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|Title: ||On theory, modeling and solutions for statics and dynamics of a nanobeam and nanobeam-like structure based on nonlocal elasticity theory|
|Other Titles: ||Na mi liang ji na mi lei liang jie gou de jing li xue he dong li xue de fei ju bu li lun, mo xing ji qiu jie|
|Authors: ||Li, Cheng ( 李成)|
|Department: ||Department of Building and Construction|
|Degree: ||Doctor of Philosophy|
|Issue Date: ||2011|
|Publisher: ||City University of Hong Kong|
|Subjects: ||Nanostructured materials -- Mechanical properties.|
|Notes: ||CityU Call Number: TA418.9.N35 L526 2011|
xvi, 212 leaves : ill. 30 cm.
Thesis (Ph.D.)--City University of Hong Kong, 2011.
Includes bibliographical references (leaves 192-206)
|Abstract: ||Nanoscale materials and structures have recently received considerable attention
as these small-scale structures offer great potential for different applications in several
areas. With rapid development of nanotechnology, miniaturized structures with
nanoscale features can be precisely manufactured and applied in
nano-electromechanical systems (NEMS). The widespread availability of NEMS
such as atomic force microscopes has resulted in renewed interest in nano-systems for
chemical, physical and biological sensors and devices as nano-systems facilitate
higher precision in sensors and higher frequency in mixers, and the performance of
these devices is extremely dependent on properties of their nanobeam-like elements.
These properties need to be well characterized in order to control their functionality.
In comparison with macro materials and structures, some effects not observable
at macro-size are clear at nanoscale and, therefore, classical mechanics have failed to
work in nanostructures. For instance, according to the classical continuum theory,
the stress is singular at a crack tip despite the weak external load. However, each
material has limited fatigue strength and in fact, atomic simulation and experiments
have proved nonsingularity of stress at the crack tip. Currently, three main
approaches are being used to investigate nanomechanics: experiment, molecular
dynamic (MD) simulation and the continuum theory. Due to the complexity of
instruments, equipment and technology, precise experiments at nanoscale are
extremely difficult to be conducted. As MD simulation considers each individual
molecule and its multiple mechanical or chemical web-interactions, its use requires
extremely fast computing facilities and thence it is largely confined to relatively
restricted systems with a limited number of molecules. That is why many
researchers focus on the new continuum theory in nanomechanics.
In this study, static and dynamic behaviors of nanobeams and nanobeam-like
structures were investigated by the method based on the nonlocal elasticity theory.
Transverse, longitudinal and torsional mechanics were considered. Particularly, subminiature belt is a common component in nanoscale devices which involves
transverse vibration of axially moving nanostructures. Therefore, this work also
concerns the dynamics of axially moving nanobeam-like structures based on the
nonlocal theory. The nonlocal elasticity is based on atomic theory of lattice
dynamics and experimental observations of phonon dispersion. In this theory, stress
at a reference point is considered to be a function of strain fields at every point in the
body. Such dependence of nonlocal stress on strains over the deformed body is
observed in lattice dynamics and can also be inferred from the continuum mechanical
model of carbon nanotubes. The nonlocal theory contains information about forces
between atoms, and the internal length scale is introduced into the constitutive
equations as a material parameter. However, it is strange to see that there are two
nonlocal models, termed the exact and the partial nonlocal models, that offer different
predictions, i.e. stiffness is enhanced in one and is weakened in the other. The two
theoretical models are compared with MD simulation and consistency with respect to
the exact nonlocal model is reported.
In order to verify the two models, a semi-continuum model with discrete atomic
layers in the thickness direction was developed to investigate the bending behaviors of
ultra-thin beams of nanoscale thickness. The relaxation effect was considered in one
atomic layer on each of the upper and lower surfaces and comparison with the two
nonlocal models are inconclusive due to different material parameters. The long
range attractive or repulsive interaction, or the looser or tighter atomic lattice near the
surface than the bulk results in different materials parameters properties and
parametric correspondence with the nonlocal models should be established before a
solid conclusion could be made.
The main aim of this project is to develop a new, exact nonlocal stress model for
analytical solutions of nanobeams subjected to an axial load with simple support
boundary conditions. It also concerns the dynamic response of a pre-tensioned
nanobeam when precise internal axial force is considered. In addition, free vibration
and stability of a nanobeam subjected to a variable axial load, and dynamic behaviors of axially moving nanobeams are also analyzed. Similarly, an exact shear nonlocal
stress model is proposed, based on the variational principle and static twist, torsional
and longitudinal vibrations of nanobeam-like structures (such as nanorods), as well as
dynamics of an axially moving nanorod were investigated in detail. Both analytical
and numerical solutions are presented in this thesis. The results conclude that
deflection decreases, or natural frequency (or structure stiffness) increases, with
increase in nonlocal effects based on the exact nonlocal model.
The results reported in this study are expected to be useful for designing NEMS
or some other nanoscale devices using nanobeam-like structures.|
|Online Catalog Link: ||http://lib.cityu.edu.hk/record=b4086362|
|Appears in Collections:||BC - Doctor of Philosophy |
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