•Optimal design of Tuned Mass Damper Inerter for base isolated structures is studied.•A straightforward numerical approach is developed for its optimization.•An analytical solution for the optimal ...design of TMDI parameters is derived.•Analyses are performed using random base excitations and real earthquake records.
In this paper the use of the Tuned Mass Damper Inerter (TMDI) to control the response of base isolated structures under stochastic horizontal base acceleration is examined. Notably, the TMDI, recently introduced as a generalization of the classical Tuned Mass Damper, allows to achieve enhanced performance compared to the other passive vibration control devices. Thus, it represents an ideal alternative for reducing displacements of base isolated structures. To this aim, firstly a straightforward numerical approach is developed for the optimal design of this device considering a white noise base excitation. Further, a simplified analytical solution for the optimal design of TMDI parameters for base isolated structures is proposed minimizing the displacement variance of the corresponding undamped base isolated system. A thorough numerical analysis is performed and related results, in terms of optimal parameters and control performance, are compared with pertinent data obtained by a more computationally demanding iterative optimization procedure on the original damped system, considering both white noise and coloured noise stationary base excitation. Analytical and numerical results are found in good agreement, especially in terms of control performance, thus establishing the reliability and efficiency of the proposed approach. Finally, numerical analyses on a five-story benchmark base isolated structure controlled with an optimally designed TMDI are performed considering real recorded ground motions as base excitation. It is concluded that the TMDI, properly optimized with the proposed procedure, can effectively reduce the response of base isolated structures even under strong earthquakes.
► Fractional model (F.M.) is the proper tool for studying visco-elastic behavior. ► F.M. captures both relaxation and creep tests, requiring only two parameters. ► A power law decay relaxation test, ...needs Caputo’s derivative for constitutive law. ► Good match between creep and/or relaxation tests and the F.M. proposed. ► Two of different polymers have been tested to assess the wide range of using F.M.
In capturing visco-elastic behavior, experimental tests play a fundamental rule, since they allow to build up theoretical constitutive laws very useful for simulating their own behavior. The main challenge is representing the visco-elastic materials through simple models, in order to spread their use. However, the wide used models for capturing both relaxation and creep tests are combinations of simple models as Maxwell and/or Kelvin, that depend on several parameters for fitting both creep and relaxation tests. This paper, following Nutting and Gemant idea of fitting experimental data through a power law function, aims at stressing the validity of fractional model. In fact, as soon as relaxation test is well fitted by power law decay then the fractional constitutive law involving Caputo’s derivative directly appears. It will be shown that fractional model is proper for studying visco-elastic behavior, since it may capture both relaxation and creep tests, requiring the identification of two parameters only. This consideration is assessed by the good agreement between experimental tests on creep and relaxation and the fractional model proposed. Experimental tests, here reported are performed on two polymers having different chemical physical properties such that the fractional model may cover a wide range of visco-elastic behavior.
Fractional visco-elastic Euler–Bernoulli beam Di Paola, M.; Heuer, R.; Pirrotta, A.
International journal of solids and structures,
10/2013, Volume:
50, Issue:
22-23
Journal Article
Peer reviewed
Open access
Aim of this paper is the response evaluation of fractional visco-elastic Euler–Bernoulli beam under quasi-static and dynamic loads. Starting from the local fractional visco-elastic relationship ...between axial stress and axial strain, it is shown that bending moment, curvature, shear, and the gradient of curvature involve fractional operators. Solution of particular example problems are studied in detail providing a correct position of mechanical boundary conditions. Moreover, it is shown that, for homogeneous beam both correspondence principles also hold in the case of Euler–Bernoulli beam with fractional constitutive law. Virtual work principle is also derived and applied to some case studies.
In this work, for the first time, a natural and almost inexpensive filler obtained by grinding the culms of Arundo donax was used to prepare PLA based biocomposites. The composites were prepared by ...melt compounding PLA with A. donax filler (ADF). The influence of the content and size of ADF on the morphology and on the mechanical and thermal properties of PLA–ADF composites was evaluated. Moreover, ADF was extracted from composites to evaluate the effect of processing on morphology and dimensions of the incorporated filler. Furthermore, the experimental elastic moduli of the biocomposites have been fitted, employing two theoretical models, i.e., Hill and Halpin–Tsai.
The results showed that the addition of ADF significantly influenced all the investigated properties. In particular, by increasing the ADF content, both tensile and flexural moduli greatly increased. On the contrary, both tensile and flexural strengths of the filled materials decreased if compared with the neat PLA.
In this paper, the steady-state dynamic response of hysteretic oscillators comprising fractional derivative elements and subjected to harmonic excitation is examined. Notably, this problem may arise ...in several circumstances, as for instance, when structures which inherently exhibit hysteretic behavior are supplemented with dampers or isolators often modeled by employing fractional terms. The amplitude of the steady-state response is determined analytically by using an equivalent linearization approach. The procedure yields an equivalent linear system with stiffness and damping coefficients which are related to the amplitude of the response, but also, to the order of the fractional derivative. Various models of hysteresis, well established in the literature, are considered. Specifically, applications to oscillators with bilinear, Bouc–Wen, and Preisach hysteretic models are reported, and related parameter studies are presented. The derived results are juxtaposed with pertinent numerical data obtained by integrating the original nonlinear fractional order equation of motion. The analytical and the numerical results are found in good agreement, establishing, thus, the accuracy and efficiency of the considered approach.
A Galerkin scheme-based approach is developed for determining the survival probability and first-passage probability of a randomly excited hysteretic systems endowed with fractional derivative ...elements. Specifically, by employing a combination of statistical linearization and of stochastic averaging, the amplitude of the system response is modeled as one-dimensional Markovian Process. In this manner the corresponding backward Kolmogorov equation which governs the evolution of the survival probability of the system is determined. An approximate solution of this equation is sought by employing a Galerkin scheme in which a convenient set of confluent hypergeometric functions is used as an orthogonal basis. This set is well documented in the literature, as it is related to the solution of the first-passage problem of a randomly excited linear oscillator with integer-order derivatives. Applications to oscillators with bilinear, Preisach, and Bouc–Wen hysteretic models are presented. Comparisons with pertinent Monte Carlo simulations data demonstrate the efficiency and reliability of the proposed semi-analytical approach.
In this study, an innovative procedure is presented for the analysis of the static behavior of plates at the micro and nano scale, with arbitrary shape and various boundary conditions. In this ...regard, the well-known Eringen’s nonlocal elasticity theory is used to appropriately model small length scale effects. The proposed mesh-free procedure, namely the Line Element-Less Method (LEM), only requires the evaluation of simple line integrals along the plate boundary parametric equation. Further, variations of appropriately introduced functionals eventually lead to a linear system of algebraic equations in terms of the expansion coefficients of the deflection function. Notably, the proposed procedure yields approximate analytical solutions for general shapes and boundary conditions, and even exact solutions for some plate geometries. In addition, several applications are discussed to show the simplicity and applicability of the procedure, and comparison with pertinent data in the literature assesses the accuracy of the proposed approach.
An innovative procedure is introduced for the identification of the mechanical parameters of orthotropic plates of arbitrary shape, under various boundary conditions, based on vibration data. The ...method employs a combination of a convenient Rayleigh-Ritz approach and Particle-Swarm Optimization to estimate elastic constants of the orthotropic material in a straightforward manner, without requiring computationally demanding iterative Finite Element analyses. Specifically, the pb-2 Rayleigh-Ritz procedure is extended and applied to deal with orthotropic plates, simplifying the approach to more easily treat generic plate shapes, taking advantage of the Green's theorem. The method is then appropriately combined with the Particle-Swarm Optimization procedure to expeditiously identify material parameters based on available vibration data. Several numerical applications are presented to show the reliability of the approach, and comparisons with pertinent results available in the literature demonstrate the efficiency and accuracy of the proposed procedure. The study is then supplemented by experimental tests developed in the Laboratory of Experimental Dynamics at the University of Palermo, Italy. In this context, because of the obvious relevance for modern additive manufacturing processes, vibration tests are performed on several 3D printed stiffened plates. Numerical vis-à-vis experimental data are examined, showing that the proposed procedure accurately capture equivalent orthotropic parameters of the stiffened plates.
► Creep and recovery tests are of interest in order to describe asphalt behavior. ► Experimental creep data follow a power decay law, rather than an exponential one. ► A simple fractional model is ...proposed for predicting creep/recovery behavior. ► A small number of parameters and low computational efforts are needed. ► The model is calibrated on experimental data from laboratory tests.
Prediction of asphalt mixtures’ behavior during their service life is a challenge due to its complexity and sensitivity to environmental and loading conditions. It has been proved that, when subjected to loading conditions comparable with most pavement operating conditions, asphalt mixtures behave as linear visco-elastic (LVE) materials. Traditionally the LVE behavior of bituminous material is modeled via creep/recovery functions. In the past, several rheological models constituted by elastic and viscous elements arranged in series or in parallel (analogical models) have been proposed and specified for both bitumen and asphalt mixtures. The corresponding constitutive laws always involve first order derivatives of time with exponential type solutions but problems in setting parameters arise when both the creep and recovery behavior have to be modeled. In this paper it is shown that experimental creep data follow a power decay law, rather than an exponential one. As a consequence, a simple fractional model is here proposed for predicting creep/recovery behavior of asphalt mixtures with a small number of parameters and low computational efforts with respect to the classical analogical models. The proposed model is then calibrated by a best fitting procedure on experimental data from creep and creep/recovery tests carried out on asphalt mixtures under different load and temperature conditions.
In this paper a new model for the liquid motion within a Tuned Liquid Column Damper (TLCD) device is developed, based on the mathematical tool of fractional calculus. Although the increasing use of ...these devices for structural vibration control, it is shown that existing model does not always lead to accurate prediction of the liquid motion. A better model is then needed for accurate simulation of the behavior of TLCD systems. As regards, it has been demonstrated how correctly including the first linear liquid sloshing mode, through the equivalent mechanical analogy well established in literature, produces numerical results that highly match the corresponding experimental ones. Since the apparent effect of sloshing is the deviation of the natural frequency from the theoretical one, the authors propose a fractional differential equation of motion. The latter choice is supported by the fact that the introduction a fractional derivative of order alpha alters simultaneously both the resonant frequency and the degree of damping of the system. It will be shown, through an extensive experimental analysis, how the proposed model accurately describes liquid surface displacements.
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