Damping of Layered and Jointed Beams with Riveted Joints

By: Mohanty, Ramesh ChandraContributor(s): Nanda, Bijay Kumar [Supervisor] | Department of Mechanical EngineeringMaterial type: TextTextLanguage: English Publisher: 2010Description: 196 pSubject(s): Engineering and Technology | Mechanical Engineering | Machine DesignOnline resources: Click here to access online Dissertation note: Thesis (Ph.D)- National Institute of Technology, Rourkela Summary: The present investigation highlights the eff ect of interfacial slip on the damping of layered cantilever beams jointed with rive ts undergoing free vibration. The inclusion of mechanical joints bears a strong influe nce in the overall system performance and behavior, particularly the damping level of the structures. In fact , the damping and its improvement in machines or structures are one of the biggest challenges to the practicing engineers. Usually, such struct ures inherently possess low structural damping necessitating the introduction of additional measures to improve their damping characteristics in order to control the harmful effects of vibration in normal operating conditions. Monolithic structures can be used as an alternative, but unfortunately these are very poor in dampi ng capacity and are not cost-effective. One of the techniques used in the present pr oblem for improving damping is fabricating these structures in layers by means of rivete d joints. The incorporation of such joints is the major source of energy dissipation th rough frictional effects associated with relative shear displacements at the interfaces of the various structural members. Most of the damping in built-up structures is thus attributed to micro-slip at the interfaces. The contribution of the micro-slip on the ove rall system damping is always significant in spite of its low magnitude. This thesis consists of two different parts: a theoretical analysis of the problem and an experimental work. The theoretical anal ysis proposes two di fferent methods to calculate damping: classical method and finite element method . The analyses are based on the assumptions of Euler-Bernoulli be am theory as the dimensions of test specimens satisfy the criterion of thin beam theory. In the first case, a continuous model is characterized by a partial differential equation with respect to spatial and time coordinates. An analytical exact soluti on is obtained for the above differential equation from which the dynamic characteri stics of the structure are represented accurately. In the latter case, the mode l is represented by one-dimensional beam elements with each element consisting of tw o nodes with two degrees of freedom, i.e. transverse displacement and rotation at each node. This model is approximate and characterized by stiffness and mass matric es from which natural frequencies and mode shapes are obtained by modal analysis . As the direct eval uation is not easy, an alternate energy approach has been us ed to derive the damping matrix. It is a general fact that the theoretically computed results will differ from the actual values due to the assumptions made in th e theoretical analyses. In view of this discrepancy in results, expe riments are conducted for different set of mild steel and aluminium specimens under different vibrating conditions. The logarithmic decrement technique has been used for measuring the damping from th e time history curve of the decaying signals recorded on the screen of digital storage oscilloscope. The experimental results are compared with the corresponding theoretical ones for establishing the authenticity of the theory developed. Finally, usef ul conclusions have been drawn from both the theoreti cal and experimental results. The damping characteristics in jointed structures are influenced by the intensity of pressure distribution, micro-slip and kinematic coefficient of friction at the interfaces and the effects of all these parameters on the mechanism of damping have been extensively studied. All the above vital parameters are largely influenced by the thickness ratio of the beam and thereby aff ect the damping capacity of the structures. In addition to this, number of layers, cantilever length and diameter of connecting rivet also play key roles on the damping capacity of the jointed structures quantitatively. The effects of all these para meters are studied vi vidly in the present investigation. It is established that the da mping capacity can be enhanced appreciably using larger cantilever length and rivet diamet ers as well as lower thickness ratio of the beams. Further improvement in damping is possible with the use of more number of layers compared to its equivalent solid one. This design concept of using layered structures with riveted joints can be effectiv ely utilized in trusse s and frames, aircraft and aerospace structures, bridges, machine members, robots and many other applications where higher damping is required
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Thesis (Ph.D)- National Institute of Technology, Rourkela

The present investigation highlights the eff
ect of interfacial slip on the damping of
layered cantilever beams jointed with rive
ts undergoing free vibration. The inclusion
of mechanical joints bears a strong influe
nce in the overall system performance and
behavior, particularly the damping level of
the structures. In fact
, the damping and its
improvement in machines or structures
are one of the biggest challenges to the
practicing engineers. Usually, such struct
ures inherently possess low structural
damping necessitating the introduction of
additional measures to improve their
damping characteristics in order to control
the harmful effects of vibration in normal
operating conditions. Monolithic structures can be used as an alternative, but
unfortunately these are very poor in dampi
ng capacity and are not cost-effective. One
of the techniques used in the present pr
oblem for improving damping is fabricating
these structures in layers by means of rivete
d joints. The incorporation of such joints
is the major source of energy dissipation th
rough frictional effects associated with
relative shear displacements at the interfaces
of the various structural members. Most
of the damping in built-up structures is thus
attributed to micro-slip at the interfaces.
The contribution of the micro-slip on the ove
rall system damping is always significant
in spite of its low magnitude.
This thesis consists of two different parts: a theoretical analysis of the problem and an
experimental work. The theoretical anal
ysis proposes two di
fferent methods to
calculate damping:
classical method
and
finite element method
. The analyses are
based on the assumptions of Euler-Bernoulli be
am theory as the dimensions of test
specimens satisfy the criterion of thin beam
theory. In the first case, a continuous
model is characterized by a partial differential equation with respect to spatial and
time coordinates. An analytical exact soluti
on is obtained for the above differential
equation from which the dynamic characteri
stics of the structure are represented
accurately. In the latter case, the mode
l is represented by one-dimensional beam
elements with each element consisting of tw
o nodes with two degrees of freedom, i.e.
transverse displacement and rotation at
each node. This model is approximate and
characterized by stiffness and mass matric
es from which natural frequencies and
mode shapes are obtained by modal analysis
. As the direct eval
uation is not easy, an
alternate energy approach has been us
ed to derive the damping matrix.
It is a general fact that the theoretically computed results will differ from the actual
values due to the assumptions made in th
e theoretical analyses. In view of this
discrepancy in results, expe
riments are conducted for different set of mild steel and
aluminium specimens under different vibrating conditions. The logarithmic decrement
technique has been used for
measuring the damping from th
e time history curve of the
decaying signals recorded on the screen
of digital storage oscilloscope. The
experimental results are compared with
the corresponding theoretical ones for
establishing the authenticity of the theory
developed. Finally, usef
ul conclusions have
been drawn from both the theoreti
cal and experimental results.
The damping characteristics in jointed structures are influenced by the intensity of
pressure distribution, micro-slip and kinematic
coefficient of friction at the interfaces
and the effects of all these parameters on the mechanism of damping have been
extensively studied. All the
above vital parameters are
largely influenced by the
thickness ratio of the beam and thereby aff
ect the damping capacity of the structures.
In addition to this, number
of layers, cantilever length
and diameter of connecting
rivet also play key roles on the damping capacity of the jointed structures
quantitatively. The effects of all these para
meters are studied vi
vidly in the present
investigation. It is established that the da
mping capacity can be enhanced appreciably
using larger cantilever length and rivet diamet
ers as well as lower thickness ratio of
the beams. Further improvement in damping
is possible with the use of more number
of layers compared to its equivalent solid
one. This design concept of using layered
structures with riveted joints can be effectiv
ely utilized in trusse
s and frames, aircraft
and aerospace structures, bridges, machine members, robots and many other
applications where higher damping is required

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