Prestressed vibrations of partially filled tanks containing a free-surface fluid: finite element and reduced order models

In linear vibration analysis of partially filled elastic tanks [1], even if the the structure is submitted by a gaz or a liquid pressure, the reference configuration is generally used without the effect of static loads. In the case of very thin structures or soft material, the static state is considered as prestressed, due to geometrical nonlinearities of the deformed tank. The global stiffness of the structure may change in function of the fluid volume amount [2, 3, 4]. The aim of the paper is to quantify the prestressed effets on the linearized dynamic behavior of the fluid-structure system. The chosen methodology is the following: (i) A quasi-static solution is computed from an empty to a fully filled state of the tank, by considering geometrical nonlinearities and hydrostatic follower forces [5] (no volumetric mesh of the fluid is needed for this step); (ii) after a volumetric remeshing of the fluid at each states, a linearized hydroelastic displacement-pressure formulation around the prestressed state, without gravity effects, is established; (iii) a reduced basis of the hydroelastic problem is generated by using prestressed dry modes to minimize the computation of the added mass matrix. Numerical examples are given to illustrate the proposed approaches

Simulation of fractionally damped mechanical systems by means of a Newmark-diffusive scheme

A Newmark-diffusive scheme is presented for the time-domain solution of dynamic systems containing fractional derivatives. This scheme combines a classical Newmark time-integration method used to solve second-order mechanical systems (obtained for example after finite element discretization), with a diffusive representation based on the transformation of the fractional operator into a diagonal system of linear differential equations, which can be seen as internal memory variables. The focus is given on the algorithm implementation into a finite element framework, the strategies for choosing diffusive parameters, and applications to beam structures with a fractional Zener model

STRUCTURAL VIBRATION REDUCTION OPTIMIZATION BY SWITCH SHUNTING OF PIEZOELECTRIC ELEMENTS

ABSTRACT This work deals with the damping of structural vibrations by means of Synchronize

Projection-based reduced order model for prestressed hydroelastic vibrations

In aerospace industry, the computations of liquid-propelled launchers vibrations are based on linear elastic tanks coupled with an inviscid, incompressible fluid with free surface. In this specific case, the fluctuation of pressure on the free surface is supposed to be zero (i.e. the sloshing effects are neglected). Those vibrations are usually called hydroelastic vibrations. The discretized finite element dynamic problem is commonly expressed only in terms of displacements considering an added mass matrix, which represents the kinetic energy of the moving liquid expressed in terms of normal displacement interface. Those computations can be performed for various fluid level configurations, but no prestressing from geometrical nonlinearity is usually considered [1]. In the present study, the evaluation of the prestressed state influence on the coupled fluid structure vibrations is estimated numerically. This prestressing is supposed to be due to a gas or liquid pressurization, acting on the internal surface of the tank, inducing relatively large static displacement compared to the tank thickness. In reference [2], we have evaluated efficiently and accurately the nonlinear displacements for various filling rate with the use of an original level-set approach. We present here the hydroelastic vibrations around each known prestressed state corresponding to different level of liquid with the use of the added mass matrix. Using the open-source computing finite element platform FEniCS [3], numerical results are in very good agreements with experimental studies from the literature [4]. Comparisons with and without prestressing illustrates the contribution of the efect. To overcome an expensive added mass matrix computation, an appropriate reduced order model obtained by projection on prestressed dry modes is also proposed and show very encouraging results

An analogue twin for piezoelectric vibration damping of multiple nonlinear resonances

peer reviewedThe objective of this study is to extend the concept of analogous piezoelectric networks to vibration mitigation of multiple nonlinear resonances. First, the undamped linear part of the electrical network is designed so as to possess similar modal characteristics as those of the underlying linear mechanical structure. Then, nonlinear electrical components possessing the same mathematical form as that of the mechanical nonlinearities are added to the network. Because both modal and nonlinear analogies are enforced, the electrical network can be seen as an analogue twin of the mechanical structure. When the network is coupled to the structure via an array of piezoelectric elements, it is shown numerically and experimentally that such an analogue twin offers important benefits for vibration mitigation over a broad range of frequencies and excitation amplitudes. © 2021 Elsevier Lt

Structural-acoustic vibration reduction using switched shunt piezoelectric patches: A finite element analysis,

Abstract. For noise and vibration attenuation, various approaches can be employed depend

A first damage modelling of SiC-SiC laminates under dynamic loading

International audienc

A first damage modelling of SiC-SiC laminates under dynamic loading

Un premier mésomodèle permettant de simuler le comportement mécanique d'un pli élémentaire au sein d'un composite SiC-SiC stratifié sous chargement dynamique est proposé. Le problème de son identification et de son utilisation pour la prévision de la rupture dynamique de structures stratifiées SiC-SiC est discuté.A first mesomodelling, which allows us to describe the mechanical behaviour of an elementary ply within a SiC-SiC laminate under dynamic loading, is proposed. Questions related to its identification and its use for the prediction of the dynamic fracture of laminated structures are discussed

Performance of a condensation procedure based on projection on propagating waves

International audienceIn this paper, we aim at reducing the cost of resolution of a system composed of an acoustic cavity coupled to a damping treatment. We use the characteristics of the waves propagating in the medium to condense the dynamics of the acoustic treatment on the surrounding cavity. These waves are predicted by using the Wave Finite Element method, and take into account lateral boundary conditions, spatial inhomogeneities and non-local reaction of poroelastic materials. The condensation procedure can be coupled with Component Mode Synthesis for the external medium. The efficiency of the method is discussed. It is shown that interesting reduction of computation times can be obtained, especially by selecting the waves which contribute to the coupling with the external media

Practical issues on the applicability of Kalman filtering for reconstructing mechanical sources in structural dynamics

International audienceKalman-type filtering tends to become one of the favorite approaches for solving joint input-state estimation problems in the structural dynamics community. This article focuses on the applicability of the Augmented Kalman Filter (AKF) for reconstructing mechanical sources, addressing a set of practical issues that are frequently encountered in the engineering practice. In particular, this paper aims to help the reader to better apprehend some of the advantages and limitations of the application of the AKF in the context of purely input estimation problems. The present paper is not a simple collection of test cases, since it introduces a novel state-space representation of dynamical systems, based on the generalized-α method, as well as further insights in the tuning of Kalman filters from the Bayesian perspective. In this work, the various practical situations considered lead us to recommend to employ collocated acceleration measurements, when reconstructing exci-tation sources from the AKF. It is also demonstrated that the violation of some of the feasibility conditions proposed in the literature doesn't necessarily imply the failure of the estimation process