The theory of nonlinear stability for a truncated shallow conical shell with variable thickness under the action of uniform pressure was presented. The fundamental equations and boundary conditions were derived by mea...The theory of nonlinear stability for a truncated shallow conical shell with variable thickness under the action of uniform pressure was presented. The fundamental equations and boundary conditions were derived by means of calculus of variations. An analytic solution for the critical buckling pressure of the shell with a hyperbolically varying thickness is obtained by use of modified iteration method. The results of numerical calculations are presented in diagrams, which show the influence of geometrical and physical parameters on the buckling behavior.展开更多
Based on the variational equation of the nonlinear bending theory of doubledeck reticulated shallow shells, equations of large deflection and boundary conditions for a double-deck reticulated circular shallow spherica...Based on the variational equation of the nonlinear bending theory of doubledeck reticulated shallow shells, equations of large deflection and boundary conditions for a double-deck reticulated circular shallow spherical shell under a uniformly distributed pressure are derived by using coordinate transformation means and the principle of stationary complementary energy. The characteristic relationship and critical buckling pressure for the shell with two types of boundary conditions are obtained by taking the modified iteration method. Effects of geometrical parameters on the buckling behavior are also discussed.展开更多
Using the modified method of multiple scales, the nonlinear stability of a truncated shallow spherical shell of variable thickness with a nondeformable rigid body at the center under compound loads is investigated. Wh...Using the modified method of multiple scales, the nonlinear stability of a truncated shallow spherical shell of variable thickness with a nondeformable rigid body at the center under compound loads is investigated. When the geometrical parameter k is larger, the uniformly valid asymptotic solutions of this problem are obtained and the remainder terms are estimated.展开更多
In this paper, to begin with. the nonlinear differential equations of a truncaled shallow spherical shell with variable thickness under uniformal distributed load are linearized by step-by-step loading method. The lin...In this paper, to begin with. the nonlinear differential equations of a truncaled shallow spherical shell with variable thickness under uniformal distributed load are linearized by step-by-step loading method. The linear differential equations can be solved by spline collocanon method. Critical loads have been obtained accordingly.展开更多
Using a singular perturbation method, the nonlinear stability of a truncated shallow, spherical shell without a nondeformable rigid body at the center under linear distributed loads along the interior edge is investig...Using a singular perturbation method, the nonlinear stability of a truncated shallow, spherical shell without a nondeformable rigid body at the center under linear distributed loads along the interior edge is investigated in this paper. When the geometrical parameter k is large, the uniformly valid asymptotic solutions are obtained.展开更多
The problem of axisymmetric nonlinear vibration for shallow thin spherical and conical shells when temperature and strain fields are coupled is studied. Based on the large deflection theories of von Krmn and the theor...The problem of axisymmetric nonlinear vibration for shallow thin spherical and conical shells when temperature and strain fields are coupled is studied. Based on the large deflection theories of von Krmn and the theory of thermoelasticity, the whole governing equations and their simplified type are derived. The time-spatial variables are separated by Galerkin's technique, thus reducing the governing equations to a system of time-dependent nonlinear ordinary differential equation. By means of regular perturbation method and multiple-scales method, the first-order approximate analytical solution for characteristic relation of frequency vs amplitude parameters along with the decay rate of amplitude are obtained, and the effects of different geometric parameters and coupling factors as well as boundary conditions on thermoelastically coupled nonlinear vibration behaviors are discussed.展开更多
Based on the variation and harmonic equations and by taking the maximum amplitude of the shell center as the perturbation parameter, nonlinear vibration of thin shallow conic shells under combined action of peripheral...Based on the variation and harmonic equations and by taking the maximum amplitude of the shell center as the perturbation parameter, nonlinear vibration of thin shallow conic shells under combined action of peripheral moment and transverse loads was solved. The linear natural frequency can be got by the first_order approximation and the more accurate nonlinear frequency is got by the second_order approximation under the action of static loads. Meanwhile the third_order approximate analytic expression is given for describing the nonlinear relation between nature frequency and peripheral moment,transverse loads, amplitude, base angle under the small deformation. Within some range, the complex and regularity of the nonlinear relation can be directly observed from the numeric results.展开更多
The dynamic response study on thermo-magneto-elastic behavior of shallow conical shell in a time-dependent magnetic field is investigated, and the dynamic responses of displacement of shallow conical shell under mecha...The dynamic response study on thermo-magneto-elastic behavior of shallow conical shell in a time-dependent magnetic field is investigated, and the dynamic responses of displacement of shallow conical shell under mechanical loads, electromagnetic fields and temperature field coupling are analyzed. Based on Maxwell’s equations, heat conduction equation and nonlinear equations of classical plates and shells, the nonlinear dynamic response governing equations are derived. The electromagnetic field and temperature field equations are solved using variable separating technique, the nonlinear elastic field equations are solved by Galerkin method. The variation of temperature, magnetic field intensity and displacement with time under the coupling effect of the applied magnetic field and the surface uniform load were obtained. The influence of frequency of the applied magnetic field on the displacement wave forms is discussed.展开更多
A set of nonlinearly coupled algebraic and differential eigenvalue equations of nonlinear axisymmetric free vibration of orthotropic shallow thin spherical and conical shells are formulated following an assumed time-m...A set of nonlinearly coupled algebraic and differential eigenvalue equations of nonlinear axisymmetric free vibration of orthotropic shallow thin spherical and conical shells are formulated following an assumed time-mode approach suggested in this paper. Analytic solutions are presented and an asymptotic relation for the amplitude-frequency response of the shells is derived. The effects of geometrical and material parameters on vibrations of the shells are investigated.展开更多
In this paper, the axisymmetric nonlinear free vibration problems of cylindrically orthotropic shallow thin spherical and conical shells under uniformly distributed static loads are studied by using MWR and Lindstedt-...In this paper, the axisymmetric nonlinear free vibration problems of cylindrically orthotropic shallow thin spherical and conical shells under uniformly distributed static loads are studied by using MWR and Lindstedt-Poincare perturbation method, from which, the characteristic relation between frequency ratio and amplitude is obtained. The effects of static loads, geometric and material parameters on vibrational behavior of shells are also discussed.展开更多
文摘The theory of nonlinear stability for a truncated shallow conical shell with variable thickness under the action of uniform pressure was presented. The fundamental equations and boundary conditions were derived by means of calculus of variations. An analytic solution for the critical buckling pressure of the shell with a hyperbolically varying thickness is obtained by use of modified iteration method. The results of numerical calculations are presented in diagrams, which show the influence of geometrical and physical parameters on the buckling behavior.
基金Project supported by the National Natural Science Foundation of China (No. 19972024)the Key Laboratory of Disaster Forecast and Control in Engineering, Ministry of Education of Chinathe Key Laboratory of Diagnosis of Fault in Engineering Structures of Guangdong Province of China
文摘Based on the variational equation of the nonlinear bending theory of doubledeck reticulated shallow shells, equations of large deflection and boundary conditions for a double-deck reticulated circular shallow spherical shell under a uniformly distributed pressure are derived by using coordinate transformation means and the principle of stationary complementary energy. The characteristic relationship and critical buckling pressure for the shell with two types of boundary conditions are obtained by taking the modified iteration method. Effects of geometrical parameters on the buckling behavior are also discussed.
文摘Using the modified method of multiple scales, the nonlinear stability of a truncated shallow spherical shell of variable thickness with a nondeformable rigid body at the center under compound loads is investigated. When the geometrical parameter k is larger, the uniformly valid asymptotic solutions of this problem are obtained and the remainder terms are estimated.
文摘In this paper, to begin with. the nonlinear differential equations of a truncaled shallow spherical shell with variable thickness under uniformal distributed load are linearized by step-by-step loading method. The linear differential equations can be solved by spline collocanon method. Critical loads have been obtained accordingly.
文摘Using a singular perturbation method, the nonlinear stability of a truncated shallow, spherical shell without a nondeformable rigid body at the center under linear distributed loads along the interior edge is investigated in this paper. When the geometrical parameter k is large, the uniformly valid asymptotic solutions are obtained.
文摘The problem of axisymmetric nonlinear vibration for shallow thin spherical and conical shells when temperature and strain fields are coupled is studied. Based on the large deflection theories of von Krmn and the theory of thermoelasticity, the whole governing equations and their simplified type are derived. The time-spatial variables are separated by Galerkin's technique, thus reducing the governing equations to a system of time-dependent nonlinear ordinary differential equation. By means of regular perturbation method and multiple-scales method, the first-order approximate analytical solution for characteristic relation of frequency vs amplitude parameters along with the decay rate of amplitude are obtained, and the effects of different geometric parameters and coupling factors as well as boundary conditions on thermoelastically coupled nonlinear vibration behaviors are discussed.
文摘Based on the variation and harmonic equations and by taking the maximum amplitude of the shell center as the perturbation parameter, nonlinear vibration of thin shallow conic shells under combined action of peripheral moment and transverse loads was solved. The linear natural frequency can be got by the first_order approximation and the more accurate nonlinear frequency is got by the second_order approximation under the action of static loads. Meanwhile the third_order approximate analytic expression is given for describing the nonlinear relation between nature frequency and peripheral moment,transverse loads, amplitude, base angle under the small deformation. Within some range, the complex and regularity of the nonlinear relation can be directly observed from the numeric results.
文摘The dynamic response study on thermo-magneto-elastic behavior of shallow conical shell in a time-dependent magnetic field is investigated, and the dynamic responses of displacement of shallow conical shell under mechanical loads, electromagnetic fields and temperature field coupling are analyzed. Based on Maxwell’s equations, heat conduction equation and nonlinear equations of classical plates and shells, the nonlinear dynamic response governing equations are derived. The electromagnetic field and temperature field equations are solved using variable separating technique, the nonlinear elastic field equations are solved by Galerkin method. The variation of temperature, magnetic field intensity and displacement with time under the coupling effect of the applied magnetic field and the surface uniform load were obtained. The influence of frequency of the applied magnetic field on the displacement wave forms is discussed.
基金Project supported by the National Natural Science Foundation of China
文摘A set of nonlinearly coupled algebraic and differential eigenvalue equations of nonlinear axisymmetric free vibration of orthotropic shallow thin spherical and conical shells are formulated following an assumed time-mode approach suggested in this paper. Analytic solutions are presented and an asymptotic relation for the amplitude-frequency response of the shells is derived. The effects of geometrical and material parameters on vibrations of the shells are investigated.
文摘In this paper, the axisymmetric nonlinear free vibration problems of cylindrically orthotropic shallow thin spherical and conical shells under uniformly distributed static loads are studied by using MWR and Lindstedt-Poincare perturbation method, from which, the characteristic relation between frequency ratio and amplitude is obtained. The effects of static loads, geometric and material parameters on vibrational behavior of shells are also discussed.
