Identification of Nonlinear Damping for Large-Amplitude Vibrations of Plates and Curved Panels

A nonlinear identification technique is presented to obtain the damping of isotropic and laminated sandwich rectangular plates and curved panels subjected to harmonic excitation as a function of the vibration amplitude. The response of the structures is approximated by (i) reduced-order models with 10 to 100 degrees of freedom and (ii) a single-degree of freedom Duffing oscillator. The method uses experimental frequency-amplitude data and the leastsquares technique to identify parameters and reconstruct frequency-response curves by spanning the excitation frequency in the neighbourhood of the lowest natural frequencies. In order to obtain the experimental data, a sophisticated measuring technique has been used. The results reveal a strongly nonlinear correlation between the damping and the vibration amplitude

Vibration of a Square Hyperelastic Plate Around Statically Pre-Loaded State

International audienceStatic deflection and free nonlinear vibrations of thin square plate made of biological material are investigated. The involved physical nonlinearity is described through Neo-Hookean, Mooney-Rivlin and Ogden hyperelastic laws; geometrical nonlinearity is modelled by Novozhilov nonlinear shell theory. The problem is solved by sequentially constructing the local models that describe the behavior of plate in the vicinity of a certain static configuration. These models are the systems of ordinary differential equations with quadratic and cubic nonlinear terms in displacement, which allows application of techniques used in analysis of thin-walled structures of physically linear materials. The comparison of static and dynamic results obtained with different material models is carried out

Circular Cylindrical Shell Made of Neo-Hookean-Fung Hyperelastic Material Under Static and Dynamic Pressure

The present study is devoted to the investigation of static and dynamic behavior of the three-layered composite shell made of hyperelastic material. Such a shell can be considered as a model of human aorta. Since soft biological materials are essentially nonlinear even in the elasticity zone, not only geometrical, but also physical nonlinearity should be taken into account. The physical nonlinearity of soft biological tissues is usually modeled by certain hyperelastic law. The law chosen for this study is the combination of the Neo- Hookean law, which describes the isotropic response at small strains, and Fung exponential law, that models the stiff anisotropic response of the collagen fibers at larger strains. Each of three shell layers has its own hyperelastic constants set. These constants are determined basing on experiential data [1]. The straindeflection relations are modeled with higher-order shear deformation theory [2]. Initially, the shell is preloaded with static pressure. Since the defection in our study is large we use the expression for pressure as a follower load [3]. The static problem is solved with the help of the local models method [4]. Afterwards, the free and forced dynamical response of the preloaded shell is studied both in vacuo and with still fluid inside. The modes of interest are the first axisymmetric mode and mode with two half-waves in circumferential direction (so-called collapse mode). It is found that static pressure decreases the dynamic nonlinearity and it is quite weak. At the same time, the presence of fluid makes the softening nonlinearity stronger as in case of shells of conventional material [5]

Static and Dynamic Behavior of Circular Cylindrical Shell Made of Hyperelastic Arterial Material

International audienceStatic and dynamic responses of a circular cylindrical shell made of hyperelastic arterial material are investigated. The material is modeled as a combination of Neo-Hookean and Fung hyperelastic materials. Two pressure loads are implemented: distributed radial force and deformation-dependent pressure. The static responses of the shell under these two different loads differ essentially at moderate strains, while the behavior is similar for small loads. The main difference is in the axial displacements that are much larger under distributed radial forces. Free and forced vibrations around pre-loaded configurations are analyzed. In both cases the nonlinearity of the single-mode (driven mode) response of the pre-loaded shell is quite weak but a resonant regime with co-existing driven and companion modes is found with more complicated nonlinear dynamics

Axisymmetric deformations of circular rings made of linear and Neo-Hookean materials under internal and external pressure: A benchmark for finite element codes

International audienceThe axisymmetric deformations of thick circular rings are investigated. Four materials are explored: linear material, incompressible Neo-Hookean material and Ogden's and Bower's forms of compressible Neo-Hookean material. Radial distributed forces and a displacement-dependent pressure are the external loads. This problem is relatively simple and allows analytical, or semi-analytical, solution; therefore it has been chosen as a benchmark to test commercial finite element software for various material laws at large strains. The solutions obtained with commercial finite element software are almost identical to the present semi-analytical ones, except for the linear material, for which commercial finite element programs give incorrect results.Highlights: Linear, incompressible and compressible Neo-Hookean materials are used. Analytical benchmark solution to test commercial programs. Two commercial FE programs give incorrect results for large strains and linear elastic material.</ol

VIBRATION OF A SQUARE HYPERELASTIC PLATE AROUND STATICALLY PRE- LOADED STATE

ABSTRACT Static deflection and free nonlinear vibrations of thi

Nonlinear vibrations and dynamic stability of viscoelastic anisotropic fiber reinforced plates

Fiber-reinforced plastic composites are one of the most widely used composite materials because they balance well between properties and cost. Despite their widespread use in the aviation and automotive industries, there is currently a lack of effective mathematical models for their calculation under various dynamic loads. The research object of this work is an anisotropic viscoelastic fiber-reinforced simply supported rectangular plate. Two dynamic problems are considered: vibrations of the plate under the influence of a uniformly distributed static load; stability of the plate compressed in one direction. Within the Kirchhoff–Love hypothesis framework, a mathematical model was built in a geometrically nonlinear formulation, taking into account the tangential forces of inertia. By the Bubnov–Galerkin method, based on a polynomial approximation of the deflection and displacement, the problem was reduced to solving systems of nonlinear ordinary integro-differential equations. With a weakly singular Koltunov–Rzhanitsyn kernel with variable coefficients, the resulting system was solved by a numerical method based on quadrature formulas. By using experimental studies, considering the directions of the fibers, the values of the rheological parameters of some plastic material (KAST-V and EDF) were obtained. The plate's dynamical behavior was investigated depending on the plate's geometric parameters and viscoelastic and inhomogeneous material properties. Results show the importance of taking into account the viscoelastic properties of the material when solving dynamic problems of anisotropic reinforced plates made of composite materials. In particular, when studying the problem of dynamic stability of an anisotropic reinforced plate made of KAST-V, the results obtained in elastic and viscoelastic formulations in some cases differ from each other by more than 20%

NONLINEAR VIBRATIONS OF FLUID-FILLED VISCOELASTIC CYLINDRICAL SHELLS

In this work the non-linear vibrations of a simply supported viscoelastic fluid-filled circular cylindrical shells subjected to lateral harmonic load is studied. Donnell's non-linear shallow shell theory is used to model the shell, assumed to be made of a Kelvin-Voigt material type, and a modal solution with six degrees of freedom is used to describe the lateral displacements. The Galerkin method is applied to derive a set of coupled non-linear ordinary differential equations of motion. The influence of shell geometry, flow velocity and dissipation parameter are studied and special attention is given to resonance curves. Obtained results show that the viscoelastic dissipation parameter, flow velocity and geometry have significant influence on the nonlinear behavior of the shells as displayed in instability loads and resonance curves

Vibrazioni di sistemi con interazione fluido-struttura: metodi analitici, numerici e sperimentali

Dottorato di ricerca in meccanica e applicata. 8. ciclo. Coordinatore V. Parenti Castelli. Tutore U. MeneghettiConsiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome; Biblioteca Nazionale Centrale - P.za Cavalleggeri, 1, Florence / CNR - Consiglio Nazionale delle RichercheSIGLEITItal