Dynamic equations of motional flexible beam elements were derived considering second-order effect. Non-linear finite element method and three-node Euler-Bernoulli beam elements were used. Because accuracy is higher in...Dynamic equations of motional flexible beam elements were derived considering second-order effect. Non-linear finite element method and three-node Euler-Bernoulli beam elements were used. Because accuracy is higher in non-linear structural analysis,three-node beam elements are used to deduce shape functions and stiffness matrices in dynamic equations of flexible elements. Static condensation method was used to obtain the finial dynamic equations of three-node beam elements. According to geometrical relations of nodal displacements in concomitant and global coordinate system,dynamic equations of elements can be transformed to global coordinate system by concomitant coordinate method in order to build the global dynamic equations. Analyzed amplitude condition of flexible arm support of a port crane,the results show that second-order effect should be considered in kinetic-elastic analysis for heavy load machinery of big flexibility.展开更多
A passive approach is developed to quench excess vibration along a harmonically driven,arbitrarily supported,nonuniform Euler-Bernoulli beam with constant thickness(height)and varying width.Vibration suppression is ac...A passive approach is developed to quench excess vibration along a harmonically driven,arbitrarily supported,nonuniform Euler-Bernoulli beam with constant thickness(height)and varying width.Vibration suppression is achieved by attaching properly tuned vibration absorbers to enforce nodes,or points of zero vibration,along the beam.An efficient hybrid method is proposed whereby the finite element method is used to model the nonuniform beams,and a formulation based on the assumed modes method is used to determine the required attachment force supplied by each absorber to induce the desired nodes.Knowing the attachment forces needed to induce nodes,design plots are generated for the absorber parameters as a function of the tolerable vibration amplitude for each absorber mass.When the node locations are judiciously chosen,it is possible to dramatically suppress the vibration along a selected region of the beam.As such,sensitive instruments can be placed in this region and will remain nearly stationary.Numerical studies illustrate the application to several systems with various types of nonuniformity,boundary conditions,and attachment and node locations;these examples validate the proposed method to passively control excess vibration by inducing nodes on nonuniform beams subjected to harmonic excitations.展开更多
文摘Dynamic equations of motional flexible beam elements were derived considering second-order effect. Non-linear finite element method and three-node Euler-Bernoulli beam elements were used. Because accuracy is higher in non-linear structural analysis,three-node beam elements are used to deduce shape functions and stiffness matrices in dynamic equations of flexible elements. Static condensation method was used to obtain the finial dynamic equations of three-node beam elements. According to geometrical relations of nodal displacements in concomitant and global coordinate system,dynamic equations of elements can be transformed to global coordinate system by concomitant coordinate method in order to build the global dynamic equations. Analyzed amplitude condition of flexible arm support of a port crane,the results show that second-order effect should be considered in kinetic-elastic analysis for heavy load machinery of big flexibility.
文摘A passive approach is developed to quench excess vibration along a harmonically driven,arbitrarily supported,nonuniform Euler-Bernoulli beam with constant thickness(height)and varying width.Vibration suppression is achieved by attaching properly tuned vibration absorbers to enforce nodes,or points of zero vibration,along the beam.An efficient hybrid method is proposed whereby the finite element method is used to model the nonuniform beams,and a formulation based on the assumed modes method is used to determine the required attachment force supplied by each absorber to induce the desired nodes.Knowing the attachment forces needed to induce nodes,design plots are generated for the absorber parameters as a function of the tolerable vibration amplitude for each absorber mass.When the node locations are judiciously chosen,it is possible to dramatically suppress the vibration along a selected region of the beam.As such,sensitive instruments can be placed in this region and will remain nearly stationary.Numerical studies illustrate the application to several systems with various types of nonuniformity,boundary conditions,and attachment and node locations;these examples validate the proposed method to passively control excess vibration by inducing nodes on nonuniform beams subjected to harmonic excitations.
