Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams with large deflections, the nonlinear equations governing dynamical behavior of Tim...Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams with large deflections, the nonlinear equations governing dynamical behavior of Timoshenko beams with damage on viscoelastic foundation were firstly derived. By using the Galerkin method in spatial domain, the nonlinear integro-partial differential (equations) were transformed into a set of integro-ordinary differential equations. The numerical methods in nonlinear dynamical systems, such as the phase-trajectory diagram, Poincare section and bifurcation figure, were used to solve the simplified systems of equations. It could be seen that simplified dynamical systems possess the plenty of nonlinear dynamical properties. The influence of load and material parameters on the dynamic behavior of nonlinear system were investigated in detail.展开更多
From the constitutive model with generalized force fields for a viscoelastic body with damage, the differential equations of motion for thin and thick plates with damage are derived under arbitrary boundary conditions...From the constitutive model with generalized force fields for a viscoelastic body with damage, the differential equations of motion for thin and thick plates with damage are derived under arbitrary boundary conditions. The convolution-type functionals for the bending of viscoelastic thin and thick plates with damage are presented, and the corresponding generalized variational principles are given. From these generalized principles, all the basic equations of the displacement and damage variables and initial and boundary conditions can be deduced. As an example, we compare the difference between the dynamical properties of plates with and without damage and consider the effect of damage on the dynamical properties of plates.展开更多
Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams, the equations governing quasi-static and dynamical behavior of Timoshenko beams wi...Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams, the equations governing quasi-static and dynamical behavior of Timoshenko beams with damage were first derived. The quasi-static behavior of the viscoelastic Timoshenko beam under step loading was analyzed and the analytical solution was obtained in the Laplace transformation domain. The deflection and damage curves at different time were obtained by using the numerical inverse transform and the influences of material parameters on the quasi-static behavior of the beam were investigated in detail.展开更多
文摘Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams with large deflections, the nonlinear equations governing dynamical behavior of Timoshenko beams with damage on viscoelastic foundation were firstly derived. By using the Galerkin method in spatial domain, the nonlinear integro-partial differential (equations) were transformed into a set of integro-ordinary differential equations. The numerical methods in nonlinear dynamical systems, such as the phase-trajectory diagram, Poincare section and bifurcation figure, were used to solve the simplified systems of equations. It could be seen that simplified dynamical systems possess the plenty of nonlinear dynamical properties. The influence of load and material parameters on the dynamic behavior of nonlinear system were investigated in detail.
基金Project supported by the National Natural Sciences Foundation of China (No. 10272069) the Shanghai Key Subject Program.
文摘From the constitutive model with generalized force fields for a viscoelastic body with damage, the differential equations of motion for thin and thick plates with damage are derived under arbitrary boundary conditions. The convolution-type functionals for the bending of viscoelastic thin and thick plates with damage are presented, and the corresponding generalized variational principles are given. From these generalized principles, all the basic equations of the displacement and damage variables and initial and boundary conditions can be deduced. As an example, we compare the difference between the dynamical properties of plates with and without damage and consider the effect of damage on the dynamical properties of plates.
基金Project supported by the National Natural Science Foundation of China (No.50278051)Shanghai Leading Academic Discipline Project (No.Y0103)
文摘Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams, the equations governing quasi-static and dynamical behavior of Timoshenko beams with damage were first derived. The quasi-static behavior of the viscoelastic Timoshenko beam under step loading was analyzed and the analytical solution was obtained in the Laplace transformation domain. The deflection and damage curves at different time were obtained by using the numerical inverse transform and the influences of material parameters on the quasi-static behavior of the beam were investigated in detail.
