الفهرس 
Nanomechanical SystemOnly 14 pages are availabe for public view
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Abstract
This thesis provides a general formularization of the nonlocal Euler Bernoulli nanobeam model for static and dynamic examination of symmetric
and asymmetric cross-sectional area of nanobeam resting over two types of
linear elastic foundations (Winkler-Pasternak elastic foundations) under effects of different forces such as axial and shear forces, by deeming various boundary conditions types (simple-simple supports, clamped-simple supports And clamped-clamped supports). The governing formulations are dissolved
numerically by Generalized Differential Quadrature Method (GDQM). A deep search analyzes parameters, such as; nonlocal (scaling effect) parameter, nonuniformity of area, presence of two linear elastic foundations (Winkler Pasternak elastic foundations), axial force and distributed load on nanobeam
deflection and vibration, with three different types of supports.
The significant deductions of deflection can be abbreviated as follows; It
was found that the nondimen sional deflection of the nanobeam to be fine with decreasing the scaling effect parameter of nanobeams. Moreover, when the nanobeam is not resting on any elastic foundations, the nondimensional
deflection increases with increasing the scaling effect parameter. Conversely,
when the nanobeam is resting on an elastic foundation, the nondimensional
deflection of the nanobeam decreases as scaling effect parameter is increased.
Also, when the cross-section area of the nanobeam varies parabolically, the
nondimensional deflection of the nonuniform nanobeam decrease in comparisonto when the cross-section area varies linearly. The significant deductions of vibration can be abbreviated as follows; the maximum frequency parameters can be found from a clamped-clamped supported nanobeam with the conditions of high values of elastic constant of spring (K1), coils internal shear coefficient (K2), tension axial force (P) and constants of nonuniformity of beam (C1) and (C2) mentioned above but low values of scaling effect parameter (𝛼). Minimizing the values of frequency parameters can be found through a simple-simple supported nanobeam with the conditions of low values of elastic constant of spring (K1), coils internal shear coefficient (K2), tension axial force (P) and constants of nonuniformity of beam
(C1) and (C2) mentioned above but high values of scaling effect parameter (𝛼).
This thesis provides a general formularization of the nonlocal EulerBernoulli nanobeam model for static and dynamic examination of symmetric and asymmetric cross-sectional area of nanobeam resting over two types of linear elastic foundations (Winkler-Pasternak elastic foundations) under effects of different forces such as axial and shear forces, by deeming various boundary conditions types (simple-simple supports, clamped-simple supports and clamped-clamped supports). The governing formulations are dissolved
numerically by Generalized Differential Quadrature Method (GDQM). A deep search analyzes parameters, such as; nonlocal (scaling effect) parameter, nonuniformity of area, presence of two linear elastic foundations (Winkler Pasternak elastic foundations), axial force and distributed load on nanobeam
deflection and vibration, with three different types of supports.
The significant deductions of deflection can be abbreviated as follows; It
was found that the nondimensional deflection of the nanobeam to be fine with decreasing the scaling effect parameter of nanobeams. Moreover, when the nanobeam is not resting on any elastic foundations, the nondimensional
deflection increases with increasing the scaling effect parameter. Conversely,
when the nanobeam is resting on an elastic foundation, the nondimensional
deflection of the nanobeam decreases as scaling effect parameter is increased.
Also, when the cross-section area of the nanobeam varies parabolically, the
nondimensional deflection of the nonuniform nanobeam decrease in comparison to when the cross-section area varies linearly. The significant deductions of vibration can be abbreviated as follows; the maximum frequency parameters can be found from a clamped-clamped supported nanobeam with the conditions of high values of elastic constant of spring (K1), coils internal shear coefficient (K2), tension axial force (P) and constants of nonuniformity of beam (C1) and (C2) mentioned above but low values of scaling effect parameter (𝛼). Minimizing the values of frequency parameters can be found through a simple-simple supported nanobeam with the conditions of low values of elastic constant of spring (K1), coils internal shear coefficient (K2), tension axial force (P) and constants of nonuniformity of beam
(C1) and (C2) mentioned above but high values of scaling effect parameter (𝛼).
This thesis provides a general formularization of the nonlocal Euler Bernoulli nanobeam model for static and dynamic examination of symmetric
and asymmetric cross-sectional area of nanobeam resting over two types of
linear elastic foundations (Winkler-Pasternak elastic foundations) under effects of different forces such as axial and shear forces, by deeming various boundary conditions types (simple-simple supports, clamped-simple supports and clamped-clamped supports). The governing formulations are dissolved
numerically by Generalized Differential Quadrature Method (GDQM). A deep
search analyzes parameters, such as; nonlocal (scaling effect) parameter,
nonuniformity of area, presence of two linear elastic foundations (Winkler Pasternak elastic foundations), axial force and distributed load on nanobeam
deflection and vibration, with three different types of supports. The significant deductions of deflection can be abbreviated as follows; It was found that the nondimensional deflection of the nanobeam to be fine with decreasing the scaling effect parameter of nanobeams. Moreover, when the
nanobeam is not resting on any elastic foundations, the nondimensional
deflection increases with increasing the scaling effect parameter. Conversely,
when the nanobeam is resting on an elastic foundation, the nondimensional
deflection of the nanobeam decreases as scaling effect parameter is increased.
Also, when the cross-section area of the nanobeam varies parabolically, the nondimensional deflection of the nonuniform nanobeam decrease in comparison to when the cross-section area varies linearly. The significant deductions of vibration can be abbreviated as follows; the maximum frequency parameters can be found from a clamped-clamped supported nanobeam with the conditions of high values of elastic constant of spring (K1), coils internal shear coefficient (K2), tension axial force (P) and constants of nonuniformity of beam (C1) and (C2) mentioned above but low
values of scaling effect parameter (𝛼). Minimizing the values of frequency
parameters can be found through a simple-simple supported nanobeam with the
conditions of low values of elastic constant of spring (K1), coils internal shear
coefficient (K2), tension axial force (P) and constants of nonuniformity of beam
(C1) and (C2) mentioned above but high values of scaling effect parameter (𝛼).
This thesis provides a general formularization of the nonlocal EulerBernoulli nanobeam model for static and dynamic examination of symmetric
and asymmetric cross-sectional area of nanobeam resting over two types of
linear elastic foundations (Winkler-Pasternak elastic foundations) under effects
of different forces such as axial and shear forces, by deeming various boundary
conditions types (simple-simple supports, clamped-simple supports and
clamped-clamped supports). The governing formulations are dissolved
numerically by Generalized Differential Quadrature Method (GDQM). A deep
search analyzes parameters, such as; nonlocal (scaling effect) parameter,
nonuniformity of area, presence of two linear elastic foundations (WinklerPasternak elastic foundations), axial force and distributed load on nanobeam
deflection and vibration, with three different types of supports.
The significant deductions of deflection can be abbreviated as follows; It
was found that the nondimensional deflection of the nanobeam to be fine with
decreasing the scaling effect parameter of nanobeams. Moreover, when the
nanobeam is not resting on any elastic foundations, the nondimensional
deflection increases with increasing the scaling effect parameter. Conversely,
when the nanobeam is resting on an elastic foundation, the nondimensional
deflection of the nanobeam decreases as scaling effect parameter is increased.
Also, when the cross-section area of the nanobeam varies parabolically, the
nondimensional deflection of the nonuniform nanobeam decrease in comparison to when the cross-section area varies linearly. The significant deductions of vibration can be abbreviated as follows; the maximum frequency parameters can be found from a clamped-clamped supported nanobeam with the conditions of high values of elastic constant of spring (K1), coils internal shear coefficient (K2), tension axial force (P) and constants of nonuniformity of beam (C1) and (C2) mentioned above but low values of scaling effect parameter (𝛼). Minimizing the values of frequency parameters can be found through a simple-simple supported nanobeam with the conditions of low values of elastic constant of spring (K1), coils internal shear coefficient (K2), tension axial force (P) and constants of nonuniformity of beam (C1) and (C2) mentioned above but high values of scaling effect parameter (𝛼).