• Smart Structures and Systems
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• v.19 no.1
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• pp.21-31
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• 2017

To control the stochastic vibration of a vibration-sensitive instrument supported on a beam, the beam is designed as a sandwich structure with magneto-rheological visco-elastomer (MRVE) core. The MRVE has dynamic properties such as stiffness and damping adjustable by applied magnetic fields. To achieve better vibration control effectiveness, the optimal bounded parametric control for the MRVE sandwich beam with supported mass under stochastic and deterministic support motion excitations is proposed, and the stochastic and shock vibration suppression capability of the optimally controlled beam with multi-mode coupling is studied. The dynamic behavior of MRVE core is described by the visco-elastic Kelvin-Voigt model with a controllable parameter dependent on applied magnetic fields, and the parameter is considered as an active bounded control. The partial differential equations for horizontal and vertical coupling motions of the sandwich beam are obtained and converted into the multi-mode coupling vibration equations with the bounded nonlinear parametric control according to the Galerkin method. The vibration equations and corresponding performance index construct the optimal bounded parametric control problem. Then the dynamical programming equation for the control problem is derived based on the dynamical programming principle. The optimal bounded parametric control law is obtained by solving the programming equation with the bounded control constraint. The controlled vibration responses of the MRVE sandwich beam under stochastic and shock excitations are obtained by substituting the optimal bounded control into the vibration equations and solving them. The further remarkable vibration suppression capability of the optimal bounded control compared with the passive control and the influence of the control parameters on the stochastic vibration suppression effectiveness are illustrated with numerical results. The proposed optimal bounded parametric control strategy is applicable to smart visco-elastic composite structures under deterministic and stochastic excitations for improving vibration control effectiveness.

• Geomechanics and Engineering
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• v.32 no.2
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• pp.159-177
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• 2023

In the present work, a simple and refined shear deformation theory is used to analyze the effect of visco-elastic foundation on the buckling response of exponentially-gradient sandwich plates under various boundary conditions. The proposed theory includes indeterminate integral variables kinematic with only four generalized parameters, in which no shear correction factor is used. The visco-Pasternak's foundation is taken into account by adding the influence of damping to the usual foundation model which characterized by the linear Winkler's modulus and Pasternak's foundation modulus. The four governing equations for FGM sandwich plates are derived by employing principle of virtual work. To solve the buckling problem, Galerkin's approach is utilized for FGM sandwich plates for various boundary conditions. The analytical solutions for critical buckling loads of several types of powerly graded sandwich plates resting on visco-Pasternak foundations under various boundary conditions are presented. Some numerical results are presented to indicate the effects of inhomogeneity parameter, elastic foundation type, and damping coefficient of the foundation, on the critical buckling loads.

• Structural Engineering and Mechanics
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• v.28 no.2
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• pp.167-188
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• 2008

This study is concerned with the establishment of the characteristic equation of a combined system consisting of a cantilever beam with a tip mass and an in-span visco-elastic helical spring-mass, considering the mass of the helical spring. After obtaining the "exact" characteristic equation of the combined system, by making use of a boundary value problem formulation, the characteristic equation is established via a transfer matrix method, as well. Further, the characteristic equation of a reduced system is obtained as a special case. Then, the characteristic equations are numerically solved for various combinations of the physical parameters. Further, comparison of the results with the massless spring case and the case in which the spring mass is partially considered, reveals the fact that neglecting or considering the mass of the spring partially can cause considerable errors for some combinations of the physical parameters of the system.

• Structural Engineering and Mechanics
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• v.24 no.6
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• pp.741-764
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• 2006

The time-dependent analysis of prestressed concrete bridges built adopting the incremental launching technique is presented. After summarizing the well known results derived from the elastic analysis, the problem is approached in the visco-elastic domain taking into account the effects consequent to the complex load history affecting the structure. In particular, the effects produced by prestressing applied both in the launching phase and after it and by application of imposed displacements and of delayed restraints during the launching phases are carefully investigated through a refined analytical procedure. The reliability of the proposed algorithm is tested by means of comparisons with reference cases for which exact solutions are known. A case study of general interest is then discussed in detail. This case study demonstrates that a purely elastic approach represents a too crude approximation, which is unable to describe the specific character of the problem.

• Structural Engineering and Mechanics
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• v.4 no.6
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• pp.631-644
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• 1996

Geomaterials such as soil and rock are composed of discrete elements of microstructures with different grains and microcracks. The studies of these microstructures are of increasing interest in geophysics and geotechnical engineering relating to underground space development We first show experimental results undertaken for direct observation of microcrack initiation and propagation by using a newly developed experimental system, and next a homogenization method for treating a viscoelastic behavior of a polycrystalline rock.

• Computers and Concrete
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• v.7 no.4
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• pp.317-329
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• 2010

The paper describes localization of deformation in a bar under tensile loading. The material of the bar is considered as non-linear viscous elastic and the bar consists of two symmetric halves. It is assumed that the model represents behavior of the quasi-brittle viscous material under uniaxial tension with different loading rates. Besides that, the bar could represent uniaxial stress-strain law on a single plane of a microplane material model. Non-linear material property is taken from the microplane material model and it is coupled with the viscous damper producing non-linear Maxwell material model. Mathematically, the problem is described with a system of two partial differential equations with a non-linear algebraic constraint. In order to obtain solution, the system of differential algebraic equations is transformed into a system of three partial differential equations. System is subjected to loadings of different rate and it is shown that localization occurs only for high loading rates. Mathematically, in such a case two solutions are possible: one without the localization (unstable) and one with the localization (stable one). Furthermore, mass is added to the bar and in that case the problem is described with a system of four differential equations. It is demonstrated that for high enough loading rates, it is the added mass that dominates the response, in contrast to the viscous and elastic material parameters that dominated in the case without mass. This is demonstrated by several numerical examples.

• Structural Engineering and Mechanics
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• v.15 no.3
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• pp.345-365
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• 2003

The adoption of fibre reinforced polymer (FRP) rebars (whose behaviour is elastic-brittle) in reinforced concrete (RC) cross sections requires the assessment of the influence of time-dependent behaviour of concrete on the load-carrying capacity of these sections. This paper presents a method of computing the load-carrying capacity of sections that are at first submitted to a constant long-term service load and then overloaded up to ultimate load. The method solves first a non-linear visco-elastic problem, and then a non-linear instantaneous analysis up to ultimate load that takes into account the self-equilibrated stress distribution previously computed. This method is then adopted to perform a parametric analysis that shows that creep and shrinkage of concrete increase the load-carrying capacity of the cross section reinforced with FRP and allows for the suggestion of simple design rules.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.16 no.6
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• pp.103-109
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• 2007

With the increase of track density, high rotational speed and the compatibility for various media in optical disk drives, the effective design to vibration reduction is very important for robust operation. Especially when a slim optical disk drive for a notebook PC is excited by a mass-unbalanced disk, internal vibration and its transmission to external case bring about severer problem than that of conventional one. In this paper a design process of a rubber mount in a slim optical disk drive for vibration reduction is presented. The characteristics of rubbery materials - hyper-elastic and visco-elastic - are measured with standard specimens. The static stiffness of a rubber mount was calculated by FEM and the dynamic stiffness is predicted with the static stiffness and the impedance test data of the standard specimen. The transmissibility tests are performed for the purpose of verification of the design process.

• International Journal of Concrete Structures and Materials
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• v.11 no.2
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• pp.261-273
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• 2017

The control of the deformative behaviour of pre-stressed concrete roof elements for a satisfactory service performance is a main issue of their structural design. Slender light-weight wing-shaped roof elements, typical of the European heritage, are particularly sensitive to this problem. The paper presents the results of deformation measurements during storage and of both torsional-flexural and purely flexural load tests carried out on a full-scale 40.5 m long innovative wing-shaped roof element. An element-based simplified integral procedure that de-couples the evolution of the deflection profile with the progressive shortening of the beam is adopted to catch the experimental visco-elastic behaviour of the element and the predictions are compared with normative close-form solutions. A linear 3D fem model is developed to investigate the torsional-flexural behaviour of the member. A mechanical non-linear beam model is used to predict the purely flexural behaviour of the roof member in the pre- and post-cracking phases and to validate the loss prediction of the adopted procedure. Both experimental and numerical results highlight that the adopted analysis method is viable and sound for an accurate simulation of the service behaviour of precast roof elements.

• Structural Engineering and Mechanics
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• v.45 no.1
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• pp.69-93
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• 2013

The present study deals with the dynamics of the flapwise (out-of-plane) vibrations of a rotating, internally damped (Kelvin-Voigt model) tapered Bernoulli-Euler beam carrying a heavy tip mass. The centroid of the tip mass is offset from the free end of the beam and is located along its extended axis. The equation of motion and the corresponding boundary conditions are derived via the Hamilton's Principle, leading to a differential eigenvalue problem. Afterwards, this eigenvalue problem is solved by using Frobenius Method of solution in power series. The resulting characteristic equation is then solved numerically. The numerical results are tabulated for a variety of nondimensional rotational speed, tip mass, tip mass offset, mass moment of inertia, internal damping parameter, hub radius and taper ratio. These are compared with the results of a conventional finite element modeling as well, and excellent agreement is obtained.