Abstract: This work aims to evaluate the free and forced vibration of a beam with two end joints subjected to a concentrated moving mass and a load using the Euler-Bernoulli method. The natural frequency is calculated for different locations of the concentrated mass and load on the beam. The analytical results are verified by the experimental data. The variations of natural frequency as a function of the location of the mass, the effect of the forced frequency on the vibrational amplitude, and the displacement amplitude versus time are investigated. It is discovered that as the concentrated mass moves toward the center of the beam, the natural frequency of the beam and the relative error between experimental and analytical data decreases. There is a close resemblance between analytical data and experimental observations.
Abstract: Role of piezoelectric energy harvesters has gained interest in supplying power for micro devices such as health monitoring sensors. In this study, in order to enhance the piezoelectric energy harvesting in capturing energy from broader range of excitation and to improve the mechanical and electrical responses, bimorph piezoelectric energy harvester beam with magnetic mass attached at the end is presented. In view of overcoming the brittleness of piezo-ceramics, functionally graded piezoelectric layers comprising of both piezo-ceramic and piezo-polymer is employed. The nonlinear equations of motions are derived using energy method and then solved analytically using perturbation scheme. The frequency responses of the forced vibration case are obtained for the near resonance case. The nonlinear dynamic responses of the MEMS scaled functionally graded piezoelectric energy harvester in this paper may be utilized in different design scenarios to increase the efficiency of the harvester.
Abstract: Forced vibration problem of a delaminated beam made of fiber metal laminates is studied in this paper. Firstly, a delamination is considered to divide the beam into four sections. The classic beam theory is assumed to dominate each section. The layers on two sides of the delamination are constrained to have the same deflection. This hypothesis approves the conditions of compatibility as well. Consequently, dynamic response of the beam is obtained by the means of differential transform method (DTM). In order to verify the correctness of the results, a model is constructed using commercial software ABAQUS 6.14. A linear spring with constant stiffness takes the effect of contact between delaminated layers into account. The attained semi-analytical outcomes are in great agreement with finite element analysis.
Abstract: In this paper, a theoretical study on the forced vibration of one degree of freedom system equipped with inerter, working under load-type or displacement-type excitation, is presented. Differential equations of movement are solved under cosinusoidal excitation, and explicit relations for the magnitude, resonant magnitude, phase angle, resonant frequency, and critical frequency are obtained. Influence of the inertance and damping on these dynamic characteristics is clarified. From the obtained results, one concludes that the inerter increases the magnitude of vibration and the phase angle of the damped mechanical system. Moreover, the magnitude ratio and difference of phase angles are not depending on the actual type of excitation. Consequently, such kind of similitude allows for the comparison of various theoretical and experimental results, which can be broadly found in the literature.
Abstract: The present paper deals with the flexural vibrations
of homogeneous, isotropic, generalized micropolar microstretch
thermoelastic thin Euler-Bernoulli beam resonators, due to
Exponential time varying load. Both the axial ends of the
beam are assumed to be at simply supported conditions. The
governing equations have been solved analytically by using Laplace
transforms technique twice with respect to time and space variables
respectively. The inversion of Laplace transform in time domain
has been performed by using the calculus of residues to obtain
deflection.The analytical results have been numerically analyzed with
the help of MATLAB software for magnesium like material. The
graphical representations and interpretations have been discussed
for Deflection of beam under Simply Supported boundary condition
and for distinct considered values of time and space as well. The
obtained results are easy to implement for engineering analysis and
designs of resonators (sensors), modulators, actuators.
Abstract: The objective of this study is to investigate the forced vibration analysis of a planar curved beam lying on elastic foundation by using the mixed finite element method. The finite element formulation is based on the Timoshenko beam theory. In order to solve the problems in frequency domain, the element matrices of two nodded curvilinear elements are transformed into Laplace space. The results are transformed back to the time domain by the well-known numerical Modified Durbin’s transformation algorithm. First, the presented finite element formulation is verified through the forced vibration analysis of a planar curved Timoshenko beam resting on Winkler foundation and the finite element results are compared with the results available in the literature. Then, the forced vibration analysis of a planar curved beam resting on Winkler-Pasternak foundation is conducted.
Abstract: The objective of this research is to develop a general technique so that one may predict the dynamic behaviour of a three-dimensional scale crane model subjected to time-dependent moving point forces by means of conventional finite element computer packages. To this end, the whole scale crane model is divided into two parts: the stationary framework and the moving substructure. In such a case, the dynamic responses of a scale crane model can be predicted from the forced vibration responses of the stationary framework due to actions of the four time-dependent moving point forces induced by the moving substructure. Since the magnitudes and positions of the moving point forces are dependent on the relative positions between the trolley, moving substructure and the stationary framework, it can be found from the numerical results that the time histories for the moving speeds of the moving substructure and the trolley are the key factors affecting the dynamic responses of the scale crane model.
Abstract: This paper presents the results of a Finite Element
based vibration analysis of a solar powered Unmanned Aerial
Vehicle (UAV). The purpose of this paper was to quantify the free
vibration, forced vibration response due to differing point inputs in
order to predict the relative response magnitudes and frequencies at
various wing locations of vibration induced power generators
(magnet in coil) excited by gust and/or control surface pulse-decays
used to help power the flight of the electric UAV. A Fluid Structure
Interaction (FSI) study was performed in order to ascertain pertinent
design stresses and deflections as well as aerodynamic parameters of
the UAV airfoil. The 10 ft span airfoil is modeled using Mylar as the
primary material. Results show that the free mode in bending is 4.8
Hz while the first forced bending mode is on range of 16.2 to 16.7 Hz
depending on the location of excitation. The free torsional bending
mode is 28.3 Hz, and the first forced torsional mode is range of 26.4
to 27.8 Hz, depending on the location of excitation. The FSI results
predict the coefficients of aerodynamic drag and lift of 0.0052 and
0.077, respectively, which matches hand-calculations used to validate
the Finite Element based results. FSI based maximum von Mises
stresses and deflections were found to be 0.282 MPa and 3.4 mm,
respectively. Dynamic pressures on the airfoil range from 1.04 to
1.23 kPa corresponding to velocity magnitudes in range of 22 to 66
m/s.
Abstract: This paper investigates the parametric stability of an
axially moving web subjected to non-uniform in-plane edge
excitations on two opposite, simply-supported edges. The web is
modeled as a viscoelastic plate whose constitutive relation obeys the
Kelvin-Voigt model, and the in-plane edge excitations are expressed
as the sum of a static tension and a periodical perturbation. Due to the
in-plane edge excitations, the moving plate may bring about
parametric instability under certain situations. First, the in-plane
stresses of the plate due to the non-uniform edge excitations are
determined by solving the in-plane forced vibration problem. Then,
the dependence on the spatial coordinates in the equation of transverse
motion is eliminated by the generalized Galerkin method, which
results in a set of discretized system equations in time. Finally, the
method of multiple scales is utilized to solve the set of system
equations analytically if the periodical perturbation of the in-plane
edge excitations is much smaller as compared with the static tension of
the plate, from which the stability boundaries of the moving plate are
obtained. Numerical results reveal that only combination resonances
of the summed-type appear under the in-plane edge excitations
considered in this work.
Abstract: The elastic period has a primary role in the seismic
assessment of buildings. Reliable calculations and/or estimates of the
fundamental frequency of a building and its site are essential during
analysis and design process. Various code formulas based on
empirical data are generally used to estimate the fundamental
frequency of a structure. For existing structures, in addition to code
formulas and available analytical tools such as modal analyses,
various methods of testing including ambient and forced vibration
testing procedures may be used to determine dynamic characteristics.
In this study, the dynamic properties of the 32 buildings located in
the Madinah of Saudi Arabia were identified using ambient motions
recorded at several, spatially-distributed locations within each
building. Ambient vibration measurements of buildings have been
analyzed and the fundamental longitudinal and transverse periods for
all tested buildings are presented. The fundamental mode of vibration
has been compared in plots with codes formulae (Saudi Building
Code, EC8, and UBC1997). The results indicate that measured
periods of existing buildings are shorter than that given by most
empirical code formulas. Recommendations are given based on the
common design and construction practice in Madinah city.
Abstract: This paper presents the scaling laws that provide the
criteria of geometry and dynamic similitude between the full-size
rotor-shaft system and its scale model, and can be used to predict the
torsional vibration characteristics of the full-size rotor-shaft system by
manipulating the corresponding data of its scale model. The scaling
factors, which play fundamental roles in predicting the geometry and
dynamic relationships between the full-size rotor-shaft system and its
scale model, for torsional free vibration problems between scale and
full-size rotor-shaft systems are firstly obtained from the equation of
motion of torsional free vibration. Then, the scaling factor of external
force (i.e., torque) required for the torsional forced vibration problems
is determined based on the Newton’s second law. Numerical results
show that the torsional free and forced vibration characteristics of a
full-size rotor-shaft system can be accurately predicted from those of
its scale models by using the foregoing scaling factors. For this reason,
it is believed that the presented approach will be significant for
investigating the relevant phenomenon in the scale model tests.