Based on the nonlocal strain gradient theory(NSGT),the static bending behaviors of an axially functionally graded(AFG)Bernoulli-Euler microbeam subjected to concentrated and distributed loads are studied.The material ...Based on the nonlocal strain gradient theory(NSGT),the static bending behaviors of an axially functionally graded(AFG)Bernoulli-Euler microbeam subjected to concentrated and distributed loads are studied.The material property of the AFG microbeam changes continuously along the longitudinal direction.On the basis of the minimum potential energy principle,the equations of motion and associated classical and non-classical boundary conditions are derived.Then,Galerkin’s weighted residual method in conjunction with the normalization technique are utilized to solve the governing differential equations.The transverse deformations of the AFG microbeam suffering the sinusoidal distributed load within the framework of NSGT,nonlocal elasticity theory(NET),strain gradient theory(SGT)and classical elasticity theory(CET)are compared.It is observed that the bending flexibility of the microbeam decreases with the increase in the ratio of the material length scale parameter to the beam height.However,the bending flexibility increases with the increase in the material nonlocal parameter.The functionally graded parameter plays an important role in controlling the transverse deformation.This study provides a theoretical basis and a technical reference for the design and analysis of AFG micro-beams in the related regions.展开更多
This paper investigated the nonlinear vibration of functionally graded beams containing an open edge crack based on Timoshenko beam theory.The cracked section is modeled by a massless elastic rotational spring.It is a...This paper investigated the nonlinear vibration of functionally graded beams containing an open edge crack based on Timoshenko beam theory.The cracked section is modeled by a massless elastic rotational spring.It is assumed that material properties follow exponential distributions through the beam thickness.The differential quadrature(DQ) method is employed to discretize the nonlinear governing equations which are then solved by a direct iterative method to obtain the nonlinear vibration frequencies of beams with different boundary conditions.The effects of the material gradient,crack depth and boundary conditions on nonlinear free vibration characteristics of the cracked FGM beams are studied in detail.展开更多
基金The National Key Research and Development Program of China(No.2017YFC0307604)the Talent Foundation of China University of Petroleum(No.Y1215042)
文摘Based on the nonlocal strain gradient theory(NSGT),the static bending behaviors of an axially functionally graded(AFG)Bernoulli-Euler microbeam subjected to concentrated and distributed loads are studied.The material property of the AFG microbeam changes continuously along the longitudinal direction.On the basis of the minimum potential energy principle,the equations of motion and associated classical and non-classical boundary conditions are derived.Then,Galerkin’s weighted residual method in conjunction with the normalization technique are utilized to solve the governing differential equations.The transverse deformations of the AFG microbeam suffering the sinusoidal distributed load within the framework of NSGT,nonlocal elasticity theory(NET),strain gradient theory(SGT)and classical elasticity theory(CET)are compared.It is observed that the bending flexibility of the microbeam decreases with the increase in the ratio of the material length scale parameter to the beam height.However,the bending flexibility increases with the increase in the material nonlocal parameter.The functionally graded parameter plays an important role in controlling the transverse deformation.This study provides a theoretical basis and a technical reference for the design and analysis of AFG micro-beams in the related regions.
基金supported by the National Natural Science Foundation of China (Grant No. 11002019)Ph.D. Programs Foundation of the Ministry of Education of China (Grant No. 20100009120018)the Fundamental Research Funds for the Central Universities (Grant No. 2009JBM073)
文摘This paper investigated the nonlinear vibration of functionally graded beams containing an open edge crack based on Timoshenko beam theory.The cracked section is modeled by a massless elastic rotational spring.It is assumed that material properties follow exponential distributions through the beam thickness.The differential quadrature(DQ) method is employed to discretize the nonlinear governing equations which are then solved by a direct iterative method to obtain the nonlinear vibration frequencies of beams with different boundary conditions.The effects of the material gradient,crack depth and boundary conditions on nonlinear free vibration characteristics of the cracked FGM beams are studied in detail.
