PARAMETRIC STUDY OF FRICTIONAL DAMPING IN JOINTED BEAMS

Abstract eng:
The study of structural damping due to frictional contact in the presence of bolt joint has become increasingly important for an accurate prediction of vibrational behavior and the control of undesirable effects in machinery design. Numerical parametric studies are in the first place conducted on a model of twolayered jointed cantilever beams in order to identify the influences the geometric dimension, interface pressure, coefficient of friction, amplitude of vibration and boundary conditions have on structural damping. The slip propagation speed is also investigated in terms of increment size and clamping pressure. An analytical method based on the slipping mechanism revealed by numerical studies is then proposed. In the numerical analysis, 2D and 3D surface-to-surface contact finite element models are created using Abaqus software. For the condition of constant imposed excitation force, it is observed that there exists an optimal combination of coefficient of friction and clamping pressure to obtain maximal damping capacity, moreover, this optimal damping capacity is a constant value for a given structure. However under the condition of constant imposed displacement, the damping capacity increases monotonically with increasing clamping pressure and coefficient of friction. The research on interface slip propagation speed reveals that the rise in clamping pressure can decelerate the slip propagation. Two different boundary conditions are then applied on the free ends of the beam, one with no constraint, one with constraint in axial direction to eliminate the in plane displacement difference. It’s shown that the constraint in axial direction results in a weaker damping capacity. In addition, special attention is paid to geometric sinus-form imperfections. The number and curvature of imperfections are proved to have no significant influence on the damping capacity. The present numerical study is also extended to the simulation of welded jointed beams by adding displacement constraints to coupled welding points. It’s concluded that more welding points leads to weaker damping capacity. In the 3D analysis, the bolt is modeled with solid elements and it is discovered that the energy dissipation principally takes place in the contact area between the bolt’s shaft and the screw hole. Based on the relation between excitation force and displacement in the numerical studies, a bilinear stiffness behavior is observed. The stiffness transition point is obtained by element stress equilibrium analysis. The global displacement can be expressed by the use of Euler-Bernoulli beam theory. An analytical method for perfectly jointed beams is thus proposed on the hypothesis that the slip is present all over the contact surface once the excitation level reaches the critical value. The damping coefficient calculated by the analytical method is compared to numerical results and they are in close agreement. An analytical expression for optimal frictional damping can then be derived.

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