Damping (Mechanics)

This research is aimed at investigating and analyzing the rain-windinduced cable vibration phenomena experienced in cables of cable-stayed bridges and also the countermeasures employed by engineers to mitigate the large-amplitude vibration problem reported by various researchers around the world. In order to investigate the problem of the water rivulet creation at the top of the cable surface, a single-degree-of-freedom (SDOF) analytical model was developed and analyzed. This thesis studies the aerodynamic instability of cables in cable-stayed bridges by doing literature review of a typical in-situ test, developing a single degree-of-freedom (SDOF) analytical model, and an ANSYS finite element model. Furthermore, a linear viscous damper that acts as a
countermeasure to the large amplitudes of vibration is reported and analyzed. The suppression characteristics and damper effectiveness of such countermeasure are summarized.

Of the many methods of introducing damping in
vibrating structures, the dissipation of energy due to
interfacial slip can significantly increase the damping loss
factor. However, because of the lack of understanding and
other phenomena such as fretting corrosion and loss of
structural rigidity, friction damping is rarely used. A
study was thus undertaken to investigate this complex
phenomenon, with emphasis on trying to gain a better
understanding of friction damping with certain parameters
such as clamping pressure, frequency, magnitude of
excitation and surface finish. Although the non-linearities
associated with friction makes this mechanism difficult to
model mathematically, finite element (FE) analysis shows
some promise. Although the results obtained using an FE
model were not exactly comparable to the experimental
results, these analytical results did show the same general
trends as observed in the experiments.

Application of modal testing techniques in the
determination of the modal parameters and mode shapes of an
edge-fixed circular plate with a free-layer viscoelastic
damping treatment extending over a portion of the plate
surface is described.
The mode shapes and modal parameters were determined
for the first five flexural modes of the plate, which had a
free-layer viscoelastic damping treatment on one side in the
form of a central circular patch of varying size.
The experimental setup and procedure is described in
detail, with particular emphasis upon problems of modal
overlap resulting from the symmetry of the test structure.
Results comparing the predicted and measured natural
frequencies and modal loss factors for varying degrees of
damping treatment are presented for select cases.

An experimental investigation to determine the effectiveness
of partial constrained layer damping treatments for a
clamped rectangular plate is described. The impulse testing
technique was used with a Hewlett Packard '5423A structural
Dynamics Analyzer' to determine modal parameters of
the first five flexural modes. The results obtained are
compared with theoretical results and they are in agreement.
The results indicate that partial constrained layer damping
treatments, if properly used, can be more effective than
complete treatments.

A theoretical analysis for predicting the system loss factors and
natural frequencies of rectangular plates with complete and partial
constrained-layer damping treatments has been presented. This analysis
is based upon an energy approach to the free vibration of plates.
Results predicted were compared with those from experiments. Satisfactory
agreement has been reached. Both the theoretical and the
experimental results presented in this thesis indicate clearly that
partial constrained-layer damping treatments can provide effective, or
even superior, amounts of damping, and that their use can lead to
significant savings in material costs and weight.

A method of analysis is presented to determine the natural
frequencies and loss factors of a plate covered with viscoelastic
coating, using experimentally obtained mode shapes.
The mode shapes for a square plate clamped on all edges are
determined using an HP 5423 A Structural Dynamics Analyzer.
A computer program, based on the method of analysis, is
developed to determine the natural frequencies and loss
factors of a rectangular plate covered with viscoelastic
material, and clamped on all edges. It was found that,
for a fully coated plate, and for a mesh with twenty-five
mesh points, the error in the fundamental frequency was
approximately 5 percent. A comparison between the mode
shapes for the bare plate and for the fully coated plate
revealed no significant difference. It was also found
that increasing the number of measurement points would
not significantly improve the results.

An energy method for predicting the natural frequency and loss
factor for square plates with partial and complete coatings is
developed. Both simply-supported and edge-fixed bonndary conditions
are considered. An impulse testing technique is used to
provide an experimental verification of the analysis for the case
of an edge-fixed square plate. The analytical and experimental
results are in close agreement, and indicate that partial coatings
can provide effective damping treatments.

Theoretical investigation is carried out into the extent to which floor accelerations of a wind-excited tall building can be reduced by increasing damping in those components in a building which are generally regarded to be non-structural elements, and by using active control. The wind loads are modeled as stochastic processes, which are correlation-stationary in time. Only the drag wind forces are considered in the analyses. The spectral densities and cross-spectral densities of two commonly used models, proposed by Davenport and by Simiu, are compared. The Davenport spectrum is used in the numerical calculation for illustration purposes. Several structural models are discussed: an ideal spatially periodic model, an ideal piece-wise spatially periodic model, a nominal spatially periodic model with random disorder in periodicity, and an ideal spatially periodic model equipped with an active mass damper control system. The problems are formulated using the transfer matrix approach in the frequency domain. Analytical solutions are obtained for the spectral densities and the mean-square values of the floor accelerations and those of the active control force. Numerical examples are given for illustration.

The feasibility of using structural modification techniques to determine the effect of added viscoelastic damping treatments on the modal properties of a distinct eigenvalue system and a degenerate system is investigated. Linear perturbation equations for the changes introduced into the system eigenproperties are derived and applied to several examples involving the flexural vibration of beams and square plates with varying degrees of damping treatment. Both large and small perturbations are considered. An FEM code has been developed to compute the dynamic system parameters which are subsequently used in an iterative method to determine the modal properties. The perturbation approach described can accommodate temperature and frequency-dependent material properties, and the procedures involved are illustrated in the examples considered. Results obtained for these examples are compared with those available from closed form or finite element solutions, or from experiments. Excellent agreement of the results of the present method with those of other contemporary methods demonstrates the validity, overall accuracy, efficiency and convergence rate of this technique. The perturbation approach appears to be particularly well suited for systems with temperature and frequency dependent material properties, and for design situations where a number of damping configurations must be investigated.