Abstract: In this paper, longitudinal vibration of a micro-beam in micro-scale fluid media has been investigated. The proposed mathematical model for this study is made up of a micro-beam and a micro-plate at its free end. An AC voltage is applied to the pair of piezoelectric layers on the upper and lower surfaces of the micro-beam in order to actuate it longitudinally. The whole structure is bounded between two fixed plates on its upper and lower surfaces. The micro-gap between the structure and the fixed plates is filled with fluid. Fluids behave differently in micro-scale than macro, so the fluid field in the gap has been modeled based on micro-polar theory. The coupled governing equations of motion of the micro-beam and the micro-scale fluid field have been derived. Due to having non-homogenous boundary conditions, derived equations have been transformed to an enhanced form with homogenous boundary conditions. Using Galerkin-based reduced order model, the enhanced equations have been discretized over the beam and fluid domains and solve simultaneously in order to obtain force response of the micro-beam. Effects of micro-polar parameters of the fluid as characteristic length scale, coupling parameter and surface parameter on the response of the micro-beam have been studied.
Abstract: Electrical current measurement is a suitable method for the performance determination of electrical devices. There are two contact and noncontact methods in this measuring process. Contact method has some disadvantages like having direct connection with wire which may endamage the system. Thus, in this paper, a bimorph piezoelectric cantilever beam which has a permanent magnet on its free end is used to measure electrical current in a noncontact way. In mathematical modeling, based on Galerkin method, the governing equation of the cantilever beam is solved, and the equation presenting the relation between applied force and beam’s output voltage is presented. Magnetic force resulting from current carrying wire is considered as the external excitation force of the system. The results are compared with other references in order to demonstrate the accuracy of the mathematical model. Finally, the effects of geometric parameters on the output voltage and natural frequency are presented.
Abstract: In this paper, vibration of a nonlinear composite beam is analyzed and then an active controller is used to control the vibrations of the system. The beam is resting on a Winkler-Pasternak elastic foundation. The composite beam is reinforced by single walled carbon nanotubes. Using the rule of mixture, the material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are determined. The beam is cantilever and the free end of the beam is under follower force. Piezoelectric layers are attached to the both sides of the beam to control vibrations as sensors and actuators. The governing equations of the FG-CNTRC beam are derived based on Euler-Bernoulli beam theory Lagrange- Rayleigh-Ritz method. The simulation results are presented and the effects of some parameters on stability of the beam are analyzed.
Abstract: Lateral torsional buckling is a global buckling mode
which should be considered in design of slender structural members
under flexure about their strong axis. It is possible to compute the
load which causes lateral torsional buckling of a beam by finite
element analysis, however, closed form equations are needed in
engineering practice for calculation ease which can be obtained by
using energy method. In lateral torsional buckling applications of
energy method, a proper function for the critical lateral torsional
buckling mode should be chosen which can be thought as the
variation of twisting angle along the buckled beam. Accuracy of the
results depends on how close is the chosen function to the exact
mode. Since critical lateral torsional buckling mode of the cantilever
I-beams varies due to material properties, section properties and
loading case, the hardest step is to determine a proper mode function
in application of energy method. This paper presents an approximate function for critical lateral
torsional buckling mode of doubly symmetric cantilever I-beams.
Coefficient matrices are calculated for concentrated load at free end,
uniformly distributed load and constant moment along the beam
cases. Critical lateral torsional buckling modes obtained by presented
function and exact solutions are compared. It is found that the modes
obtained by presented function coincide with differential equation
solutions for considered loading cases.
Abstract: Composite materials, due to their unique properties
such as high strength to weight ratio, corrosion resistance, and impact
resistance have huge potential as structural materials in automotive,
construction and transportation applications. However, these
properties often come at higher cost owing to complex design
methods, difficult manufacturing processes and raw material cost.
Traditionally, tapered laminated composite structures are
manufactured using autoclave manufacturing process by ply drop off
technique. Autoclave manufacturing though very powerful suffers
from high capital investment and higher energy consumption. As per
the current trends in composite manufacturing, Out of Autoclave
(OoA) processes are looked as emerging technologies for
manufacturing the structural composite components for aerospace
and defense applications. However, there is a need for improvement
among these processes to make them reliable and consistent. In this
paper, feasibility of using out of autoclave process to manufacture the
variable thickness cantilever beam is discussed. The minimum weight
design for the composite beam is obtained using constant stress beam
concept by tailoring the thickness of the beam. Ply drop off
techniques was used to fabricate the variable thickness beam from
glass/epoxy prepregs. Experiments were conducted to measure
bending stresses along the span of the cantilever beam at different
intervals by applying the concentrated load at the free end.
Experimental results showed that the stresses in the bean at different
intervals were constant. This proves the ability of OoA process to
manufacture the constant stress beam. Finite element model for the
constant stress beam was developed using commercial finite element
simulation software. It was observed that the simulation results
agreed very well with the experimental results and thus validated
design and manufacturing approach used.
Abstract: Excavation and retaining walls are of challenging
issues in civil engineering. In this study, the behavior of one
important type of supporting systems called Contiguous Bored Pile
(CBP) retaining wall is investigated using a physical model. Besides,
a comparison is made between two modes of free end piles (soft bed)
and fixed end piles (stiff bed). Also a back calculation of effective
length (the real free length of pile) is done by measuring lateral
deflection of piles in different stages of excavation in both
aforementioned cases. Based on observed results, for the fixed end
mode, the effective length to free length ratio (Leff/L0) is equal to
unity in initial stages of excavation and less than 1 in its final stages
in a decreasing manner. While this ratio for free end mode, remains
constant during all stages of excavation and is always less than unity.
Abstract: This paper deals with the design of a periodic output
feedback controller for a flexible beam structure modeled with
Timoshenko beam theory, Finite Element Method, State space
methods and embedded piezoelectrics concept. The first 3 modes are
considered in modeling the beam. The main objective of this work is
to control the vibrations of the beam when subjected to an external
force. Shear piezoelectric sensors and actuators are embedded into
the top and bottom layers of a flexible aluminum beam structure, thus
making it intelligent and self-adaptive. The composite beam is
divided into 5 finite elements and the control actuator is placed at
finite element position 1, whereas the sensor is varied from position 2
to 5, i.e., from the nearby fixed end to the free end. 4 state space
SISO models are thus developed. Periodic Output Feedback (POF)
Controllers are designed for the 4 SISO models of the same plant to
control the flexural vibrations. The effect of placing the sensor at
different locations on the beam is observed and the performance of
the controller is evaluated for vibration control. Conclusions are
finally drawn.
Abstract: Active vibration control is an important problem in
structures. The objective of active vibration control is to reduce the vibrations of a system by automatic modification of the system-s
structural response. In this paper, the modeling and design of a fast
output sampling feedback controller for a smart flexible beam system embedded with shear sensors and actuators for SISO system using
Timoshenko beam theory is proposed. FEM theory, Timoshenko beam theory and the state space techniques are used to model the
aluminum cantilever beam. For the SISO case, the beam is divided into 5 finite elements and the control actuator is placed at finite
element position 1, whereas the sensor is varied from position 2 to 5, i.e., from the nearby fixed end to the free end. Controllers are
designed using FOS method and the performance of the designed FOS controller is evaluated for vibration control for 4 SISO models
of the same plant. The effect of placing the sensor at different locations on the beam is observed and the performance of the
controller is evaluated for vibration control. Some of the limitations of the Euler-Bernoulli theory such as the neglection of shear and
axial displacement are being considered here, thus giving rise to an accurate beam model. Embedded shear sensors and actuators have
been considered in this paper instead of the surface mounted sensors
and actuators for vibration suppression because of lot of advantages. In controlling the vibration modes, the first three dominant modes of
vibration of the system are considered.
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: A pressure-based implicit procedure to solve Navier-
Stokes equations on a nonorthogonal mesh with collocated finite
volume formulation is used to simulate flow around the smart and
conventional flaps of spoiler under the ground effect. Cantilever
beam with uniformly varying load with roller support at the free end
is considered for smart flaps. The boundedness criteria for this
procedure are determined from a Normalized Variable diagram
(NVD) scheme. The procedure incorporates es the k -ε eddyviscosity
turbulence model. The method is first validated against
experimental data. Then, the algorithm is applied for turbulent
aerodynamic flows around a spoiler section with smart and
conventional flaps for different attack angle, flap angle and ground
clearance where the results of two flaps are compared.