Based on the linear theories of thin cylindrical shells and viscoelastic materials, a governing equation describing vibration of a sandwich circular cylindrical shell with a viscoelastic core under harmonic excitation...Based on the linear theories of thin cylindrical shells and viscoelastic materials, a governing equation describing vibration of a sandwich circular cylindrical shell with a viscoelastic core under harmonic excitation is derived. The equation can be written as a matrix differential equation of the first order, and is obtained by considering the energy dissipation due to the shear deformation of the viscoelastic core layer and the interaction between all layers. A new matrix method for solving the governing equation is then presented With an extended homogeneous capacity precision integration approach. Having obtained these, vibration characteristics and damping effect of the sandwich cylindrical shell can be studied. The method differs from a recently published work as the state vector in the governing equation is composed of displacements and internal forces of the sandwich shell rather than displacements and their derivatives. So the present method can be applied to solve dynamic problems of the kind of sandwich shells with various boundary conditions and partially constrained layer damping. Numerical examples show that the proposed approach is effective and reliable compared with the existing methods.展开更多
It is impossible,mathematically, to use a time series which is regarded as a set of observational facts of a dynamicsystem to reconstruct the particular system.Physically, however, with a few assumptions put, a dynami...It is impossible,mathematically, to use a time series which is regarded as a set of observational facts of a dynamicsystem to reconstruct the particular system.Physically, however, with a few assumptions put, a dynamic system canbe rebuilt approximately by means of observational facts.This is the goal of the so called invariant quantity method(IQM),whose research and experiment are of potential significance to atmospheric sciences.展开更多
The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear...The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear deformation theory, only considering the shearing deformation of the viscoelastic layer, the integrated first order differential matrix equation of a passive constrained layer damping rotational shell is established by combining with the normal equilibrium equation of the viscoelastic layer.A highly precise transfer matrix method is developed by extended homogeneous capacity precision integration technology.The numerical results show that present method is accurate and effective.展开更多
Based on the classical theory of thin plate and Biot theory, a precise model of the transverse vibrations of a thin rectangular porous plate is proposed. The first order differential equations of the porous plate are ...Based on the classical theory of thin plate and Biot theory, a precise model of the transverse vibrations of a thin rectangular porous plate is proposed. The first order differential equations of the porous plate are derived in the frequency domain. By considering the coupling effect between the solid phase and the fluid phase and without any hypothesis for the fluid displacement, the model presented here is rigorous and close to the real materials. Owing to the use of extended homogeneous capacity precision integration method and precise element method, the model can be applied in higher frequency range than pure numerical methods. This model also easily adapts to various boundary conditions. Numerical results are given for two different porous plates under different excitations and boundary conditions.展开更多
Under the sign assumptions we investigate the global existence of solutions of the initial value problem x＇ =f（t, x, x＇）, x（0） = A, where the scalar function f（t, x,p） may be singular at x = A.
基金supported by the National Natural Science Foundation of China (No. 10662003)the Doctoral Fund of Ministry of Education of China (No. 20040787013)
文摘Based on the linear theories of thin cylindrical shells and viscoelastic materials, a governing equation describing vibration of a sandwich circular cylindrical shell with a viscoelastic core under harmonic excitation is derived. The equation can be written as a matrix differential equation of the first order, and is obtained by considering the energy dissipation due to the shear deformation of the viscoelastic core layer and the interaction between all layers. A new matrix method for solving the governing equation is then presented With an extended homogeneous capacity precision integration approach. Having obtained these, vibration characteristics and damping effect of the sandwich cylindrical shell can be studied. The method differs from a recently published work as the state vector in the governing equation is composed of displacements and internal forces of the sandwich shell rather than displacements and their derivatives. So the present method can be applied to solve dynamic problems of the kind of sandwich shells with various boundary conditions and partially constrained layer damping. Numerical examples show that the proposed approach is effective and reliable compared with the existing methods.
文摘It is impossible,mathematically, to use a time series which is regarded as a set of observational facts of a dynamicsystem to reconstruct the particular system.Physically, however, with a few assumptions put, a dynamic system canbe rebuilt approximately by means of observational facts.This is the goal of the so called invariant quantity method(IQM),whose research and experiment are of potential significance to atmospheric sciences.
基金supported by the National Natural Science Foundation of China (No.10662003)Educational Commission of Guangxi Province of China (No.200807MS109)
文摘The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear deformation theory, only considering the shearing deformation of the viscoelastic layer, the integrated first order differential matrix equation of a passive constrained layer damping rotational shell is established by combining with the normal equilibrium equation of the viscoelastic layer.A highly precise transfer matrix method is developed by extended homogeneous capacity precision integration technology.The numerical results show that present method is accurate and effective.
基金Project supported by the National Natural Science Foundation of China(nos.11162001,11502056 and 51665006)
文摘Based on the classical theory of thin plate and Biot theory, a precise model of the transverse vibrations of a thin rectangular porous plate is proposed. The first order differential equations of the porous plate are derived in the frequency domain. By considering the coupling effect between the solid phase and the fluid phase and without any hypothesis for the fluid displacement, the model presented here is rigorous and close to the real materials. Owing to the use of extended homogeneous capacity precision integration method and precise element method, the model can be applied in higher frequency range than pure numerical methods. This model also easily adapts to various boundary conditions. Numerical results are given for two different porous plates under different excitations and boundary conditions.
文摘Under the sign assumptions we investigate the global existence of solutions of the initial value problem x＇ =f（t, x, x＇）, x（0） = A, where the scalar function f（t, x,p） may be singular at x = A.
