结构在静流场中振动时的附加质量分布

结构在静流场中振动时,附加质量的分布形式对其振动特性有非常大的影响,尤其是对较为轻薄的结构,但截至目前,对附加质量显式分布的研究甚少。基于三维问题的边界元法,在合适的Dirichlet及Neumann条件下,提出了一种较简单的方法,可求解结构以任意给定模式在不可压缩单相静流场中振动时的附加质量显式分布。数值计算表明,该方法的求解结果与理论解及实验结果吻合良好,可较好地应用于复杂形状结构在有界或无界静流场中振动时的附加质量分布计算。     

Vibration analyses of a portal frame under the action of a moving distributed mass using moving mass element

Four kinds of moving mass elements, 1st‐node, 2nd‐node, full and short‐range mass elements, are presented, where the 1st‐node (or 2nd‐node) mass element refers to that with mass distributed from the first node (or second node) to the arbitrary position of a two‐node beam element, the full mass element is the special case of the 1st‐node (or 2nd‐node) mass element with mass distributed over the full length of the beam element, while the short‐range mass element is the case with its location arbitrary on a beam element. If the total range of a distributed mass is denoted by R and the length of each beam element is denoted by ??, then, for the case of R???, one may model the distributed mass on the beam using the combination of the 1st‐node, 2nd‐node and full mass elements, while for the case of R<??, one may model the distributed mass using the short‐range mass element. It has been found that the effects of the vertical (?) and horizontal (x?) inertia forces, Coriolis force and centrifugal force induced by the moving distributed mass can be easily taken into the formulations by means of the last concept. To illustrate the application of the presented theory, the dynamic analysis of a pinned–pinned beam and that of a portal frame under the action of a moving uniformly distributed mass are performed by means of the finite element method and the Newmark integration method. Numerical results show that some pertinent factors, such as Coriolis force, centrifugal force, acceleration, velocity and total range of the moving distributed mass, have significant influences on the vertical (?) and horizontal (x?) response of a structure. Copyright © 2005 John Wiley & Sons, Ltd.     

Use of moving distributed mass element for the dynamic analysis of a flat plate undergoing a moving distributed load

This paper presents the theory regarding a moving distributed mass element, so that the dynamic responses of a rectangular plate subjected to a moving distributed mass, with the effects of inertia force, Coriolis force and centrifugal force considered, can be easily determined. In which, the property matrices of the moving distributed mass element are derived by means of the principle of superposition and the definition of shape functions, and the overall property matrices of the entire vibrating system are determined from the combination of the last element property matrices of the moving distributed mass element and those of the plate itself. Since the property matrices of the moving distributed mass element have something to do with the instantaneous position and the distribution of the moving mass, they are time-dependent and so are the overall property matrices of the entire vibrating system. Based on the last concept, the equations of motion for a rectangular plate subjected to a moving distributed mass are established and solved to yield the dynamic responses of the entire vibrating system. Numerical results reveal that the factors such as the contact area (between the moving distributed mass and the plate), moving-load speed, inertia force, Coriolis force and centrifugal force affect the vibration characteristics of the plate to some degree. Copyright © 2006 John Wiley & Sons, Ltd.     

On the motion of a spherical bubble deforming near a plane wall

Equations of motion are derived for an expanding spherical bubble in potential flow near a plane wall using the Lagrange-Thomson method and an extended Rayleigh dissipation function to account for the drag. This method is shown to yield the same acceleration of the bubble center as that obtained using the Lagally theorem. An extended Rayleigh-Plesset equation is derived to describe deformation in the vicinity of a plane wall, and expressions relating the drag force to the distance from the wall and the bubble growth rate are derived. The solution method for the velocity potential can also be applied to the case of non-spherical deformation.     

An accurate solution for the responses of circular curved beams subjected to a moving load

In this paper, an accurate and effective solution for a circular curved beam subjected to a moving load is proposed, which incorporates the dynamic stiffness matrix into the Laplace transform technique. In the Laplace domain, the dynamic stiffness matrix and equivalent nodal force vector for a moving load are explicitly formulated based on the general closed‐form solution of the differential equations for a circular curved beam subjected to a moving load. A comparison with the modal superposition solution for the case of a simply supported curved beam confirms the high accuracy and applicability of the proposed solution. The internal reactions at any desired location can easily be obtained with high accuracy using the proposed solution, while a large number of elements are usually required for using the finite element method. Furthermore, the jump behaviour of the shear force due to passage of the load is clearly described by the present solution without the Gibb's phenomenon, which cannot be achieved by the modal superposition solution. Finally, the present solution is employed to study the dynamic behaviour of circular curved beams subjected to a moving load considering the effects of the loading characteristics, including the moving speed and excitation frequency, and the effects of the characteristics of curved beams such as the radius of curvature, number of spans, opening angles and damping. The impact factors for displacement and internal reactions are presented. Copyright © 2000 John Wiley & Sons, Ltd.