Analytical investigation of squeeze film dampers

Squeeze film damping effects naturally occur if structures are subjected to loading situations such that a very thin film of fluid is trapped within structural joints, interfaces, etc. An accurate estimate of squeeze film effects is important to predict the performance of dynamic structures. Starting from linear Reynolds equation which governs the fluid behavior coupled with structure domain which is modeled by Kirchhoff plate equation, the effects of nondimensional parameters on the damped natural frequencies are presented using boundary characteristic orthogonal functions. For this purpose, the nondimensional coupled partial differential equations are obtained using Rayleigh-Ritz method and the weak formulation, are solved using polynomial and sinusoidal boundary characteristic orthogonal functions for structure and fluid domain respectively. In order to implement present approach to the complex geometries, a two dimensional isoparametric coupled finite element is developed based on Reissner-Mindlin plate theory and linearized Reynolds equation. The coupling between fluid and structure is handled by considering the pressure forces and structural surface velocities on the boundaries. The effects of the driving parameters on the frequency response functions are investigated. As the next logical step, an analytical method for solution of squeeze film damping based upon Green’s function to the nonlinear Reynolds equation considering elastic plate is studied. This allows calculating modal damping and stiffness force rapidly for various boundary conditions. The nonlinear Reynolds equation is divided into multiple linear non-homogeneous Helmholtz equations, which then can be solvable using the presented approach. Approximate mode shapes of a rectangular elastic plate are used, enabling calculation of damping ratio and frequency shift as well as complex resistant pressure. Moreover, the theoretical results are correlated and compared with experimental results both in the literature and in-house experimental procedures including comparison against viscoelastic dampers.

STRUCTURAL CONTROL OF A SMALL-SCALE TEST-BED SHAKER STRUCTURE USING A SPONGE-TYPE MAGNETO-RHEOLOGICAL FLUID DAMPER

Semi-active damping devices have been shown to be effective in mitigating unwanted vibrations in civil structures. These devices impart force indirectly through real-time alterations to structural properties. Simulating the complex behavior of these devices for laboratory-scale experiments is a major challenge. Commercial devices for seismic applications typically operate in the 2-10 kN range; this force is too high for small-scale testing applications where requirements typically range from 0-10 N. Several challenges must be overcome to produce damping forces at this level. In this study, a small-scale magneto-rheological (MR) damper utilizing a fluid absorbent metal foam matrix is developed and tested to accomplish this goal. This matrix allows magneto-rheological (MR) fluid to be extracted upon magnetic excitation in order to produce MR-fluid shear stresses and viscosity effects between an electromagnetic piston, the foam, and the damper housing. Dampers for uniaxial seismic excitation are traditionally positioned in the horizontal orientation allowing MR-fluid to gather in the lower part of the damper housing when partially filled. Thus, the absorbent matrix is placed in the bottom of the housing relieving the need to fill the entire device with MR-fluid, a practice that requires seals that add significant unwanted friction to the desired low-force device. The damper, once constructed, can be used in feedback control applications to reduce seismic vibrations and to test structural control algorithms and wireless command devices. To validate this device, a parametric study was performed utilizing force and acceleration measurements to characterize damper performance and controllability for this actuator. A discussion of the results is presented to demonstrate the attainment of the damper design objectives.