization ap-proach for analyzing the free vibration of the coupled laminated composite elliptical-cylindrical-elliptical shells...In this paper,an efficient,convenient and explicit method based on the Haar wavelet discretization ap-proach for analyzing the free vibration of the coupled laminated composite elliptical-cylindrical-elliptical shells(ECESs)with elastic boundary conditions is presented.Two elliptical double curved shells are cou-pled on both end of cylindrical shell.Based on the first-order shear deformation theory the equations of motion for ECES are derived by means of Hamilton’s principle.The separation of variables is first per-formed;i.e.displacement components and rotations of any point of the ECES are expanded to the Haar wavelet series in the meridian direction and Fourier series in circumferential direction.The constants appearing from the integrating process are determined by boundary conditions,and thus the partial dif-ferential equations are transformed into algebraic equations.By solving the characteristic equation,the natural frequencies and mode shapes of coupled laminated composite ECES are obtained.The present re-sults have been compared with those of the published literature.The comparison results show that this method has high accuracy,high reliability and also a higher convergence rate in attaining the frequencies of the coupled laminated composite ECESs.Then,the effects of the main parameters such as material properties,geometrical parameters,and various boundary conditions,on the vibrational behavior of the coupled ECESs,are investigated.Finally,new free vibration analysis results of the coupled laminated com-posited ECES,which can be used as benchmark data for researchers in this field,are reported through the parameter study.展开更多
Free vibration of elastically constrained rectangular single-layered M0S_(2)is investigated by using a nonlocal Kirchhoff plate model with an initial stress.The variationally consistent elastically constrained boundar...Free vibration of elastically constrained rectangular single-layered M0S_(2)is investigated by using a nonlocal Kirchhoff plate model with an initial stress.The variationally consistent elastically constrained boundary conditions are obtained by using the weighted residual method,while the governing equations of the nonlocal Kirchhoff plate model are known.A modified Fourier series method is applied to study the vibrational behaviors of elastically constrained nonlocal Kirchhoff plate models.The convergence and reliability of the modified Fourier series method is verified via comparison with the finite element method.A comprehensive parametric study is performed to show the influences of the boundary elastic constant,nonlocal parameter and initial stress on the vibrational behaviors of single-layered M0S2.The results should be good for the design of nanoresonators.展开更多
Investigation on vibration of laminated composite beam(LCB)is an important issue owing to its wide use as fundamental component.In the present work,we study the free vibration of arbitrarily LCB with generalized elast...Investigation on vibration of laminated composite beam(LCB)is an important issue owing to its wide use as fundamental component.In the present work,we study the free vibration of arbitrarily LCB with generalized elastic boundary condition(BC)by using Haar wavelet discretization method(HWDM).Timoshenko beam theory is utilized to model the free vibration of LCB.The LCB is first split into several segments,and then the displacement for each segment is obtained from the Haar wavelet series and their integral.Hamilton’s principle is applied to construct governing equations and the artificial spring boundary technique is adopted to obtain the general elastic boundary and continuity conditions at two ends of LCB.The vibration characteristics of beam with different fiber orientations and lamina numbers is investigated and its displacements are compared with those in previous works.Numerical results are shown graphically and demonstrate the validation of our method.展开更多
This work uses isogeometric analysis(IGA),which is based on nonlocal hypothesis and higher-order shear beam hypothesis,to investigate the static bending and free oscillation of a magneto-electro-elastic functionally g...This work uses isogeometric analysis(IGA),which is based on nonlocal hypothesis and higher-order shear beam hypothesis,to investigate the static bending and free oscillation of a magneto-electro-elastic functionally graded(MEE-FG)nanobeam subject to elastic boundary constraints(BCs).The magneto-electric boundary condition and the Maxwell equation are used to calculate the variation of electric and magnetic potentials along the thickness direction of the nanobeam.This study is innovative since it does not use the conventional boundary conditions.Rather,an elastic system of straight and torsion springs with controllable stiffness is used to support nanobeams’beginning and end positions,creating customizable BCs.The governing equations of motion of nanobeams are established by applying Hamilton’s principle and IGA is used to determine deflections and natural frequency values.Verification studies were performed to evaluate the convergence and accuracy of the proposed method.Aside from this,the impact of the input parameters on the static bending and free oscillation of the MEE-FG nanobeam is examined in detail.These findings could be valuable for analyzing and designing innovative structures constructed of functionally graded MEE materials.展开更多
基金support of this work by the National Natural Science Foundation of China(No.51405096)the Fundamental Research Funds for the Central Universities(HEUCF210710).
文摘Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method(ICCM).The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate.The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method.From the continuity condition of the vibration displacement function at the cutout,the transition matrix between the two coordinate systems is constructed,and the mass and stiffness matrices are completely obtained.As a result,the calculation is simplified and the computational efficiency of the solution is improved.In this paper,numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods,and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics.
基金Project supported by the National Natural Science Foundation of China(No.12472003)the Key Research Project of Zhejiang Market Supervision Administration(No.ZD2024013)the Technical Project of Research Institute of Highway Ministry of Transport of China(No.0225KF12SC1002)。
文摘Moving-load induced vibrations can,in certain instances,exceed those caused by equivalent static loads,especially at the critical velocity of moving loads.Suppressing these vibrations is of critical practical importance in various engineering fields,including the design of precision robotics and advanced aerospace structures where components are subject to moving loads.In this paper,an inertial nonlinear energy sink(NES)is used for the first time to reduce the vibration response of graphene platelet(GPL)-reinforced nanocomposite beams with elastic boundaries under moving loads.Based on the von Kármán nonlinear theory,the governing equations of the beam-NES system are derived using the Lagrange equation.The Newmark-Newton method,in conjunction with the Heaviside step function,is used to obtain the nonlinear responses of the beam under moving loads.The effects of the boundary spring stiffness,the GPL parameters,as well as the velocity and frequency of the moving loads on the beam response and the performance of the NES are thoroughly studied.The results of this work provide insights into applying NESs to suppress the nonlinear vibrations induced by moving loads in composite structures with elastic boundaries.
文摘In this paper,an efficient,convenient and explicit method based on the Haar wavelet discretization ap-proach for analyzing the free vibration of the coupled laminated composite elliptical-cylindrical-elliptical shells(ECESs)with elastic boundary conditions is presented.Two elliptical double curved shells are cou-pled on both end of cylindrical shell.Based on the first-order shear deformation theory the equations of motion for ECES are derived by means of Hamilton’s principle.The separation of variables is first per-formed;i.e.displacement components and rotations of any point of the ECES are expanded to the Haar wavelet series in the meridian direction and Fourier series in circumferential direction.The constants appearing from the integrating process are determined by boundary conditions,and thus the partial dif-ferential equations are transformed into algebraic equations.By solving the characteristic equation,the natural frequencies and mode shapes of coupled laminated composite ECES are obtained.The present re-sults have been compared with those of the published literature.The comparison results show that this method has high accuracy,high reliability and also a higher convergence rate in attaining the frequencies of the coupled laminated composite ECESs.Then,the effects of the main parameters such as material properties,geometrical parameters,and various boundary conditions,on the vibrational behavior of the coupled ECESs,are investigated.Finally,new free vibration analysis results of the coupled laminated com-posited ECES,which can be used as benchmark data for researchers in this field,are reported through the parameter study.
基金We gratefully acknowledge the support from the Natural Science Foundation of Chongqing(cstc2020jcyj-msxmX0037)State Key Laboratory of Mechanics and Control of Mechanical Structures(Nanjing University of Aeronautics and astronautics)under Grants MCMS-E-0120G01National Natural Science Foundation of China under Grants Nos.11925205 and 51921003,and the Fundamental Research Funds for the Central Universities of China.
文摘Free vibration of elastically constrained rectangular single-layered M0S_(2)is investigated by using a nonlocal Kirchhoff plate model with an initial stress.The variationally consistent elastically constrained boundary conditions are obtained by using the weighted residual method,while the governing equations of the nonlocal Kirchhoff plate model are known.A modified Fourier series method is applied to study the vibrational behaviors of elastically constrained nonlocal Kirchhoff plate models.The convergence and reliability of the modified Fourier series method is verified via comparison with the finite element method.A comprehensive parametric study is performed to show the influences of the boundary elastic constant,nonlocal parameter and initial stress on the vibrational behaviors of single-layered M0S2.The results should be good for the design of nanoresonators.
文摘Investigation on vibration of laminated composite beam(LCB)is an important issue owing to its wide use as fundamental component.In the present work,we study the free vibration of arbitrarily LCB with generalized elastic boundary condition(BC)by using Haar wavelet discretization method(HWDM).Timoshenko beam theory is utilized to model the free vibration of LCB.The LCB is first split into several segments,and then the displacement for each segment is obtained from the Haar wavelet series and their integral.Hamilton’s principle is applied to construct governing equations and the artificial spring boundary technique is adopted to obtain the general elastic boundary and continuity conditions at two ends of LCB.The vibration characteristics of beam with different fiber orientations and lamina numbers is investigated and its displacements are compared with those in previous works.Numerical results are shown graphically and demonstrate the validation of our method.
文摘This work uses isogeometric analysis(IGA),which is based on nonlocal hypothesis and higher-order shear beam hypothesis,to investigate the static bending and free oscillation of a magneto-electro-elastic functionally graded(MEE-FG)nanobeam subject to elastic boundary constraints(BCs).The magneto-electric boundary condition and the Maxwell equation are used to calculate the variation of electric and magnetic potentials along the thickness direction of the nanobeam.This study is innovative since it does not use the conventional boundary conditions.Rather,an elastic system of straight and torsion springs with controllable stiffness is used to support nanobeams’beginning and end positions,creating customizable BCs.The governing equations of motion of nanobeams are established by applying Hamilton’s principle and IGA is used to determine deflections and natural frequency values.Verification studies were performed to evaluate the convergence and accuracy of the proposed method.Aside from this,the impact of the input parameters on the static bending and free oscillation of the MEE-FG nanobeam is examined in detail.These findings could be valuable for analyzing and designing innovative structures constructed of functionally graded MEE materials.
