N. Impollonia

A new approach for the stochastic analysis of finite element modelled structures with uncertain parameters

A method for evaluating the static response of uncertain finite element (FE) discretised structures is presented. The method is comparable with the perturbation procedures from a computational point of view, but it overcomes the drawbacks related to these procedures. In fact the present method gives excellent level of accuracy, even for high amount of uncertainties. Moreover, it produces the exact solution for statically determinate structures. The accuracy is remarkable even in the evaluation of high order statistics and probability density function of the response, so that reliability consideration can be drawn.

Improved dynamic analysis of structures with mechanical uncertainties under deterministic input

This paper addresses the dynamic analysis of linear systems with uncertain parameters subjected to deterministic excitation. The conventional methods dealing with stochastic structures are based on series expansion of stochastic quantities with respect to uncertain parameters, by means of either Taylor expansion, perturbation technique or Neumann expansion and evaluate the first- and second-order moments of the response by solving deterministic equations. Unfortunately, these methods lead to significant error when the coefficients of variation of uncertainties are relatively large. Herein, an improved first-order perturbation approach is proposed, which considers the stochastic quantities as the sum of their mean and deviation. Comparisons with conventional second-order perturbation approach and Monte Carlo simulations illustrate the efficiency of the proposed method. Applications are discussed in order to investigate the influence of mass, damping and stiffness uncertainty on the dynamic response of the system.

A response surface approach for the static analysis of stochastic structures with geometrical nonlinearities

A response surface approach for the finite element analysis of uncertain structures undergoing large displacements is presented. This method is based on the use of ad hoc response surface functions built up by ratios of polynomials. As opposite to commonly used linear or quadratic polynomials, such functions are insensitive to the sampling point positions. Once the response surface form is defined, response statistics can be approximated by analytical relationships or statistical simulation taking full advantage of sensitivity analysis. Numerical investigations demonstrated that a remarkable accuracy is achieved in the evaluation of both statistical moments and probability density functions of the response.

Static and Dynamic Analysis of Non-Linear Uncertain Structures

The procedures usually adopted in the evaluation of the stochastic response of structures with uncertain parameters, the so-called stochastic structures, are affected by some limits. Namely, the major drawbacks are: the conspicuous computational time required for the analysis of many degree of freedom systems and the loss of accuracy in the case of large uncertainty in the parameters. A method able to reduce the previous inconveniences was recently introduced in the study of statically loaded linear structures. The method, named improved perturbation method, was also extended to the field of linear dynamics. In both cases, the improved perturbation method provides a good approximation, even in the case of moderately large deviation of the uncertain parameters, and the computational time required is comparable to conventional first order perturbation. The present paper intends to apply the improved perturbation method in the second order analysis of geometrically non-linear uncertain systems subjected to static and dynamic deterministic forces.

Does a Partial Elastic Foundation Increase the Flutter Velocity of a Pipe Conveying Fluid

The effect of the elastic Winkler and rotatory foundations on the stability of a pipe conveying fluid is investigated in this paper. Both elastic foundations are partially attached to the pipe, It turns out that the single foundation, either translational or rotatory, which is attached to the pipe along its entire length, increases the critical velocity. Such an intuitively anticipated strengthening effect is surprisingly missing for the elastic column on Winkler foundation subjected to the so-called statically applied follower forces. Yet, partial foundation for the pipe conveying fluid is associated with a nonmonotonous dependence of the critical velocity versus the attachment ratio defined as the length of the partial foundation over the entire length of the pipe. It is concluded that such a paradoxical nonmonotonicity is shared by both the realistic structure (pipe conveying fluid) and in the imagined system. to use the terminology of Herrmann pertaining to the column under to follower forces.

New exact solutions for randomly loaded beams with stochastic flexibility

Abstract Presently there exist several hundred papers on so-called stochastic finite element technique but extremely few closed-form solutions are available for meaningful comparison. This paper intends to fill this huge gap. This study deals with deformation of deterministic beams or stochastic beams subjected to random excitation. Exact solutions are formulated for four different classes of problems. These solutions can serve as benchmark solutions to be utilized for assessing the performance of various approximate, analytical or numerical techniques.

Dynamic Behavior of Stay Cables with Rotational Dampers

Vibration reduction in stay cables by means of viscous dampers is of great interest in cable damage prevention and serviceability of structural system supported by such cables. This paper presents a study on the effectiveness, as well as the limits, of rotational viscous dampers and springs inserted at the 2 ends of a bending-stiff taut cable; influence of rotational stiffness of the springs is also studied. After a nondimensional expression of the equation of motion has been obtained, as in other cases of nonproportionally damped continuous structures, complex modal analysis is pursued, obtaining complex eigenvalues and eigenfunctions. Comparison with intermediate dampers, widely used in bridge engineering, is performed showing the range of nondimensional parameters for which the proposed approach is of interest. Finally, a numerical technique based on complex mode superposition is presented in order to evaluate time domain responses for transversal distributed excitation. As an example, the procedure is applied to a wind-exposed cable.

DYNAMICS OF SHALLOW CABLES UNDER TURBULENT WIND: A NONLINEAR FINITE ELEMENT APPROACH

In classic cable theory, vibrations are usually analyzed by writing the equations of motion in the neighborhood of the initial equilibrium configuration. Furthermore, a fundamental difference exists between out-of-plane motions, which basically corresponds to the linear behavior of a taut string and in-plane motion, where self-weight determines a sagged initial profile. This work makes use of a continuous approach to establish the initial shape of the cable when it is subjected to wind or fluid flow arbitrarily directed and employed a novel nonlinear finite element technique in order to investigate the dynamics present around the initial equilibrium shape of the cable. Stochastic solutions in the frequency domain are derived for a wind-exposed cable after linearization of the problem. By applying the proper orthogonal decomposition (POD) technique with the aim of reducing computational effort, an approach to simulate modal wind forces is proposed and applied to the nonlinear equations of motion.

Exact and approximate solutions, and variational principles for stochastic shear beams under deterministic loading

Probabilistic response of shear beams with stochastic flexibility, and subjected to deterministic static loads is studied in this paper. The differential equations governing the probabilistic responses, as well as the variational principles for the probabilistic responses are formulated apparently for the first time. New exact solutions are also derived for specific cases. Stochastic versions of Galerkin and Rayleigh-Ritz method are then applied to obtain approximate solutions when exact solution is unfeasible to derive. Both the exact and the approximate solutions possess a unique characteristic: they are applicable to any value of the coefficient of variation. Previous investigations were unable to capture this remarkable characteristic.

Parametric Statistical Moment Method for Damage Detection and Health Monitoring

AbstractThis paper enriches the statistical moment-based damage detection method with approximate parametric solutions of the stationary second-order moments of nodal displacements and velocity, which are explicitly related to stiffness and modal damping parameters. Then, a weighted least-squares approach is employed to search for the stiffness and damping inversely when the objective function is minimized. The method is able to detect both stiffness reduction, simulating damage, and modal damping ratio of relevant modes, the latter being a decisive issue for damage detection. After the procedure to get an approximate explicit solution is recalled, the steps involved in the identification process are stated and an eventual modal truncation is proposed to allow the analysis of larger systems. Applications on a pinned beam and a two-dimensional panel are reported to check the consistency of the method and to investigate to effects of measurement noise on the identification procedure.