1,721,024 research outputs found
Free vibrations of simply supported double plate on two models of elastic soils
No full textIn this paper the free vibrations of simply supported rectangular plates, resting on two different models
of soils, are considered. The first model called Het ́enyi, by the name of the deviser, assumes a continuous
plate, embedded in a Winkler-type soil to realize the foundation partial continuity. The upper plate rests
on a multiple layer characterized by a Winkler-type soil, a continuous plate and another Winkler-type
soil in sequence. The two Winkler-type soils have different modules. In the second model, the plate will
be embedded in two layers of soils, whose behavior is similar to that of the Pasternak–Kerr-type soil.
The two models have been already used for the study of the double beam system. The free motions, in
both cases, are described by a homogeneous set of partial differential equations, based on Kirchhoff–Love
theory. Next, the homogeneous equations of motion are solved by using the classical Navier method. The
free frequencies and associated vibration mode shapes of double plate system are found and numerical
examples are illustrated to compare the two models
HAMILTON PRINCIPLE FOR SWCN AND A MODIFIED APPROACH FOR NONLOCAL FREQUENCY ANALYSIS OF NANOSCALE BIOSENSOR
No full textIn the present paper, the free vibration response of single-walled carbon nanotubes (SWCNTs) is investigated. The governing equations of motion are derived using a variation approach and the free vibration frequencies are obtained employing two different formulations. In the first part of the paper, the case of the cantilever nanotube with concentrated mass at its free end, in the presence of nonlocal effects, is considered and the Hamilton principle is reformulated, in order to find the equation of motion and the boundary conditions; it turns out that they are the same
limit conditions obtained by Reddy and Pang, using a direct approach. In the second one, instead, by employing two different approaches two approximate formulas are deduced the first
one is derived by applying the Rayleigh Principle, as defined to Meirovitch, whereas the second approximate formula is derived by a formulation given in energy terms.
Numerical examples end the paper and some comparisons with existing results are offered.
Comparisons of the present numerical results with those from the open literature show an excellent agreement
Free Vibration Analysis of DWCNTs Using CDM and Rayleigh-Schmidt Based on Nonlocal Euler-Bernoulli Beam Theory
No full textThe free vibration response of double-walled carbon nanotubes (DWCNTs) is investigated. The DWCNTs are modelled as two
beams, interacting between them through the van der Waals forces, and the nonlocal Euler-Bernoulli beam theory is used. The
governing equations of motion are derived using a variational approach and the free frequencies of vibrations are obtained
employing two different approaches. In the first method, the two double-walled carbon nanotubes are discretized by means of
the so-called “cell discretization method” (CDM) in which each nanotube is reduced to a set of rigid bars linked together by elastic
cells. The resulting discrete system takes into account nonlocal effects, constraint elasticities, and the van der Waals forces. The
second proposed approach, belonging to the semianalytical methods, is an optimized version of the classical Rayleigh quotient, as
proposed originally by Schmidt. The resulting conditions are solved numerically. Numerical examples end the paper, in which the
two approaches give lower-upper bounds to the true values, and some comparisons with existing results are offered. Comparisons
of the present numerical results with those from the open literature show an excellent agreement
NON-CLASSICAL BOUNDARY CONDITIONS AND DQM FOR DOUBLE-BEAMS
No full textThe present paper deals with the free vibrations of parallel double-beams joined by a Winkler-type homogeneous elastic
foundation. The numerical approach adopted for solving two partial differential equations system is the differential quadrature
method (henceforth DQM). A first-rate description of this approach has been furnished by Bert et al. (1996) and
Chen et al. [Chen, W., Stritz, A.G., Bert, C.W., 1997. A new approach to the differential quadrature method for
fourth-order equations. Int. J. Numer. Meth. Eng. 40, 1941–1956]; a modified version of this method has been proposed
by De Rosa and Franciosi (1998). In this paper the differential quadrature method is applied to finding free vibrations of
beams system having to the ends translation and rotation elastic constraints. The free vibration frequencies for some classical
and non-conventional cases are determined
Free vibration analysis of SWCNT using CDM in the presence of nonlocal effect.
No full textThis paper deals with the free vibration analysis of single-walled carbon nanotube (SWCNT) bounded at the ends, with translational and elastic constraints, and attached mass. The nanotube is modelled as a beam and the effect of small length scale based on the nonlocal elasticity theory is considered. The governing equations of motion are derived using a variational approach and the free frequencies of vibrations are obtained employing the cell
discretization method (CDM) in which the nanotube is reduced to a set of rigid bars linked together by elastic cells. The resulting discrete system takes into account nonlocal effects,
constraint elasticities and added mass. The natural frequencies and corresponding shift frequencies are calculated and numerical results for different boundary conditions are illustrated. Comparisons of the present numerical results with those from the open literature show an excellent agreement
Dynamic analysis of a column under axial load and a concentrated mass with rotational inertia at the top
No full text- …
