Based on Reddy's theory of plates with higher order shear deformations and the Boltzmann superposition principles, the governing equations were established for dynamic stability of viscoelastic plates with finit...Based on Reddy's theory of plates with higher order shear deformations and the Boltzmann superposition principles, the governing equations were established for dynamic stability of viscoelastic plates with finite deformations taking account of shear effects. The Galerkin method was applied to simplify the set of equations. The numerical methods in nonlinear dynamics were used to solve the simplified system. It could be seen that there are plenty of dynamic properties for this kind of viscoelastic plates under transverse harmonic loads. The influences of the transverse shear deformations and material parameter on the dynamic behavior of nonlinear viscoelastic plates were investigated.展开更多
This paper deals with nonlinear free vibration of reticulated shallow spherical shells taking into account the effect of transverse shear deformation. The shell is formed by beam members placed in two orthogonal direc...This paper deals with nonlinear free vibration of reticulated shallow spherical shells taking into account the effect of transverse shear deformation. The shell is formed by beam members placed in two orthogonal directions. The nondimensional fundamental governing equations in terms of the deflection, rotational angle, and force function are presented, and the solution for the nonlinear free frequency is derived by using the asymptotic iteration method. The asymptotic solution can be used readily to perform the parameter analysis of such space structures with numerous geometrical and material parameters. Numerical examples are given to illustrate the characteristic amplitudefrequency relation and softening and hardening nonlinear behaviors as well as the effect of transverse shear on the linear and nonlinear frequencies of reticulated shells and plates.展开更多
Classical bending theories for beams and plates can not be used for short, stubby beams and thick plates since transverse shearing effect is excluded, and ordinary theories with multiple generalized displacements can ...Classical bending theories for beams and plates can not be used for short, stubby beams and thick plates since transverse shearing effect is excluded, and ordinary theories with multiple generalized displacements can not be used for long, slender beams and thin plates since the innate relation between rotation angle and deflection is ignored. These two types of theories are not consistent due to the contradiction of dependence and independence of the rotation angle. Based on several basic assumptions, a new type of theories which not only include the transverse shearing effect is presented, but also the relation between potation angle and deflection is obtained. Analytical solutions of several simple beams are given. It has been testified by numerical examples that the new theories can be used for either long, slender beams and thin plates or short, stubby beams and thick plates.展开更多
文摘Based on Reddy's theory of plates with higher order shear deformations and the Boltzmann superposition principles, the governing equations were established for dynamic stability of viscoelastic plates with finite deformations taking account of shear effects. The Galerkin method was applied to simplify the set of equations. The numerical methods in nonlinear dynamics were used to solve the simplified system. It could be seen that there are plenty of dynamic properties for this kind of viscoelastic plates under transverse harmonic loads. The influences of the transverse shear deformations and material parameter on the dynamic behavior of nonlinear viscoelastic plates were investigated.
文摘This paper deals with nonlinear free vibration of reticulated shallow spherical shells taking into account the effect of transverse shear deformation. The shell is formed by beam members placed in two orthogonal directions. The nondimensional fundamental governing equations in terms of the deflection, rotational angle, and force function are presented, and the solution for the nonlinear free frequency is derived by using the asymptotic iteration method. The asymptotic solution can be used readily to perform the parameter analysis of such space structures with numerous geometrical and material parameters. Numerical examples are given to illustrate the characteristic amplitudefrequency relation and softening and hardening nonlinear behaviors as well as the effect of transverse shear on the linear and nonlinear frequencies of reticulated shells and plates.
文摘Classical bending theories for beams and plates can not be used for short, stubby beams and thick plates since transverse shearing effect is excluded, and ordinary theories with multiple generalized displacements can not be used for long, slender beams and thin plates since the innate relation between rotation angle and deflection is ignored. These two types of theories are not consistent due to the contradiction of dependence and independence of the rotation angle. Based on several basic assumptions, a new type of theories which not only include the transverse shearing effect is presented, but also the relation between potation angle and deflection is obtained. Analytical solutions of several simple beams are given. It has been testified by numerical examples that the new theories can be used for either long, slender beams and thin plates or short, stubby beams and thick plates.
