1,721,322 research outputs found
Analytical treatment of the transient motion of inertial beams attached to coupling inertial resonators
Full text linkThis paper presents, for the first time, an analytical formulation to determine the transient response of an elastic beam possessing distributed inertia and connected to a coupling inertial resonator, represented by a gyroscopic spinner. The latter couples the transverse displacement components of the beam in the two perpendicular directions, thus producing roto-flexural vibrations. A detailed parametric study is presented that illustrates the effects of the beam’s distributed inertia and of the resonator’s characteristics. The limit case of massless beam is examined and it is shown that in some situations the distributed inertia in the beam should not be neglected. Analytical results are also validated by finite element computations. An illustration is also presented that demonstrates the effectiveness of using the considered inertial devices to mitigate hazardous vibrations in structural systems. It is envisaged that this paper may be useful in the analysis of flexural waveguides and metamaterials consisting of inertial elastic beam elements
Evaluation of the structural response of reinforced concrete beams failing in flexure under blast loads
No full textIn this paper, the structural responses of reinforced concrete (RC) beams subjected to blast loading are investigated.
In particular, RC beams with a low reinforcement ratio are examined, which are more likely to fail in flexure than in
shear. In order to assess the response of the beam, two analytical approaches are developed. In the first one, the
beam is modeled as a continuous element by means of Euler-Bernoulli’s theory, which neglects the contributions of
shear deformation and rotary inertia. The nonlinear behaviour of the beam in the elastic-plastic range is approximated
by a single smooth relationship between bending moment and curvature, which allows to derive an original
expression of the differential equation of motion of the beam. The parameters appearing in the latter are easily determined
from the geometric and constitutive properties of the beam. The second approach described in this paper
consists in evaluating the response of the beam through an equivalent single degree of freedom (SDOF) system. The
latter is a mass-spring oscillator, and its constitutive behaviour is expressed through a bilateral relationship between
force and displacement. The main drawback of this simplified approach is the need to introduce empirical quantities,
such as the equivalent mass and the length of the plastic hinge. In both approaches, strain rate effects are taken into
account. In fact, these effects should not be ignored in problems concerning blast loads, since the mechanical properties
of both concrete and steel strongly depend on the rate of deformation. In this paper, strain rate effects are considered
by changing the parameters related to the material properties during time, in accordance with the rules provided
by the CEB Information Bulletin n. 187 and the fib Bulletin n. 55. Finally, in order to test the validity of the
two approaches, the theoretical results are compared with some experimental data found in literature. In particular,
the time-histories of the maximum deflections of several simply supported RC beams under uniformly distributed
loads generated by explosions are analyzed. It is shown that the first approach is capable of predicting both the maximum
displacement time-history and the deflection at collapse of any beam accurately. On the other hand, the
second approach gives a less precise assessment of the structural response of the beam; nonetheless, the method
based on the equivalent SDOF model is simpler to use and its differential equation of motion is faster to integrate
Predicting the earthquake ductility demand through a rigid-plastic approach
No full textAssessing the earthquake ductility of seismic resistant structures usually requires a non-linear dynamic analysis involving both elastic and plastic motion of the structure. A simpler way to estimate the inelastic displacements can be neglecting the elastic motion altogether and referring to a rigid-plastic model. The latter may in fact give a good estimate of the maximum plastic displacement for elastoplastic oscillators of a comparatively short period in the elastic range. The same model also bounds the plastic response for sufficiently high periods of the oscillators. For medium-period oscillators, however, the rigid-plastic approximation needs to be corrected. Recently, the authors presented a simple procedure to predict in which ranges of periods the rigid-plastic approximation can be adopted as it stands. Subsequently, they also provided an empirical formula to obtain a suitable correction to apply outside these ranges. Both contributions make the rigid-plastic approach ready to be applied in practice. By referring to some real earthquakes, the present paper applies this approach to various elastoplastic oscillators. The results found show that the rigid-plastic approach proposed by the authors gives quite good –and almost always conservative- predictions of the maximum inelastic displacements of the elastoplastic oscillators
Curve di maggiorazione dell’errore per l’analisi sismica di oscillatori elasto-plastici attraverso il modello rigido-plastico
No full textRigid-Plastic Bound to the Seismic Inelastic Response of Flexible Elastoplastic Oscillators
No full textRigid-plastic models may well approximate the
peak plastic response of igid enough elastoplastic oscillators.
The more flexible the oscillator, however, the less reLiable the
approximation is expected to be. Contrary to this expectation,
the present paper shows thctt, under seismic conditions, a rigidplastic
model may also give a good estimate of the peak plastic
response of quite Jlexible elastoplastic oscillcttors. In particular,
it is shown that the rigid-plastic approximation is even conservative
when the natural period T of the elastoplastic oscillator falls
within a particular range, the ends of which are marked by two
characteristic values. A simple graphical procedure is pntvided
to obtain these characteistic periods directly from the elastic respotlse
spectrum of the earthquake, for a given value of the oscillator
yield acceleration. It spots the range in which the simpler
rigid-plastic model can be adopted to bound the plastic response
of elastopLastic oscillators and the range where, on the contrary,
such a model underestimates the same response. The procedure
also gives the value of the peiod above which the earthquake is
no longer able to produce plastic yielding in elastoplastic oscillators
of a given yield accelerotion. These results can be useful
to estimate the earthquake inelastic demand in a simple way
Rigid-Plastic Seismic Analysis to predict the structural ductility demand
No full textAn earthquake resistant structure will suffer large plastic deformations under
strong ground motions. This paper presents a practical method to evaluate the
maximum plastic displacement of a structure, when the latter is modelled as
an elastoplastic oscillator. The method exploits the results from a rigid-plastic
model possessing the same ratio between yield strength and mass as the actual
elastoplastic oscillator. The rigid-plastic model is shown to give a good
estimate of the maximum plastic displacement of an elastoplastic oscillator
when the natural period of the actual elastoplastic oscillator is comparatively
short or comparatively high. For medium-period oscillators, however, the
rigid-plastic approximation needs to be corrected. The present paper provides
an empirical formula to calculate the required corrections, whatever the
oscillator and the earthquake. This formula leads to a good –and almost
always conservative– estimate of the seismic ductility demand and makes the
rigid-plastic approach readily applicable to seismic design
A better rigid-plastic estimate for earthquake-induced plastic displacements
No full textThe earthquake ductility demand on structures may be predicted by means of a rigid-plastic method, which derives the maximum plastic response of elastic-plastic oscillators from that of a simpler rigid-plastic model. The maximum response of the latter is a purely plastic one and may be obtained from the earthquake rigid-plastic pseudo-spectrum, as a function of the oscillator yield acceleration. The results of a wide investigation presented in this paper show that such a method generally leads to a conservative and reliable enough estimate of the maximum plastic displacements. Small mean errors are in fact found for both comparatively short-period and long-period oscillators. In the medium-period range, however, the rigid-plastic prediction is found to be less satisfactory. This is due to the appliance in that range of an empirical formula, which estimates the discrepancy between the elastic-plastic and the rigid-plastic peak response. To improve the rigid-plastic prediction in the medium-period range, a new semi-empirical formula is derived in the paper which is shown to halve, on average, the error in estimating the earthquake ductility demand on medium-period oscillators. Thanks to the new formula, the mean relative errors are always kept below 15%, whatever the earthquake and the oscillator. This makes the rigid-plastic method competitive with respect to other approximate methods, as discussed in the paper
Localized waves in elastic plates with perturbed honeycomb arrays of constraints
Full text linkIn this paper, we study wave propagation in elastic plates incorporating honeycomb arrays of rigid pins. In particular, we demonstrate that topologically non-trivial band-gaps are obtained by perturbing the honeycomb arrays of pins such that the ratio between the lattice spacing and the distance of pins is less than 3; conversely, a larger ratio would lead to the appearance of trivial stop-bands. For this purpose, we investigate band inversion of modes and calculate the valley Chern numbers associated with the dispersion surfaces near the band opening, since the present problem has analogies with the quantum valley Hall effect. In addition, we determine localized eigenmodes in strips, repeating periodically in one direction, that are subdivided into a topological and a trivial section. Finally, the outcomes of the dispersion analysis are corroborated by numerical simulations, where a time-harmonic point source is applied to a plate with finite arrays of rigid pins to create localized waves immune to backscattering. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'
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