Abstract: This paper studies mechanical buckling of
functionally graded beams subjected to axial compressive load that is
simply supported at both ends lies on a continuous elastic foundation.
The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. Applying the Hamilton's principle, the
equilibrium equation is established. The influences of dimensionless geometrical parameter, functionally graded index and foundation
coefficient on the critical buckling load of beam are presented. To investigate the accuracy of the present analysis, a compression study
is carried out with a known data.
Abstract: The flexible follower response of a translating cam with
four different profiles for rise-dwell-fall-dwell (RDFD) motion is
investigated. The cycloidal displacement motion, the modified
sinusoidal acceleration motion, the modified trapezoidal acceleration
motion, and the 3-4-5 polynomial motion are employed to describe the
rise and the fall motions of the follower and the associated four kinds of
cam profiles are studied. Since the follower flexibility is considered,
the contact point of the roller and the cam is an unknown. Two
geometric constraints formulated to restrain the unknown position are
substituted into Hamilton-s principle with Lagrange multipliers.
Applying the assumed mode method, one can obtain the governing
equations of motion as non-linear differential-algebraic equations. The
equations are solved using Runge-Kutta method. Then, the responses of
the flexible follower undergoing the four different motions are
investigated in time domain and in frequency domain.
Abstract: In the present article, nonlinear vibration analysis of
single layer graphene sheets is presented and the effect of small
length scale is investigated. Using the Hamilton's principle, the three
coupled nonlinear equations of motion are obtained based on the von
Karman geometrical model and Eringen theory of nonlocal
continuum. The solutions of Free nonlinear vibration, based on a one
term mode shape, are found for both simply supported and clamped
graphene sheets. A complete analysis of graphene sheets with
movable as well as immovable in-plane conditions is also carried out.
The results obtained herein are compared with those available in the
literature for classical isotropic rectangular plates and excellent
agreement is seen. Also, the nonlinear effects are presented as
functions of geometric properties and small scale parameter.
Abstract: In this paper smooth trajectories are computed in the Lie group SO(2, 1) as a motion planning problem by assigning a Frenet frame to the rigid body system to optimize the cost function of the elastic energy which is spent to track a timelike curve in Minkowski space. A method is proposed to solve a motion planning problem that minimizes the integral of the Lorentz inner product of Darboux vector of a timelike curve. This method uses the coordinate free Maximum Principle of Optimal control and results in the theory of integrable Hamiltonian systems. The presence of several conversed quantities inherent in these Hamiltonian systems aids in the explicit computation of the rigid body motions.
Abstract: In the last decade, energy based control theory has undergone a significant breakthrough in dealing with underactated mechanical systems with two successful and similar tools, controlled Lagrangians and controlled Hamiltanians (IDA-PBC). However, because of the complexity of these tools, successful case studies are lacking, in particular, MIMO cases. The seminal theoretical paper of controlled Lagrangians proposed by Bloch and his colleagues presented a benchmark example–a 4 d.o.f underactuated pendulum on a cart but a detailed and completed design is neglected. To compensate this ignorance, the note revisit their design idea by addressing explicit control functions for a similar device motivated by a vector thrust body hovering in the air. To the best of our knowledge, this system is the first MIMO, underactuated example that is stabilized by using energy based tools at the courtesy of the original design idea. Some observations are given based on computer simulation.
Abstract: In this paper, an analytical approach is used to study the coupled lateral-torsional vibrations of laminated composite beam. It is known that in such structures due to the fibers orientation in various layers, any lateral displacement will produce a twisting moment. This phenomenon is modeled by the bending-twisting material coupling rigidity and its main feature is the coupling of lateral and torsional vibrations. In addition to the material coupling, the effects of shear deformation and rotary inertia are taken into account in the definition of the potential and kinetic energies. Then, the governing differential equations are derived using the Hamilton-s principle and the mathematical model matches the Timoshenko beam model when neglecting the effect of bending-twisting rigidity. The equations of motion which form a system of three coupled PDEs are solved analytically to study the free vibrations of the beam in lateral and rotational modes due to the bending, as well as the torsional mode caused by twisting. The analytic solution is carried out in three steps: 1) assuming synchronous motion for the kinematic variables which are the lateral, rotational and torsional displacements, 2) solving the ensuing eigenvalue problem which contains three coupled second order ODEs and 3) imposing different boundary conditions related to combinations of simply, clamped and free end conditions. The resulting natural frequencies and mode shapes are compared with similar results in the literature and good agreement is achieved.
Abstract: Previous research has demonstrated that negative
attitudes towards people with physical disabilities and obesity are
predicted by a component of perceived vulnerability to disease; germ
aversion. These findings have been suggested as illustrations of an
evolved but over-active mechanism which promotes the avoidance of
pathogen-carrying individuals. To date, this interpretation of attitude
formation has not been explored with regard to people with
intellectual disability, and no attempts have been made to examine
possible mediating factors. This study examined attitudes in 333
adults and demonstrated that the moderate positive relationship
between germ aversion and negative attitudes toward people with
intellectual disability is fully mediated by social dominance
orientation, a general preference for hierarchies and inequalities
among social groups. These findings have implications for the
design of programs which attempt to promote community acceptance
and inclusion of people with disabilities.
Abstract: Let a and b be nonnegative integers with 2 ≤ a < b, and
let G be a Hamiltonian graph of order n with n ≥ (a+b−4)(a+b−2)
b−2 .
An [a, b]-factor F of G is called a Hamiltonian [a, b]-factor if F
contains a Hamiltonian cycle. In this paper, it is proved that G has a
Hamiltonian [a, b]-factor if |NG(X)| > (a−1)n+|X|−1
a+b−3 for every nonempty
independent subset X of V (G) and δ(G) > (a−1)n+a+b−4
a+b−3 .
Abstract: Study of the vibration cylindrical shells made of
a functionally gradient material (FGM) composed of stainless
steel and nickel is important. Material properties are graded in
the thickness direction of the shell according to volume
fraction power law distribution. The objective is to study the
natural frequencies, the influence of constituent volume
fractions and the effects of boundary conditions on the natural
frequencies of the FG cylindrical shell. The study is carried
out using third order shear deformation shell theory. The
governing equations of motion of FG cylindrical shells are
derived based on shear deformation theory. Results are
presented on the frequency characteristics, influence of
constituent volume fractions and the effects of clampedclamped
boundary conditions.
Abstract: Fractional Fourier Transform, which is a
generalization of the classical Fourier Transform, is a powerful tool
for the analysis of transient signals. The discrete Fractional Fourier
Transform Hamiltonians have been proposed in the past with varying
degrees of correlation between their eigenvectors and Hermite
Gaussian functions. In this paper, we propose a new Hamiltonian for
the discrete Fractional Fourier Transform and show that the
eigenvectors of the proposed matrix has a higher degree of
correlation with the Hermite Gaussian functions. Also, the proposed
matrix is shown to give better Fractional Fourier responses with
various transform orders for different signals.
Abstract: In the present work, study of the vibration of thin cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. Material properties are graded in the thickness direction of the shell according to volume fraction power law distribution. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of boundary conditions on the natural frequencies of the FG cylindrical shell. The study is carried out using third order shear deformation shell theory. The analysis is carried out using Hamilton's principle. The governing equations of motion of FG cylindrical shells are derived based on shear deformation theory. Results are presented on the frequency characteristics, influence of constituent volume fractions and the effects of clamped-free boundary conditions
Abstract: In this paper by using the port-controlled Hamiltonian
(PCH) systems theory, a full-order nonlinear controlled model is first
developed. Then a nonlinear passivity-based robust adaptive control
(PBRAC) of switched reluctance motor in the presence of external
disturbances for the purpose of torque ripple reduction and
characteristic improvement is presented. The proposed controller
design is separated into the inner loop and the outer loop controller.
In the inner loop, passivity-based control is employed by using
energy shaping techniques to produce the proper switching function.
The outer loop control is employed by robust adaptive controller to
determine the appropriate Torque command. It can also overcome the
inherent nonlinear characteristics of the system and make the whole
system robust to uncertainties and bounded disturbances. A 4KW 8/6
SRM with experimental characteristics that takes magnetic saturation
into account is modeled, simulation results show that the proposed
scheme has good performance and practical application prospects.
Abstract: Modeling and vibration of a flexible link manipulator
with tow flexible links and rigid joints are investigated which can
include an arbitrary number of flexible links. Hamilton principle and
finite element approach is proposed to model the dynamics of
flexible manipulators. The links are assumed to be deflection due to
bending. The association between elastic displacements of links is
investigated, took into account the coupling effects of elastic motion
and rigid motion. Flexible links are treated as Euler-Bernoulli beams
and the shear deformation is thus abandoned. The dynamic behavior
due to flexibility of links is well demonstrated through numerical
simulation. The rigid-body motion and elastic deformations are
separated by linearizing the equations of motion around the rigid
body reference path. Simulation results are shown on for both
position and force trajectory tracking tasks in the presence of varying
parameters and unknown dynamics remarkably well. The proposed
method can be used in both dynamic simulation and controller
design.
Abstract: Let G be a Hamiltonian graph. A factor F of G is called
a Hamiltonian factor if F contains a Hamiltonian cycle. In this paper,
two sufficient conditions are given, which are two neighborhood
conditions for a Hamiltonian graph G to have a Hamiltonian factor.
Abstract: Motion control of flexible arms is more difficult than
that of rigid arms, however utilizing its dynamics enables improved
performance such as a fast motion in short operation time. This paper
investigates a ball throwing robot with one rigid link and one flexible
link. This robot throws a ball at a set speed with a proper control torque.
A mathematical model of this ball throwing robot is derived through
Hamilton’s principle. Several patterns of torque input are designed and
tested through the proposed simulation models. The parameters of
each torque input pattern is optimized and determined by chaos
embedded vector evaluated particle swarm optimization (CEVEPSO).
Then, the residual vibration of the manipulator after throwing is
suppressed with input shaping technique. Finally, a real experiment is
set up for the model checking.
Abstract: In this paper a study on the vibration of thin
cylindrical shells with ring supports and made of functionally graded
materials (FGMs) composed of stainless steel and nickel is presented.
Material properties vary along the thickness direction of the shell
according to volume fraction power law. The cylindrical shells have
ring supports which are arbitrarily placed along the shell and impose
zero lateral deflections. The study is carried out based on third order
shear deformation shell theory (T.S.D.T). The analysis is carried out
using Hamilton-s principle. The governing equations of motion of
FGM cylindrical shells are derived based on shear deformation
theory. Results are presented on the frequency characteristics,
influence of ring support position and the influence of boundary
conditions. The present analysis is validated by comparing results
with those available in the literature.
Abstract: In this paper a study on the vibration of thin
cylindrical shells with ring supports and made of functionally graded
materials (FGMs) composed of stainless steel and nickel is presented.
Material properties vary along the thickness direction of the shell
according to volume fraction power law. The cylindrical shells have
ring supports which are arbitrarily placed along the shell and impose
zero lateral deflections. The study is carried out based on third order
shear deformation shell theory (T.S.D.T). The analysis is carried out
using Hamilton-s principle. The governing equations of motion of
FGM cylindrical shells are derived based on shear deformation
theory. Results are presented on the frequency characteristics,
influence of ring support position and the influence of boundary
conditions. The present analysis is validated by comparing results
with those available in the literature.
Abstract: We propose the use of magneto-optic Kerr effect (MOKE) to realize single-qubit quantum gates. We consider longitudinal and polar MOKE in reflection geometry in which the magnetic field is parallel to both the plane of incidence and surface of the film. MOKE couples incident TE and TM polarized photons and the Hamiltonian that represents this interaction is isomorphic to that of a canonical two-level quantum system. By varying the phase and amplitude of the magnetic field, we can realize Hadamard, NOT, and arbitrary phase-shift single-qubit quantum gates. The principal advantage is operation with magnetically non-transparent materials.
Abstract: In present work are considered the scheme of
evaluation the transition probability in quantum system. It is based on
path integral representation of transition probability amplitude and its
evaluation by means of a saddle point method, applied to the part of
integration variables. The whole integration process is reduced to
initial value problem solutions of Hamilton equations with a random
initial phase point. The scheme is related to the semiclassical initial
value representation approaches using great number of trajectories. In
contrast to them from total set of generated phase paths only one path
for each initial coordinate value is selected in Monte Karlo process.
Abstract: Analytical solution of the first-order and third-order
shear deformation theories are developed to study the free vibration
behavior of simply supported functionally graded plates. The
material properties of plate are assumed to be graded in the thickness
direction as a power law distribution of volume fraction of the
constituents. The governing equations of functionally graded plates
are established by applying the Hamilton's principle and are solved
by using the Navier solution method. The influence of side-tothickness
ratio and constituent of volume fraction on the natural
frequencies are studied. The results are validated with the known
data in the literature.