Dynamic Analysis With Second-Order Effect For Flexible Beam Systems And Its Application In Crane

Crane with flexible booms is a typical heavy-duty flexible machinery, and the accurate dynamic analysis is the major means to ensuring its safe operation. Crane as the research background and application object, the flexible multibody system dynamic method as tool, the elastic dynamic analysis method of mobile flexible beam system with the second-order effect considerated is researched and the typical mobile case of crane is analysis as instance.Because the precision of the conventional beam element with the second-order effect considerated is poor, the planar and spatial three-node Euler-Bernoulli beam elements are developed firstly in static mechanics based on the finite element theory. The displacement fields of three-node Euler-Bernoulli beam element are construced: the quintic Hermite interpolation polynomial for the transverse displacement fields and the quadratic Lagrange interpolation polynomial for the longitudinal and torsional displacement fields. The tangent stiffness matrix of three-node beam element is derived using the nonlinear finite element theory. A new two-node beam element with the same derees of freedom(DOFs) and location as the conventional beam element, can be called as condensation beam element, is obtained by eliminating the DOFs of the interior node of the three-node beam element using the static condensation method.Several classical examples in the stability and second-order effect of beam structures are analysised. The results show that the precision of the new beam element is much higher than the one of the conventional two-node beam element and the critical forces and second-order displacements and internal forces with high precision can be obtained even each beam is discretized into one element. So the used elements'number of each beam may be ignored when this condensation beam element is used for the geometric nonlinear static analysis of beam structures, and there are some dominances in calculation precision and efficiency.The kinetic equations of beam and link element in the location coordination system are derived through accurately describing the motional status of flexible body. Because the stiffness matrixes correlates with the differential coefficient of the shape function, while other dynamic characteristic matrixes as the mass matrix directly correlate with the shape function. So the stiffness matrix is derived by using the shape function of the three-node beam element and other dynamic characteristic matrixes using the shape function of the convensional two-node beam element. The kinetic equations are condensated and the stiffness matrix in the final kinetic equations is same as the the stiffness matrix of condensation beam element. The mobile coordination system is used and the dymamic equations in the global coordination system are developed using the relation of nodes'displacement in mobile and global coordination system. All inertial coupled matrixes are included in the dynamic equations, and the interrelationship and couple of rigid motion and elastic deformation are considerated. The integration method of system dynamic equations and leading-in method of lump parameters are introduced. The solution method and program organization are discussed and the corresponding finite element program is generated. Take the mobile beam mechanism and the slider crank mechanism for examples, the precision of the theory of model building and program are proved.Crane has some mobile cases and the modifying-amplitude is important and dangerous. The modifying-amplitude case of port crane'boom system is analysed using above method and the emphasis is the influence to beams'displacements and internal forces with second-order effect considerated. The results show that the displacement and internal force of crane increase when the second-order effect is considerated. So the heavy-duty important cranes must be analysed using the elastic dynamics with second-order effect.The viewpoint that the analysis precision can not be increased using multi-node Euler-Bernoulli beam element is rectificated. The precision of three-node beam element is much higher the one of two conventional two-node beam elements in nonlinear analysis. The second-order effect is included into the nonlinear dynamic analysis of motional flexible beam system, and high flexibility and transverse load largely influence its dynamic responses. The heavy-duty crane with high flexibility should be analysed included the second-order effect.