Numerical simulation data for the dynamic properties of rainbow metamaterials

Simulation data are presented for identifying and analysing the dynamic properties of the rainbow metamaterials as presented in the articles “Rainbow metamaterials for broadband multifrequency vibration attenuation: numerical analysis and experimental validation” (Meng et al., 2019 [1]) and “Optimal design of rainbow elastic metamaterials” (Meng et al., 2019 [2]). In this data article, the frequency response functions and mode shapes of the rainbow metamaterials are numerically calculated by Finite Element models set up in Ansys Mechanical APDL. Harmonic analysis was performed to figure out the receptance function values of the rainbow metamaterials within the frequency regime 0e500 Hz. Modal analysis was applied to estimate the mode shapes, which could be used to explain the critical peaks and dips in the receptance function curve. Source files of Finite Element models are provided in the data. The Finite Element simulation is not only an effective alternative way to estimate the dynamic properties of the rainbow metamaterials, the mode shape analysis, which is unlikely to be achieved with the analytical model, provides direct insights into the underlying vibration mechanism of the rainbow metamaterials

A NUMERICAL ANALYSIS OF THE ELECTRICAL OUTPUT RESPONSE OF A NONLINEAR PIEZOELECTRIC OSCILLATOR SUBJECTED TO A HARMONIC AND RANDOM EXCITATION

The renewable energy is in the focus of many researches in the last decades, and the use of piezoelectric material can be used to obtain one source of this renewable energy. In this case, energy harvesting explores mainly the source of ambient motion and the piezoelectric material convert mechanical energy, present in the ambient motion, into electrical energy. In the work, we present a nonlinear bistable piezomagnetoelastic structure subjected to harmonic and random base excitation. At first, harmonic excitation is of concern and then, the system subjected to random excitation is analyzed. The goal of the numerical analysis is to present an investigation of the best electrical output response of the system given harmonic and random excitations

Stochastic analysis of structural dynamic behavior via probabilistic methods

Orientador: José Roberto de França ArrudaDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: Esta dissertação tem como objetivo geral levar 'a realidade industrial subsídios para a modelagem e análise de sistemas mecânicos lineares com variabilidade, assim como metodologias computacionais para quantificação de incertezas, para fins de aplicação em projeto. Neste sentido, foram realizados estudos sobre técnicas de modelagem e análise estocástica de sistemas mecânicos lineares aplicadas, inicialmente, a algumas estruturas simples, de baixo custo computacional, por meio de simulações em MatLabR. Propõe-se uma abordagem probabilística para a modelagem de incertezas baseada no Princípio da Máxima Entropia para a flexibilidade relativa a uma trinca aberta e não propagante em uma barra modelada através do Método do Elemento Espectral (SEM). Também é apresentada uma abordagem para o tratamento de problemas de campo aleatório utilizando o SEM, onde são utilizadas soluções analíticas da decomposição de Karhunen-Lo'eve. Uma formulação para elementos de viga do tipo Euler-Bernoulli é apresentada e um exemplo em que a rigidez à flexão é modelada como um campo aleatório Gaussiano é tratado. Uma abordagem para análise estocástica do comportamento dinâmico de uma tampa de compressor hermético é proposta. Uma aproximação por elementos finitos obtida com o software Ansys R foi utilizada para representar o comportamento determinístico de uma tampa de compressor, e duas abordagens de modelagem estocástica são comparadas. Um ensaio experimental foi realizado com tampas nominalmente idênticas, sendo medidas apenas frequências naturais com excitação por impacto, de modo a se poder compará-las com os valores obtidos teoricamenteAbstract: This dissertation has as a general objective to bring to the industrial reality subsidies for modeling and analysis of linear mechanical systems with variability, as well as computational methodologies to the uncertainty quantification, aiming industrial design applications. In that sense, theoretical studies about stochastic modeling and analysis for mechanical linear systems were performed. They were applied, firstly, to simple and computationally low cost structures using MatlabR. In that sense, a probabilistic modeling approach based on the Maximum Entropy Principle was proposed to treat the flexibility related to an open and nonpropagating crack in a rod modeled using the Spectral Element Method (SEM). An approach for the treatment of random field problems using SEM, which uses analytical solutions of the Karhunen-Lo'eve Decomposition, is also addressed. An Euler-Bernoulli beam formulation was used, and an example where the flexural stiffness is modeled as a Gaussian random field is presented. A finite element approximation obtained with the software Ansys R was used to represent the deterministic dynamic behavior of a compressor cap shell, and two stochastic modeling approaches were compared. Experiments were performed using nominally identical cap samples. Natural frequencies were measured using impact excitation in order to compare with the theoretical resultsMestradoMecanica dos Sólidos e Projeto MecanicoMestre em Engenharia Mecânic

Propagation in waveguides with slowly changing variability

This thesis investigates structural wave propagation in waveguides with randomly varying material and geometrical properties along the axis of propagation, specifically when the properties vary slowly enough such that there is no or negligible backscattering due to any changes in the propagation medium. This variability plays a significant role in the so called mid-frequency region, but wave-based methods are typically only applicable to homogeneous and uniform waveguides.An analytical tool, the WKB (after Wentzel, Kramers and Brillouin) approximation, is used in order to find a suitable generalisation of the wave solutions for finite waveguides undergoing longitudinal and flexural motion. An alternative wave formulation approximation with piecewise constant properties is derived so that the internal reflections are taken into account, requiring a discretisation of the waveguide. In addition, a Finite Element approximation using an enriched hierarchical basis or Hierarchical Finite Element (HFE) is created, where the variability in the properties of the waveguide is included within the element formulation, thus not requiring a mesh discretisation as opposed to a standard FE solution.A Fourier like series, the Karhunen-Loeve expansion, is used to represent homogeneous and spatially correlated randomness and statistics of the natural frequencies and forced response are derived. Experimental validation is carried out, using firstly a cantilever beam with small masses attached along its length according to a given random field. In the second experiment, an ensemble of glass-fibre reinforced free-free beams, whose variability is characterised by light transmissibility images, is measured. It has been found that the correlation length of the random fields or the scale of the spatial fluctuation is shown to play an important role in the dynamic response statistics. Moreover, the proposed formulations show good agreement with the standard approaches but at a fraction of the computational cost, providing a good framework for uncertainty quantification

Correlated disorder in rainbow metamaterials for vibration attenuation

Metastructures are typically composed of periodic unit cells designed to present enhanced dynamic properties in which either single or multiple resonators are periodically distributed. Even though the periodic metamaterials can obtain bandgaps with outstanding vibration attenuation, the widths of bandgaps can still be narrow for some practical applications. Rainbow metamaterials have been proposed based on gradient or random profiles to provide further improved attenuation. Nonetheless, the effects of correlated random disorder on their attenuation performance remains an open challenge. This work presents an investigation on the effects of correlated disorder on the vibration attenuation of rainbow metamaterials. An analytical model using the transfer matrix approach is used to calculate the receptance functions in a finite length metastructure composed of evenly spaced non-symmetric resonators attached to a beam with Π-shaped cross-section, thus a multi-frequency metastructure. The correlated disorder is modelled using random fields and an analytical expression of the Karhunen-Loève expansion is used such that spatial correlation on the resonator properties is modified by various correlation lengths, i.e., the level of spatial smoothness. Individual samples of random fields are used to investigate the effects of the correlated disorder in the vibration attenuation of a multi-frequency metastructure. It is shown that the bandgap can be further widened when compared to uncorrelated disorder. The obtained results indicates that a combination of the gradient profile with some level of disorder, typically resulting from random fields with larger correlation lengths, tends to give improved vibration attenuation when compared to a optimized gradient rainbow metamaterial. It opens new and innovative ways for the design of broadband rainbow metastructures for vibration attenuation

Natural frequency statistics of waveguides with slowly changing spatially correlated material variability

This paper concerns wave propagation in random waveguides and, in particular, when there is spatially correlated variability in the material and/or geometric properties. The one dimensional waveguide is modelled using an analytical formulation for wave propagation and a formulation for the wavenumber is given considering slowly varying proprieties, i.e. the change given by the random field is such that there is no backscattering from a propagating wave. When propagating over a finite distance, the total phase change of a wave is given by the integral of the spatially distributed wavenumber. Spatial correlation is then seen to be important in determining the statistics of this phase (mean, variance, etc.). This information can in turn be used to calculate the natural frequencies and forced response of finite structures. Longitudinal motion in a finite length thin rod is then considered and, given a second order homogenous random field with a certain kind of autocorrelation function, an analytical solution for its Karhunen-Loeve expansion is used for deriving an expression for its natural frequencies. The slowly varying proprieties assumption is used in order to find an analytical expression the for probability density function of the natural frequencies. A FE model of the waveguide is also assembled, with the random field discretized on the FE mesh and assumed piecewise constant within the element proprieties. Monte Carlo sampling is used to evaluate statistics of the natural frequencies and the results are compared to those obtained by the wave approach

Wavenumber and natural frequency statistics of waveguides with spatially correlated material variability from finite element analysis

This paper concerns wave propagation in random waveguides and, in particular, when there is spatially correlated variability in the material and/or geometric properties. The one dimensional waveguide is modelled using a wave and finite element method to evaluate the wave-number. In the numerical examples presented the case of longitudinal motion in a thin rod is considered. The random field is discretized on the FE mesh and the element properties assumed piecewise constant. Analytical solutions for the wavenumbers are then found for each element of the random field mesh. When propagating over a finite distance, the total phase change of a wave is given by the summation of the phase changing in each element. Its statistics can be found by propagating the variability through an eigenvalue problem, by a sensitivity analysis or by Monte Carlo simulation. Spatial correlation is then seen to be important in determining the statistics of this phase (mean, variance, etc). This information can in turn be used to calculate the natural frequencies and forced response of finite structures. The statistics of the natural frequencies of rods of finite length are found by this wave approach are compared to those obtained by solving the full finite element problem

Broadband vibration attenuation from a one‐dimensional acoustic black hole resonator for plate‐on‐plate structures

This paper investigates the vibrational behaviour and attenuation performance of a plate connected to a plate-like resonator equipped with a 1D acoustic black hole. The ABH principle relies on trapping the incident waves and consequently absorbing the incoming mechanical energy. Conversely, the ABH acts as a conventional dynamic absorber in which the vibration modes of the wedge act as a multifrequency resonator when attached to a host structure. The typically added damping layer enriches its dynamic, providing superior attenuation across a broader frequency band. This plate-like resonator can be used as a vibration control alternative to the use of single or multiple resonators attached to the host structure. In this work, a mobility-based approach is used to connect both the host plate and the plate-like resonator with an ABH termination. The response of both structures is given by a Finite Element model implemented by the authors in MATLAB, and the point connections are assumed to be rigid. The results are compared to that of a uniform plate acting as a multifrequency resonator, and it is shown that the ABH-based vibration attenuation leads to a reduction of up to 20 dB across multiple third-octave bands in the mobility response of the coupled system. Additionally, the energy flow is also investigated, and it is shown that the ABH-plate resonator yields up to 50 dB reduction also over multiple third-octave bands in the spatially averaged kinetic energy spectra. The addition of the film of viscoelastic material enhances its attenuation performance by up to 30 dB compared to the geometric effect due to the ABHs. The results suggest that this ABH-based solution can be a viable engineering approach and opens the way for new and innovative solutions in vibration control

Wave propagation in one-dimensional waveguides with slowly varying random spatially correlated variability

This paper investigates structural wave propagation in waveguides with randomly varying material and geometrical properties along the axis of propagation. More specifically, it is assumed that the properties vary slowly enough such that there is no or negligible backscattering due to any changes in the propagation medium. This variability plays a significant role in the so called mid-frequency region for dynamics and vibration, but wave-based methods are typically only applicable to homogeneous and uniform waveguides. The WKB approximation is used to find a suitable generalization of the wave solutions for finite waveguides undergoing longitudinal and flexural motion. An alternative wave formulation approximation with piecewise constant properties is also derived and included, so that the internal reflections are taken into account, but this requires a discretization of the waveguide. Moreover, a Fourier like series, the Karhunen–Loeve expansion, is used to represent homogeneous and spatially correlated randomness and subsequently the wave propagation approach allows the statistics of the natural frequencies and the forced response to be derived. Experimental validation is presented using a cantilever beam whose mass per unit length is randomized by adding small discrete masses to an otherwise uniform beam. It is shown how the correlation length of the random material properties affects the natural frequency statistics and comparison with the predictions using the WKB approach is given