The nonlinear vibration of graphene platelets reinforced composite corrugated(GPRCC)rectangular plates with shallow trapezoidal corrugations is investigated.Since graphene platelets are prone to agglomeration,a multi-...The nonlinear vibration of graphene platelets reinforced composite corrugated(GPRCC)rectangular plates with shallow trapezoidal corrugations is investigated.Since graphene platelets are prone to agglomeration,a multi-layer distribution is adopted here to match the engineering requirements.Firstly,an equivalent composite plate model is obtained,and then nonlinear equations of motion are derived by the von Kármán nonlinear geometric relationship and Hamilton’s principle.Afterwards,the Galerkin method and harmonic balance method are used to obtain an approximate analytical solution.Results show that the unit cell half period,unit cell inclination angle,unit cell height,graphene platelet dispersion pattern and graphene platelet weight fraction and geometry play important roles in the nonlinear vibration of the GPRCC plates.展开更多
An element-free Galerkin method(EFGM) is used to solve the two-dimensional(2D) ground penetrating radar(GPR)modelling problems, due to its simple pre-processing, the absence of elements and high accuracy. Different fr...An element-free Galerkin method(EFGM) is used to solve the two-dimensional(2D) ground penetrating radar(GPR)modelling problems, due to its simple pre-processing, the absence of elements and high accuracy. Different from element-based numerical methods, this approach makes nodes free from the elemental restraint and avoids the explicit mesh discretization. First, we derived the boundary value problem for the 2D GPR simulation problems. Second, a penalty function approach and a boundary condition truncated method were used to enforce the essential and the absorbing boundary conditions, respectively. A three-layered GPR model was used to verify our element-free approach. The numerical solutions show that our solutions have an excellent agreement with solutions of a finite element method(FEM). Then, we used the EFGM to simulate one more complex model to show its capability and limitations. Simulation results show that one obvious advantage of EFGM is the absence of element mesh, which makes the method very flexible. Due to the use of MLS fitting, a key feature of EFM, is that both the dependent variable and its gradient are continuous and have high precision.展开更多
基金Project(11972204) supported by the National Natural Science Foundation of China。
文摘The nonlinear vibration of graphene platelets reinforced composite corrugated(GPRCC)rectangular plates with shallow trapezoidal corrugations is investigated.Since graphene platelets are prone to agglomeration,a multi-layer distribution is adopted here to match the engineering requirements.Firstly,an equivalent composite plate model is obtained,and then nonlinear equations of motion are derived by the von Kármán nonlinear geometric relationship and Hamilton’s principle.Afterwards,the Galerkin method and harmonic balance method are used to obtain an approximate analytical solution.Results show that the unit cell half period,unit cell inclination angle,unit cell height,graphene platelet dispersion pattern and graphene platelet weight fraction and geometry play important roles in the nonlinear vibration of the GPRCC plates.
基金Project(41074085)supported by the National Natural Science Foundation of ChinaProject(NCET-12-0551)supported by the Funds for New Century Excellent Talents in University,ChinaProject supported by Shenghua Yuying Program of Central South University,China
文摘An element-free Galerkin method(EFGM) is used to solve the two-dimensional(2D) ground penetrating radar(GPR)modelling problems, due to its simple pre-processing, the absence of elements and high accuracy. Different from element-based numerical methods, this approach makes nodes free from the elemental restraint and avoids the explicit mesh discretization. First, we derived the boundary value problem for the 2D GPR simulation problems. Second, a penalty function approach and a boundary condition truncated method were used to enforce the essential and the absorbing boundary conditions, respectively. A three-layered GPR model was used to verify our element-free approach. The numerical solutions show that our solutions have an excellent agreement with solutions of a finite element method(FEM). Then, we used the EFGM to simulate one more complex model to show its capability and limitations. Simulation results show that one obvious advantage of EFGM is the absence of element mesh, which makes the method very flexible. Due to the use of MLS fitting, a key feature of EFM, is that both the dependent variable and its gradient are continuous and have high precision.
