Abstract: The free and forced in-plane vibrations of axially
moving plates are investigated in this work. The plate possesses an
internal damping of which the constitutive relation obeys the
Kelvin-Voigt model, and the excitations are arbitrarily distributed on
two opposite edges. First, the equations of motion and the boundary
conditions of the axially moving plate are derived. Then, the extended
Ritz method is used to obtain discretized system equations. Finally,
numerical results for the natural frequencies and the mode shapes of
the in-plane vibration and the in-plane response of the moving plate
subjected to arbitrary edge excitations are presented. It is observed that
the symmetry class of the mode shapes of the in-plane vibration
disperses gradually as the moving speed gets higher, and the u- and
v-components of the mode shapes belong to different symmetry class.
In addition, large response amplitudes having shapes similar to the
mode shapes of the plate can be excited by the edge excitations at the
resonant frequencies and with the same symmetry class of distribution
as the u-components.
Abstract: In this paper motion analysis on a winding
stair-climbing is investigated using our proposed rotational arm type
of robotic wheelchair. For now, the robotic wheelchair is operated in
an open mode to climb winding stairs by a dynamic turning, therefore,
the dynamics model is required to ensure a passenger-s safety.
Equations of motion based on the skid-steering analysis are developed
for the trajectory planning and motion analysis on climbing winding
stairs. Since the robotic wheelchair must climb a winding staircase
stably, the winding trajectory becomes a constraint equation to be
followed, and the Baumgarte-s method is used to solve for the
constrained dynamics equations. Experimental results validate the
behavior of the prototype as it climbs a winding stair.
Abstract: The integral form of equations of motion of composite
beams subjected to varying time loads are discretized using a
developed finite element model. The model consists of a straight five
node twenty-two degrees of freedom beam element. The stability
analysis of the beams is studied by solving the matrix form
characteristic equations of the system. The principle of virtual work
and the first order shear deformation theory are employed to analyze
the beams with large deformation and small strains. The regions of
dynamic instability of the beam are determined by solving the
obtained Mathieu form of differential equations. The effects of nonconservative
loads, shear stiffness, and damping parameters on
stability and response of the beams are examined. Several numerical
calculations are presented to compare the results with data reported
by other researchers.
Abstract: A full six degrees of freedom (6-DOF) flight dynamics
model is proposed for the accurate prediction of short and long-range
trajectories of high spin and fin-stabilized projectiles via atmospheric
flight to final impact point. The projectiles is assumed to be both rigid
(non-flexible), and rotationally symmetric about its spin axis launched
at low and high pitch angles. The mathematical model is based on the
full equations of motion set up in the no-roll body reference frame and
is integrated numerically from given initial conditions at the firing
site. The projectiles maneuvering motion depends on the most
significant force and moment variations, in addition to wind and
gravity. The computational flight analysis takes into consideration the
Mach number and total angle of attack effects by means of the
variable aerodynamic coefficients. For the purposes of the present
work, linear interpolation has been applied from the tabulated database
of McCoy-s book. The developed computational method gives
satisfactory agreement with published data of verified experiments and
computational codes on atmospheric projectile trajectory analysis for
various initial firing flight conditions.
Abstract: A two dimensional three segments coupled pendulum system that mathematically models human arm configuration was developed along with constructing and solving the equations of motions for this model using the energy (work) based approach of Lagrange. The equations of motion of the model were solved iteratively both as an initial value problem and as a two point boundary value problem. In the initial value problem solutions, both the initial system configuration (segment angles) and initial system velocity (segment angular velocities) were used as inputs, whereas, in the two point boundary value problem solutions initial and final configurations and time were used as inputs to solve for the trajectory of motion. The results suggest that the model solutions are sensitive to small changes in the dynamic forces applied to the system as well as to the initial and boundary conditions used. To overcome the system sensitivity a new approach is suggested.
Abstract: Analytical seismic response of multi-story building
supported on base isolation system is investigated under real
earthquake motion. The superstructure is idealized as a shear type
flexible building with lateral degree-of-freedom at each floor. The
force-deformation behaviour of the isolation system is modelled by
the bi-linear behaviour which can be effectively used to model all
isolation systems in practice. The governing equations of motion of
the isolated structural system are derived. The response of the system
is obtained numerically by step-by-method under three real recorded
earthquake motions and pulse motions associated in the near-fault
earthquake motion. The variation of the top floor acceleration, interstory
drift, base shear and bearing displacement of the isolated
building is studied under different initial stiffness of the bi-linear
isolation system. It was observed that the high initial stiffness of the
isolation system excites higher modes in base-isolated structure and
generate floor accelerations and story drift. Such behaviour of the
base-isolated building especially supported on sliding type of
isolation systems can be detrimental to sensitive equipment installed
in the building. On the other hand, the bearing displacement and base
shear found to reduce marginally with the increase of the initial
stiffness of the initial stiffness of the isolation system. Further, the
above behaviour of the base-isolated building was observed for
different parameters of the bearing (i.e. post-yield stiffness and
characteristic strength) and earthquake motions (i.e. real time history
as well as pulse type motion).
Abstract: This paper deals with a numerical analysis of the
transient response of composite beams with strain rate dependent
mechanical properties by use of a finite difference method. The
equations of motion based on Timoshenko beam theory are derived.
The geometric nonlinearity effects are taken into account with von
Kármán large deflection theory. The finite difference method in
conjunction with Newmark average acceleration method is applied to
solve the differential equations. A modified progressive damage
model which accounts for strain rate effects is developed based on
the material property degradation rules and modified Hashin-type
failure criteria and added to the finite difference model. The
components of the model are implemented into a computer code in
Mathematica 6. Glass/epoxy laminated composite beams with
constant and strain rate dependent mechanical properties under
dynamic load are analyzed. Effects of strain rate on dynamic
response of the beam for various stacking sequences, load and
boundary conditions are investigated.