1,721,194 research outputs found
Optimal control of base-isolated systems with sliding TLCD under stochastic process
No full textIn this study, an innovative hybrid passive vibration control strategy, combining a base-isolated (BI) structure with a novel sliding version of a Tuned Liquid Column Damper (STLCD) to enhance the dynamic performance of BI structures, is explored from both theoretical and experimental perspectives. In contrast to conventional fixed TLCDs, the proposed STLCD consists of a U-shaped tank partially filled with water, mounted on a roller support, and linked to the BI subsystem through a spring-dashpot system. This configuration results in a more versatile tuning procedure utilizing the spring for tuning and obtaining supplementary damping through the dashpot. The optimal design of the STLCD device is discussed assuming a Gaussian white noise process as base excitation and the credibility of the presented mathematical formulation is assessed through a shaking table testing campaign, carried out at the Laboratory of Experimental Dynamics at the University of Palermo (Italy). For the experimentation, a reduced-scale model of a BI structure with the integrated STLCD is constructed, and its effectiveness is experimentally evaluated. Finally, comparisons to traditional TLCDs and TMDs are presented, emphasizing control efficiency and the reduction of base displacement in the BI syste
Optimal design of inerter-based absorbers with amplified inertance: from the improved tuned liquid column damper inerter (ITLCDI) to the improved tuned mass damper inerter (ITMDI) and improved tuned inerter damper (ITID)
No full textThis paper presents the optimal design of improved inerter-based absorbers to effectively mitigate vibrations in structural systems. The improvement of the inerter is achieved by integrating it within a rhombus truss, composed of rigid rods interconnected by hinges. This arrangement exploits the geometrical amplification effect to enhance inertial properties, thus leading to superior control performance. Specifically, both ends of the inerter are anchored to opposite points along one diagonal of the rhombus, while along the other diagonal, one end is grounded, and the other is linked to the structural system itself or other mechanical systems. The motion of these systems triggers the activation of the inerter, contributing to vibration dissipation. Previous studies have combined this improved inerter with a spring-dashpot unit proposing the so-called Improved Tuned Inerter Damper (ITID). Extending prior research, this study integrates the improved inerter with common passive control devices, such as the Tuned Liquid Column Damper (TLCD) and Tuned Mass Damper (TMD), resulting in the development of the novel Improved Tuned Liquid Column Damper Inerters (ITLCDI) and Improved Tuned Mass Damper Inerter (ITMDI). The optimal calibration for the ITLCDI through an analytical approach is presented, assuming stochastic processes for modeling seismic actions. Furthermore, it discusses how the ITLCDI configuration can be adapted to yield the ITMDI and ITID configurations, providing closed-form solutions for all three absorbers. Validation of the proposed method is performed through numerical simulations, with a thorough analysis conducted to assess the effectiveness of the ITLCDI relative to the ITMDI and ITID configurations
Mellin transform for the probabilistic characterization of random variables and stochastic processes
Full text linkThe probabilistic characterization of random variables and stochastic processes involves the evaluation of the probability density function or characteristic function. The latter is typically obtained by using integer-order statistical moments, that could lead to divergence problem for high-order moments especially in case of heavy-tailed distributions, such as the distribution of the α-stable random variables. On the other hand, recent approaches that use complex fractional moments, offer a more robust probabilistic description, but for particular cases. In this paper, a novel approach based on Mellin transform for the probabilistic characterization of random variables is proposed. Starting from numerical data, this approach is effective for the evaluation of both the probability density function and the characteristic function, and then is valid for a wide class of random variables. Further, an extension of the approach from random variables to stochastic processes is proposed. The reliability of the proposed approach is assessed through several numerical simulations involving α-stable distributions, Gaussian distributions and α-stable stochastic processes
Line element-less method (LEM) for arbitrarily shaped nonlocal nanoplates: exact and approximate analytical solutions
Full text linkThis paper presents an innovative procedure for the analysis of nonlocal plates with arbitrary shape and various boundary conditions. In this regard, the Eringen’s nonlocal model is used to capture small length scale effects. The proposed procedure, referred to as Line ElementLess Method (LEM), is a completely meshfree approach requiring the evaluations of simple line integrals along the plate boundary parametric equation. Further, the deflection function is represented by a series expansion is terms of harmonic polynomials whose coefficients are found by performing variations of appropriately introduced functionals, leading to a linear system of algebraic. Notably, the proposed procedure yields approximate analytical solutions for general shapes and boundary conditions, and even exact solutions for some plate geometries
Efficient path integral approach via analytical asymptotic expansion for nonlinear systems under Gaussian white noise
Full text linkIn this paper an efficient formulation of the Path integral (PI) approach is developed for determining the response probability density functions (PDFs) and first-passage statistics of nonlinear oscillators subject to stationary and time-modulated external Gaussian white noise excitations. Specifically, the evolution of the response PDF is obtained in short time steps, by using a discrete version of the Chapman-Kolmogorov equation and assuming a Gaussian form for the conditional response PDF. Next, the technique involves proceeding to treating the problem via an analytical asymptotic expansion procedure, namely the Laplace’s method of integration. In this manner, the repetitive double integrals involved in the standard implementation of the PI approach are evaluated in a closed form, while the response and first-passage PDFs are obtained by mundane step-by-step application of the derived approximate analytical expression. It is shown that the herein proposed formulation can drastically decrease the associated computational cost by several orders of magnitude, as compared to both the standard PI technique and Monte Carlo solution (MCS) approach. A number of nonlinear oscillators are considered in the numerical examples. Notably, for these systems both response PDFs and first-passage probabilities are presented, whereas comparisons with pertinent MCS data demonstrate the efficiency and accuracy of the technique
Fokker-Planck equation of the fractional Brownian motion
No full textThe fractional Brownian motion X-beta (t) is the solution of the Sturm-Liouville fractional differential equation of order beta, (with beta a positive real number), enforced by a zero mean normal white noise. The main aim of this paper is to derive the fractional Fokker-Planck equation (FFP) related to the above fractional differential equation. It is shown that FFP is ruled by the fractional derivative of order 2H, with Hurst index H = beta-1/2. This means that the diffusive term in the FFP equation is found. Further studies are necessary for the complete FFP equation in the more general case in which the equation is enforced not only by the white noise, but also by a nonlinear transformation of the response itself
Simplified analytical solution for the optimal design of Tuned Mass Damper Inerter for base isolated structures
No full textIn 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
An innovative only-output method to identify a structural system
Full text linkStructural Health Monitoring (SHM) is nowadays common in many branches of engineering since it allows to have a continuous or periodic report of the structural conditions and therefore to promptly intervene if there are incipient damages. The first step to perform a SHM is the identification of the dynamic parameters, i.e. natural frequencies, damping ratios and modal shapes, and it is a crucial step since a modification of the structural parameters can be a direct consequence of structural damages. Among the structural identification methods, Operational Modal Analysis (OMA) methods have received increasing attention from the researchers since they do not require the knowledge of the structural excitation that is due to ambient vibrations and that is usually modeled as a white noise. This aspect makes this kind of methods cheaper and simpler than the classical Experimental Modal Analysis (EMA) methods.
In this paper an innovative OMA method is proposed. It is a semi - automated method that allows to identify natural frequencies, damping ratios and modal shapes of a structural system and that can be used also from users that have not knowledge in stochastic dynamics and signal analysis. First of all, the modal shapes are estimated through the use of signal filtering techniques applied on the stochastic properties of the output process and then natural frequencies and damping ratios can be estimated from the mono - component analytical signals obtained by performing a decomposition of the analytical signals matrix. The proposed method has been used to perform the dynamic identification of a real historic building situated in Palermo, i.e. Chiaramonte palace, and the results obtained have been compared with those obtained by using other OMA methods
Innovative Formulation for the Bending of Plates with Reentrant Angles
No full textVery recently, an innovative mesh-free method, the so-called line element-less method (LEM), has been proposed to determine the response of plates under uniformly distributed edge moments. However, the previous formulations do not solve the problem related to plates with reentrant angles. In this paper, an innovative formulation is introduced to evaluate the deflection function of a simply supported plate possessing reentrant angles at the boundary and loaded by uniformly distributed edge moments. Framed in the LEM, this formulation consents to obtain a plate deflection function, implementing a simple algorithm within Mathematica software. Compelling savings in terms of time and computational costs are achieved, since there is no need to discretize the domain or the contour. Finally, the accuracy of the proposed results is highlighted by a good match with those achieved by classical methods and the finite-element method
Extension of the line element-less method to dynamic problems
Full text linkThe line element-less method is an efficient approach for the approximate solution of the Laplace or biharmonic equation on a general bidimensional domain.Introducing generalized harmonic polynomials as approximation functions, we extend the line element-less method to the inhomogeneous Helmholtz equation and to the eigenvalue problem for the Helmholtz equation. The obtained approximate solutions are critically discussed and advantages as well as limitations of the approach are pointed out
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