Abstract: Hydrodynamic pressures acting on upstream of concrete dams during an earthquake are an important factor in designing and assessing the safety of these structures in Earthquake regions. Due to inherent complexities, assessing exact hydrodynamic pressure is only feasible for problems with simple geometry. In this research, the governing equation of concrete gravity dam reservoirs with effect of fluid viscosity in frequency domain is solved and then compared with that in which viscosity is assumed zero. The results show that viscosity influences the reservoir-s natural frequency. In excitation frequencies near the reservoir's natural frequencies, hydrodynamic pressure has a considerable difference in compare to the results of non-viscose fluid.
Abstract: In this study, a vibration analysis was carried out of
symmetric angle-ply laminated composite plates with and without
square hole when subjected to compressive loads, numerically. A
buckling analysis is also performed to determine the buckling load of
laminated plates. For each fibre orientation, the compression load is
taken equal to 50% of the corresponding buckling load. In the
analysis, finite element method (FEM) was applied to perform
parametric studies, the effects of degree of orthotropy and stacking
sequence upon the fundamental frequencies and buckling loads are
discussed. The results show that the presence of a constant
compressive load tends to reduce uniformly the natural frequencies
for materials which have a low degree of orthotropy. However, this
reduction becomes non-uniform for materials with a higher degree of
orthotropy.
Abstract: Active vibration isolation systems are less commonly
used than passive systems due to their associated cost and power
requirements. In principle, semi-active isolation systems can deliver
the versatility, adaptability and higher performance of fully active
systems for a fraction of the power consumption. Various semi-active
control algorithms have been suggested in the past. This paper
studies the 4DOF model of semi-active suspension performance
controlled by on–off and continuous skyhook damping control
strategy. The frequency and transient responses of model are
evaluated in terms of body acceleration, roll angle and tire deflection
and are compared with that of a passive damper. The results show
that the semi-active system controlled by skyhook strategy always
provides better isolation than a conventional passively damped
system except at tire natural frequencies.
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: The dynamic model of a drill in drilling process was
proposed and investigated in this study. To assure a good drilling quality, the vibration variation on the drill tips during high speed
drilling is needed to be investigated. A pre-twisted beam is used to
simulate the drill. The moving Winkler-Type elastic foundation is used to characterize the tip boundary variation in drilling. Due to the
variation of the drill depth, a time dependent dynamic model for the drill is proposed. Results simulated from this proposed model indicate that an abrupt natural frequencies drop are experienced as the drill tip
tough the workpiece, and a severe vibration is induced. The effects of parameters, e.g. drilling speed, depth, drill size and thrust force on the
drill tip responses studied.
Abstract: An accurate procedure to determine free vibrations of
beams and plates is presented.
The natural frequencies are exact solutions of governing vibration
equations witch load to a nonlinear homogeny system.
The bilinear and linear structures considered simulate a bridge.
The dynamic behavior of this one is analyzed by using the theory of
the orthotropic plate simply supported on two sides and free on the
two others. The plate can be excited by a convoy of constant or
harmonic loads. The determination of the dynamic response of the
structures considered requires knowledge of the free frequencies and
the shape modes of vibrations. Our work is in this context. Indeed,
we are interested to develop a self-consistent calculation of the Eigen
frequencies.
The formulation is based on the determination of the solution of
the differential equations of vibrations. The boundary conditions
corresponding to the shape modes permit to lead to a homogeneous
system. Determination of the noncommonplace solutions of this
system led to a nonlinear problem in Eigen frequencies.
We thus, develop a computer code for the determination of the
eigenvalues. It is based on a method of bisection with interpolation
whose precision reaches 10 -12. Moreover, to determine the
corresponding modes, the calculation algorithm that we develop uses
the method of Gauss with a partial optimization of the "pivots"
combined with an inverse power procedure. The Eigen frequencies
of a plate simply supported along two opposite sides while
considering the two other free sides are thus analyzed. The results
could be generalized with the case of a beam by regarding it as a
plate with low width.
We give, in this paper, some examples of treated cases. The
comparison with results presented in the literature is completely
satisfactory.
Abstract: A method based on the power series solution is proposed to solve the natural frequency of flapping vibration for the rotating inclined Euler beam with constant angular velocity. The vibration of the rotating beam is measured from the position of the corresponding steady state axial deformation. In this paper the governing equations for linear vibration of a rotating Euler beam are derived by the d'Alembert principle, the virtual work principle and the consistent linearization of the fully geometrically nonlinear beam theory in a rotating coordinate system. The governing equation for flapping vibration of the rotating inclined Euler beam is linear ordinary differential equation with variable coefficients and is solved by a power series with four independent coefficients. Substituting the power series solution into the corresponding boundary conditions at two end nodes of the rotating beam, a set of homogeneous equations can be obtained. The natural frequencies may be determined by solving the homogeneous equations using the bisection method. Numerical examples are studied to investigate the effect of inclination angle on the natural frequency of flapping vibration for rotating inclined Euler beams with different angular velocity and slenderness ratio.
Abstract: A new mechanism responsible for structural life
consumption due to resonant fatigue in turbine blades, or vanes, is
presented and explained. A rotating blade or vane in a gas turbine can
change its contour due to erosion and/or material build up, in any of
these instances, the surface pressure distribution occurring on the
suction and pressure sides of blades-vanes can suffer substantial
modification of their pressure and temperatures envelopes and flow
characteristics. Meanwhile, the relative rotation between the blade
and duct vane while the pressurized gas flows and the consequent
wake crossings, will induce a fluctuating thrust force or lift that will
excite the blade.
An actual totally used up set of vane-blade components in a HP
turbine power stage in a gas turbine is analyzed. The blade suffered
some material erosion mostly at the trailing edge provoking a
peculiar surface pressure envelope which evolved as the relative
position between the vane and the blade passed in front of each other.
Interestingly preliminary modal analysis for this eroded blade
indicates several natural frequencies within the aeromechanic power
spectrum, moreover, the highest frequency component is 94% of one
natural frequency indicating near resonant condition.
Independently of other simultaneously occurring fatigue cycles
(such as thermal, centrifugal stresses).
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: In the paper the results of calculations of the dynamic
response of a multi-storey reinforced concrete building to a strong
mining shock originated from the main region of mining activity in
Poland (i.e. the Legnica-Glogow Copper District) are presented. The
representative time histories of accelerations registered in three
directions were used as ground motion data in calculations of the
dynamic response of the structure. Two variants of a numerical model
were applied: the model including only structural elements of the
building and the model including both structural and non-structural
elements (i.e. partition walls and ventilation ducts made of brick). It
turned out that non-structural elements of multi-storey RC buildings
have a small impact of about 10 % on natural frequencies of these
structures. It was also proved that the dynamic response of building
to mining shock obtained in case of inclusion of all non-structural
elements in the numerical model is about 20 % smaller than in case
of consideration of structural elements only. The principal stresses
obtained in calculations of dynamic response of multi-storey building
to strong mining shock are situated on the level of about 30% of
values obtained from static analysis (dead load).
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: A minimal complexity version of component mode
synthesis is presented that requires simplified computer
programming, but still provides adequate accuracy for modeling
lower eigenproperties of large structures and their transient
responses. The novelty is that a structural separation into components
is done along a plane/surface that exhibits rigid-like behavior, thus
only normal modes of each component is sufficient to use, without
computing any constraint, attachment, or residual-attachment modes.
The approach requires only such input information as a few (lower)
natural frequencies and corresponding undamped normal modes of
each component. A novel technique is shown for formulation of
equations of motion, where a double transformation to generalized
coordinates is employed and formulation of nonproportional damping
matrix in generalized coordinates is shown.
Abstract: The paper deals with the analysis of the dynamic
response of footbridges under human - induced dynamic loads.
This is a frequently occurring and often dominant load for
footbridges as it stems from the very purpose of a footbridge - to
convey pedestrian. Due to the emergence of new materials and
advanced engineering technology, slender footbridges are
increasingly becoming popular to satisfy the modern transportation
needs and the aesthetical requirements of the society. These
structures however are always lively with low stiffness, low mass,
low damping and low natural frequencies. As a consequence, they are
prone to vibration induced by human activities and can suffer severe
vibration serviceability problems, particularly in the lateral direction.
Pedestrian bridges are designed according to first and second limit
states, these are the criteria involved in response to static design load.
However, it is necessary to assess the dynamic response of bridge
design load on pedestrians and assess it impact on the comfort of the
user movement. Usually the load is considered a person or a small
group which can be assumed in perfect motion synchronization.
Already one person or small group can excite significant vibration of
the deck. In order to calculate the dynamic response to the movement
of people, designer needs available and suitable computational model
and criteria. For the calculation program ANSYS based on finite
element method was used.
Abstract: In the recent years, functionally gradient materials (FGMs) have gained considerable attention in the high temperature environment applications. In this paper, free vibration of thin functionally graded cylindrical shell with hole composed of stainless steel and zirconia is studied. The mechanical properties vary smoothly and continuously from one surface to the other according to a volume fraction power-law distribution. The Influence of shell geometrical parameters, variations of volume fractions and boundary conditions on natural frequency is considered. The equations of motion are based on strains-displacement relations from Love-s shell theory and Rayleigh method. The results have been obtained for natural frequencies of cylindrical shell with holes for different shape, number and location in this paper.
Abstract: In this paper the Differential Quadrature Method (DQM) is employed to study the coupled lateral-torsional free vibration behavior of the laminated composite beams. In such structures due to the fiber orientations in various layers, the lateral displacement leads to a twisting moment. The coupling of lateral and torsional vibrations is modeled by the bending-twisting material coupling rigidity. In the present study, 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 of the beam. The governing differential equations of motion which form a system of three coupled PDEs are solved numerically using DQ procedure under different boundary conditions consist of the combinations of simply, clamped, free and other end conditions. The resulting natural frequencies and mode shapes for cantilever beam are compared with similar results in the literature and good agreement is achieved.
Abstract: There are lots of different ways to find the natural
frequencies of a rotating system. One of the most effective methods
which is used because of its precision and correctness is the
application of the transfer matrix. By use of this method the entire
continuous system is subdivided and the corresponding differential
equation can be stated in matrix form. So to analyze shaft that is this
paper issue the rotor is divided as several elements along the shaft
which each one has its own mass and moment of inertia, which this
work would create possibility of defining the named matrix. By
Choosing more elements number, the size of matrix would become
larger and as a result more accurate answers would be earned. In this
paper the dynamics of a rotor-bearing system is analyzed,
considering the gyroscopic effect. To increase the accuracy of
modeling the thickness of the disk and bearings is also taken into
account which would cause more complicated matrix to be solved.
Entering these parameters to our modeling would change the results
completely that these differences are shown in the results. As said
upper, to define transfer matrix to reach the natural frequencies of
probed system, introducing some elements would be one of the
requirements. For the boundary condition of these elements, bearings
at the end of the shaft are modeled as equivalent spring and dampers
for the discretized system. Also, continuous model is used for the
shaft in the system. By above considerations and using transfer
matrix, exact results are taken from the calculations. Results Show
that, by increasing thickness of the bearing the amplitude of vibration
would decrease, but obviously the stiffness of the shaft and the
natural frequencies of the system would accompany growth.
Consequently it is easily understood that ignoring the influences of
bearing and disk thicknesses would results not real answers.
Abstract: In this paper, an analytical approach for free vibration
analysis of rectangular and circular membranes is presented. The
method is based on wave approach. From wave standpoint vibration
propagate, reflect and transmit in a structure. Firstly, the propagation
and reflection matrices for rectangular and circular membranes are
derived. Then, these matrices are combined to provide a concise and
systematic approach to free vibration analysis of membranes.
Subsequently, the eigenvalue problem for free vibration of membrane
is formulated and the equation of membrane natural frequencies is
constructed. Finally, the effectiveness of the approach is shown by
comparison of the results with existing classical solution.
Abstract: Study is on the vibration of thin cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. The effects of the FGM configuration are studied by studying the frequencies of FG cylindrical shells. In this case FG cylindrical shell has Nickel on its inner surface and stainless steel on its outer surface. The study is carried out based on third order shear deformation shell theory. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of configurations of the constituent materials on the frequencies. The properties are graded in the thickness direction according to the volume fraction power-law distribution. Results are presented on the frequency characteristics, the influence of the constituent various volume fractions on the frequencies.
Abstract: Responses of the dynamical systems are highly affected by the natural frequencies and it has a huge impact on design and operation of high-rise and high-speed elevators. In the present paper, the variational iteration method (VIM) is employed to investigate better understanding the dynamics of elevator cable as a single-degree-of-freedom (SDOF) swing system. Comparisons made among the results of the proposed closed-form analytical solution, the traditional numerical iterative time integration solution, and the linearized governing equations confirm the accuracy and efficiency of the proposed approach. Furthermore, based on the results of the proposed closed-form solution, the linearization errors in calculating the natural frequencies in different cases are discussed.
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.