A dynamic analysis approcach to investigate the state of load distribution among contact bearings of double circular are belical gears is proposed and a computer program is developed for calculating the factor of iced...A dynamic analysis approcach to investigate the state of load distribution among contact bearings of double circular are belical gears is proposed and a computer program is developed for calculating the factor of iced distribution based on the theory of W-N gears. The changing situations of load distribution among contact bearings of the gears influenced by main issues are analyzed by a series of parametric studies.展开更多
The non-linear dynamic behaviors of thermoelastic circular plate with varying thickness subjected to radially uniformly distributed follower forces are considered. Two coupled non-linear differential equations of moti...The non-linear dynamic behaviors of thermoelastic circular plate with varying thickness subjected to radially uniformly distributed follower forces are considered. Two coupled non-linear differential equations of motion for this problem are derived in terms of the transverse deflection and radial displacement component of the mid-plane of the plate. Using the Kantorovich averaging method, the differential equation of mode shape of the plate is derived, and the eigenvalue problem is solved by using shooting method. The eigencurves for frequencies and critical loads of the circular plate with unmovable simply supported edge and clamped edge are obtained. The effects of the variation of thickness and temperature on the frequencies and critical loads of the thermoelastic circular plate subjected to radially uniformly distributed follower forces are then discussed.展开更多
Using the boundary integral equation method, the problem of an external circular crack in a three_dimensional infinite elastic body under asymmetric loadings is investigated. The two_dimensional singular boundary inte...Using the boundary integral equation method, the problem of an external circular crack in a three_dimensional infinite elastic body under asymmetric loadings is investigated. The two_dimensional singular boundary integral equations of the problem were reduced to a system of Abel integral equations by means of Fourier series and hypergeometric functions. The exact solutions of stress intensity factors are obtained for the problem of an external circular crack under asymmetric loadings, which are even more universal than the results obtained by the use of Hankel transform method. The results demonstrate that the boundary integral equation method has great potential as a new analytic method.展开更多
In this paper, an experimental study for an eccentrically loaded circular footing, resting on a geogridreinforced sand bed, is performed. To achieve this aim, the steel model footing of 120 mm in diameterand sand in r...In this paper, an experimental study for an eccentrically loaded circular footing, resting on a geogridreinforced sand bed, is performed. To achieve this aim, the steel model footing of 120 mm in diameterand sand in relative density of 60% are used. Also, the effects of depth of first and second geogrid layersand number of reinforcement layers （1e4） on the settlement-load response and tilt of footing undervarious load eccentricities （0 cm, 0.75 cm, 1.5 cm, 2.25 cm and 3 cm） are investigated. Test results indicatethat ultimate bearing capacity increases in comparison with unreinforced condition. It is observed thatwhen the reinforcements are placed in the optimum embedment depth （u/D ？0.42 and h/D ？0.42）, thebearing capacity ratio （BCR） increases with increasing load eccentricity to the core boundary of footing,and that with further increase of load eccentricity, the BCR decreases. Besides, the tilt of footing increaseslinearly with increasing settlement. Finally, by reinforcing the sand bed, the tilt of footing decreases at 2layers of reinforcement and then increases by increasing the number of reinforcement layers.展开更多
The differential equations of the axisymmetric large amplitude free vibration for circular sandwich plates under static load are derived, and a set of nonlinearly coupled algebraic and differential eigenvalue equation...The differential equations of the axisymmetric large amplitude free vibration for circular sandwich plates under static load are derived, and a set of nonlinearly coupled algebraic and differential eigenvalue equations of the problem are formulated following an assumed time mode approach suggested. The analytic solutions are presented and a relation for amplitude frequency-load of the plates with edge clamped is derived by modified iteration method. The effects of static load on vibrations of plates are investigated.展开更多
The foundations of some ocean engineering structures are built to withstand not only the vertical gravity load V, but also the horizontal load H induced by sea waves and current. The horizontal load includes the conce...The foundations of some ocean engineering structures are built to withstand not only the vertical gravity load V, but also the horizontal load H induced by sea waves and current. The horizontal load includes the concentrated force load, the moment load M, and the torque load T termed also as combined loading. It is of academic and engineering significance to study the deformation law of submarine seabed due to combined loading. On the basis of the three-dimensional elastic mechanics solution of circular foundation, numerical methods are used to analyze the deformation law of submarine soil under circular foundation with six degrees of freedom. The finite element analysis results give the elastic deformation law of soil in three dimensional spaces, modify the theoretical elasticity solution, and presents nonlinear soil deformation mechanism under the circular foundation with six degrees of freedom.展开更多
The rotating circular plate is widely used in mechanical engineering, meanwhile the plates are often in the electromagnetic field in modern industry with complex loads. In order to study the resonance of a rotating ci...The rotating circular plate is widely used in mechanical engineering, meanwhile the plates are often in the electromagnetic field in modern industry with complex loads. In order to study the resonance of a rotating circular plate under static loads in magnetic field, the nonlinear vibration equation about the spinning circular plate is derived according to Hamilton principle. The algebraic expression of the initial deflection and the magneto elastic forced disturbance differential equation are obtained through the application of Galerkin integral method. By mean of modified Multiple scale method, the strongly nonlinear amplitude-frequency response equation in steady state is established. The amplitude frequency characteristic curve and the relationship curve of amplitude changing with the static loads and the excitation force of the plate are obtained according to the numerical calculation. The influence of magnetic induction intensity, the speed of rotation and the static loads on the amplitude and the nonlinear characteristics of the spinning plate are analyzed. The proposed research provides the theory reference for the research of nonlinear resonance of rotating plates in engineering.展开更多
The nonlinear vibration fundamental equation of circular sandwich plate under uniformed load and circumjacent load and the loosely clamped boundary condi- tion were established by von Karman plate theory, and then acc...The nonlinear vibration fundamental equation of circular sandwich plate under uniformed load and circumjacent load and the loosely clamped boundary condi- tion were established by von Karman plate theory, and then accordingly exact solution of static load and its numerical results were given. Based on time mode hypothesis and the variational method, the control equation of the space mode was derived, and then the amplitude frequency-load character relation of circular sandwich plate was obtained by the modified iteration method. Consequently the rule of the effect of the two kinds of load on the vibration character of the circular sandwich plate was investigated. When circumjacent load makes the lowest natural frequency zero, critical load is obtained.展开更多
Using the boundary integral equation method, the problem of an external circular crack in a three-dimensional infinite elastic body under asymmetric loadings is investigated. The two-dimensional singular boundary inte...Using the boundary integral equation method, the problem of an external circular crack in a three-dimensional infinite elastic body under asymmetric loadings is investigated. The two-dimensional singular boundary integral equations of the problem were reduced to a system of Abel integral equations by means of Fourier series and hypergeometric functions. The exact solutions of stress intensity factors ore obtained for the problem of an external circular crack under asymmetric loadings, which are even more universal than the results obtained by the use of Hankel transform method. The results demonstrate that the boundary integral equation method has great potential as a new analytic method.展开更多
Based upon the fundamental equations of three dimensional elasticity, the state equation for axisymmetric bending of laminated transversely isotropic circular plate is established and the concentrated force on plate s...Based upon the fundamental equations of three dimensional elasticity, the state equation for axisymmetric bending of laminated transversely isotropic circular plate is established and the concentrated force on plate surface is expanded into Fourier_Bessel's series, therefore, an analytical solution for the problem is presented. Every fundamental equation of three dimensional elasticity can be exactly satisfied by the solution and all the independent elastic constants can be taken into account fully, furthermore, the continuity conditions between plies can also be satisfied.展开更多
By using the modified iteration method of large deflection theory of plates with variable thichness[1], we solve the problem of circular plates with variable thickness subjected to combined loads under the boundary co...By using the modified iteration method of large deflection theory of plates with variable thichness[1], we solve the problem of circular plates with variable thickness subjected to combined loads under the boundary conditions of the clamped edges and get comparatively more accurate second-order approximate analytical solution. If the results of this paper are degraded into the special cases, the results coinciding with those of papers [1,2] can be obtained. In this paper, the characteristic curves are plotted and some comparisons are made. The results of this paper are satisfactory.展开更多
Based on theory of mechanical dynamics, meshing characteristic as well as thedynamic model of double circular arc helical gearing, an analysis approach and a computer programhave been developed for studying the state ...Based on theory of mechanical dynamics, meshing characteristic as well as thedynamic model of double circular arc helical gearing, an analysis approach and a computer programhave been developed for studying the state of dynamic load and factor of dynamic load of thegearing, the changing situation of dynamic load and dynamic load factor vs some affecting factorssuch as gear width, helix angle and accuracy grade etc are investigated. A series of conclusions areobtained: ①With the increasing in the values of gear width, the dynamic load factor appears slowdecreasing tendency in most region of gear width. ②When the accuracy grades of the gearing areimproved, the values of dynamic load factor decrease. ③The value of dynamic load factor appears adecreasing tendency with the increasing of value of helix angle at the same ratio of criticalrotational speed.展开更多
In this paper, we derive the analytical solutions in a three-dimensional anisotropic magnetoelectroelastic bimaterial space subject to uniform extended dislocations and tractions within a horizontal circular area. By ...In this paper, we derive the analytical solutions in a three-dimensional anisotropic magnetoelectroelastic bimaterial space subject to uniform extended dislocations and tractions within a horizontal circular area. By virtue of the Stroh formalism and Fourier transformation, the final expression of solutions in the physical domain contains only line integrals over [0, 2π] rather than infinite integrals. As the reduced cases, the half-space and homogeneous full-space solutions can be directly derived from the present solutions. Also, in terms of material domains, the present solutions can be reduced to the piezoelectric, piezomagnetic, purely elastic materials with different symmetries of material prop- erty. To carry out numerical calculations, Gauss quadrature is adopted. In the numerical examples, the effect of different loading locations on the response at the interface is analyzed. It is shown that, when the magnetic traction or electric dislocation is applied, the physical quantities on the interface may not decrease monotonically as the loading area moves away from the interface. The distributions of different in-plane physical quantities on the upper and lower interfaces under various extended horizontal loadings are compared and the differences are discussed. The work presented in this paper can serve as benchmarks for future numerical studies in related research fields.展开更多
A series of physical tests are conducted to examine the characteristics of the wave loading exerted on circular-front breakwaters by regular waves. It is found that the wave trough instead of wave crest plays a major ...A series of physical tests are conducted to examine the characteristics of the wave loading exerted on circular-front breakwaters by regular waves. It is found that the wave trough instead of wave crest plays a major role in the failure of submerged circular caissons due to seaward sliding. The difference in the behavior of seaward and shoreward horizontal wave forces is explained based on the variations of dynamic pressure with wave parameters. A wave load model is proposed based on a modified first-order solution for the dynamic pressure on submerged circular-front caissons under a wave trough. This wave loading model is very useful for engineering design. Further studies are needed to include model uncertainties in the reliability assessment of the breakwater.展开更多
This paper is concerned with the in-plane elastic stability of arches subjected to a radial concentrated load. The equilibrium equation for pin-ended circular arches is established by using energy method, and it is pr...This paper is concerned with the in-plane elastic stability of arches subjected to a radial concentrated load. The equilibrium equation for pin-ended circular arches is established by using energy method, and it is proved that the axial force is nearly a constant along the circumference of the circular arches. Based on force method, the equation for the primary eigen function is derived and solved, and the approximate analytical solution of critical instability load is obtained. Numerical examples are given and discussed.展开更多
This work aims to look for a simplifying surface that can represent the effect of the dual wheels on the variation of the stress and deformation state prevailing during the passage of traffic loads. This was facilitat...This work aims to look for a simplifying surface that can represent the effect of the dual wheels on the variation of the stress and deformation state prevailing during the passage of traffic loads. This was facilitated by the results of Thiam (2016) [4] obtained on the distribution of the vertical contact stress in the space described by the dual wheels. The analysis of the results of this study, on all the loading circles considered, shows that the radius loading circle equal to 0.181 m makes it possible to most probably represent the effect of the dual wheels. With this new surface, the effect of the dual wheels can be determined in 2D. The choice of this load is confirmed by a study in case of overload. Thus, the single axle with dual wheels is represented by a simplified diagram equipped on each side by a disk of radius 0.181 m. These results are obtained using a numerical simulation under Cast3M with a gravelly lateritic pavement.展开更多
文摘A dynamic analysis approcach to investigate the state of load distribution among contact bearings of double circular are belical gears is proposed and a computer program is developed for calculating the factor of iced distribution based on the theory of W-N gears. The changing situations of load distribution among contact bearings of the gears influenced by main issues are analyzed by a series of parametric studies.
基金Natural Science Research Project of Education Department of Shaanxi Province,China(No.08JK394).
文摘The non-linear dynamic behaviors of thermoelastic circular plate with varying thickness subjected to radially uniformly distributed follower forces are considered. Two coupled non-linear differential equations of motion for this problem are derived in terms of the transverse deflection and radial displacement component of the mid-plane of the plate. Using the Kantorovich averaging method, the differential equation of mode shape of the plate is derived, and the eigenvalue problem is solved by using shooting method. The eigencurves for frequencies and critical loads of the circular plate with unmovable simply supported edge and clamped edge are obtained. The effects of the variation of thickness and temperature on the frequencies and critical loads of the thermoelastic circular plate subjected to radially uniformly distributed follower forces are then discussed.
文摘Using the boundary integral equation method, the problem of an external circular crack in a three_dimensional infinite elastic body under asymmetric loadings is investigated. The two_dimensional singular boundary integral equations of the problem were reduced to a system of Abel integral equations by means of Fourier series and hypergeometric functions. The exact solutions of stress intensity factors are obtained for the problem of an external circular crack under asymmetric loadings, which are even more universal than the results obtained by the use of Hankel transform method. The results demonstrate that the boundary integral equation method has great potential as a new analytic method.
文摘In this paper, an experimental study for an eccentrically loaded circular footing, resting on a geogridreinforced sand bed, is performed. To achieve this aim, the steel model footing of 120 mm in diameterand sand in relative density of 60% are used. Also, the effects of depth of first and second geogrid layersand number of reinforcement layers （1e4） on the settlement-load response and tilt of footing undervarious load eccentricities （0 cm, 0.75 cm, 1.5 cm, 2.25 cm and 3 cm） are investigated. Test results indicatethat ultimate bearing capacity increases in comparison with unreinforced condition. It is observed thatwhen the reinforcements are placed in the optimum embedment depth （u/D ？0.42 and h/D ？0.42）, thebearing capacity ratio （BCR） increases with increasing load eccentricity to the core boundary of footing,and that with further increase of load eccentricity, the BCR decreases. Besides, the tilt of footing increaseslinearly with increasing settlement. Finally, by reinforcing the sand bed, the tilt of footing decreases at 2layers of reinforcement and then increases by increasing the number of reinforcement layers.
文摘The differential equations of the axisymmetric large amplitude free vibration for circular sandwich plates under static load are derived, and a set of nonlinearly coupled algebraic and differential eigenvalue equations of the problem are formulated following an assumed time mode approach suggested. The analytic solutions are presented and a relation for amplitude frequency-load of the plates with edge clamped is derived by modified iteration method. The effects of static load on vibrations of plates are investigated.
基金The financial support for this study is through the grants 50909050 from the National Natural Science Foundation of ChinaZR2009FQ004 from the Natural Science Foundation of Shandong Province
文摘The foundations of some ocean engineering structures are built to withstand not only the vertical gravity load V, but also the horizontal load H induced by sea waves and current. The horizontal load includes the concentrated force load, the moment load M, and the torque load T termed also as combined loading. It is of academic and engineering significance to study the deformation law of submarine seabed due to combined loading. On the basis of the three-dimensional elastic mechanics solution of circular foundation, numerical methods are used to analyze the deformation law of submarine soil under circular foundation with six degrees of freedom. The finite element analysis results give the elastic deformation law of soil in three dimensional spaces, modify the theoretical elasticity solution, and presents nonlinear soil deformation mechanism under the circular foundation with six degrees of freedom.
基金Supported by National Natural Science Foundation of China(Grant No11472239)Hebei Provincial Natural Science Foundation of China(Grant No.A2015203023)Key Project of Science and Technology Research of Higher Education of Hebei Province of China(Grant No.ZD20131055)
文摘The rotating circular plate is widely used in mechanical engineering, meanwhile the plates are often in the electromagnetic field in modern industry with complex loads. In order to study the resonance of a rotating circular plate under static loads in magnetic field, the nonlinear vibration equation about the spinning circular plate is derived according to Hamilton principle. The algebraic expression of the initial deflection and the magneto elastic forced disturbance differential equation are obtained through the application of Galerkin integral method. By mean of modified Multiple scale method, the strongly nonlinear amplitude-frequency response equation in steady state is established. The amplitude frequency characteristic curve and the relationship curve of amplitude changing with the static loads and the excitation force of the plate are obtained according to the numerical calculation. The influence of magnetic induction intensity, the speed of rotation and the static loads on the amplitude and the nonlinear characteristics of the spinning plate are analyzed. The proposed research provides the theory reference for the research of nonlinear resonance of rotating plates in engineering.
文摘The nonlinear vibration fundamental equation of circular sandwich plate under uniformed load and circumjacent load and the loosely clamped boundary condi- tion were established by von Karman plate theory, and then accordingly exact solution of static load and its numerical results were given. Based on time mode hypothesis and the variational method, the control equation of the space mode was derived, and then the amplitude frequency-load character relation of circular sandwich plate was obtained by the modified iteration method. Consequently the rule of the effect of the two kinds of load on the vibration character of the circular sandwich plate was investigated. When circumjacent load makes the lowest natural frequency zero, critical load is obtained.
基金国家自然科学基金，West Foundation of Ministry Education of China
文摘Using the boundary integral equation method, the problem of an external circular crack in a three-dimensional infinite elastic body under asymmetric loadings is investigated. The two-dimensional singular boundary integral equations of the problem were reduced to a system of Abel integral equations by means of Fourier series and hypergeometric functions. The exact solutions of stress intensity factors ore obtained for the problem of an external circular crack under asymmetric loadings, which are even more universal than the results obtained by the use of Hankel transform method. The results demonstrate that the boundary integral equation method has great potential as a new analytic method.
文摘Based upon the fundamental equations of three dimensional elasticity, the state equation for axisymmetric bending of laminated transversely isotropic circular plate is established and the concentrated force on plate surface is expanded into Fourier_Bessel's series, therefore, an analytical solution for the problem is presented. Every fundamental equation of three dimensional elasticity can be exactly satisfied by the solution and all the independent elastic constants can be taken into account fully, furthermore, the continuity conditions between plies can also be satisfied.
文摘By using the modified iteration method of large deflection theory of plates with variable thichness[1], we solve the problem of circular plates with variable thickness subjected to combined loads under the boundary conditions of the clamped edges and get comparatively more accurate second-order approximate analytical solution. If the results of this paper are degraded into the special cases, the results coinciding with those of papers [1,2] can be obtained. In this paper, the characteristic curves are plotted and some comparisons are made. The results of this paper are satisfactory.
基金This project is supported by Science and Technology Developing Foundation of Tianjin Higher Education (No.20030703).
文摘Based on theory of mechanical dynamics, meshing characteristic as well as thedynamic model of double circular arc helical gearing, an analysis approach and a computer programhave been developed for studying the state of dynamic load and factor of dynamic load of thegearing, the changing situation of dynamic load and dynamic load factor vs some affecting factorssuch as gear width, helix angle and accuracy grade etc are investigated. A series of conclusions areobtained: ①With the increasing in the values of gear width, the dynamic load factor appears slowdecreasing tendency in most region of gear width. ②When the accuracy grades of the gearing areimproved, the values of dynamic load factor decrease. ③The value of dynamic load factor appears adecreasing tendency with the increasing of value of helix angle at the same ratio of criticalrotational speed.
基金supported by the National Natural Science Foundation of China (10772024)
文摘In this paper, we derive the analytical solutions in a three-dimensional anisotropic magnetoelectroelastic bimaterial space subject to uniform extended dislocations and tractions within a horizontal circular area. By virtue of the Stroh formalism and Fourier transformation, the final expression of solutions in the physical domain contains only line integrals over [0, 2π] rather than infinite integrals. As the reduced cases, the half-space and homogeneous full-space solutions can be directly derived from the present solutions. Also, in terms of material domains, the present solutions can be reduced to the piezoelectric, piezomagnetic, purely elastic materials with different symmetries of material prop- erty. To carry out numerical calculations, Gauss quadrature is adopted. In the numerical examples, the effect of different loading locations on the response at the interface is analyzed. It is shown that, when the magnetic traction or electric dislocation is applied, the physical quantities on the interface may not decrease monotonically as the loading area moves away from the interface. The distributions of different in-plane physical quantities on the upper and lower interfaces under various extended horizontal loadings are compared and the differences are discussed. The work presented in this paper can serve as benchmarks for future numerical studies in related research fields.
基金financially supported by the Open Fund of the State Key Laboratory of Hydraulic Engineering Simulation and Safety from Tianjin University(Gtant No.HESS-1310)the Natural Science Foundation of Tianjin,China(Gtant No.14JCYBJC22100)+5 种基金the National Natural Science Foundation of China(Gtant No.51509178)supported by the State Scholarship Fund of China Scholarship Council(Gtant No.201308120008)supported by the Physical Oceanography Program of National Science Foundation(Grant No.1436642)the Maine Sea Grant and NOAA for Grant No.NA10OAR4170072part of EFRaCC project funded by the British Council under its Global Innovation Initiativethe open fund research at the State Key Laboratory of Hydraulics and Mountain River at Sichuan University(Grant No.SKHL1311)
文摘A series of physical tests are conducted to examine the characteristics of the wave loading exerted on circular-front breakwaters by regular waves. It is found that the wave trough instead of wave crest plays a major role in the failure of submerged circular caissons due to seaward sliding. The difference in the behavior of seaward and shoreward horizontal wave forces is explained based on the variations of dynamic pressure with wave parameters. A wave load model is proposed based on a modified first-order solution for the dynamic pressure on submerged circular-front caissons under a wave trough. This wave loading model is very useful for engineering design. Further studies are needed to include model uncertainties in the reliability assessment of the breakwater.
文摘This paper is concerned with the in-plane elastic stability of arches subjected to a radial concentrated load. The equilibrium equation for pin-ended circular arches is established by using energy method, and it is proved that the axial force is nearly a constant along the circumference of the circular arches. Based on force method, the equation for the primary eigen function is derived and solved, and the approximate analytical solution of critical instability load is obtained. Numerical examples are given and discussed.
文摘This work aims to look for a simplifying surface that can represent the effect of the dual wheels on the variation of the stress and deformation state prevailing during the passage of traffic loads. This was facilitated by the results of Thiam (2016) [4] obtained on the distribution of the vertical contact stress in the space described by the dual wheels. The analysis of the results of this study, on all the loading circles considered, shows that the radius loading circle equal to 0.181 m makes it possible to most probably represent the effect of the dual wheels. With this new surface, the effect of the dual wheels can be determined in 2D. The choice of this load is confirmed by a study in case of overload. Thus, the single axle with dual wheels is represented by a simplified diagram equipped on each side by a disk of radius 0.181 m. These results are obtained using a numerical simulation under Cast3M with a gravelly lateritic pavement.
