Dynamics of Piezo-Embedded Negative Stiffness Mechanical Metamaterials: A Study on Electromechanical Bandgaps

2020 ◽  
Author(s):  
Ankur Dwivedi ◽  
Arnab Banerjee ◽  
Bishakh Bhattacharya
Keyword(s):  
Sound Propagation ◽  
Periodic Structures ◽  
Negative Stiffness ◽  
Early 21St Century ◽  
Mechanical Metamaterials ◽  
Specific Frequency ◽  
A Chain ◽  
Bloch’S Theorem ◽  
Periodic Materials ◽  
Coupled Equation

Abstract Dynamics of periodic materials and structures have a profound historic background starting from Newton’s first effort to find sound propagation in the air to Rayleigh’s exploration of continuous periodic structures. This field of interest has received another surge from the early 21st century. Elastic mechanical metamaterials are the exemplars of periodic structures that exhibit interesting frequency-dependent properties like negative Young’s modulus, negative mass and negative Poisson’s ratio in a specific frequency band due to additional feature of local resonance. In this research, we present the modeling of piezo-embedded negative stiffness metamaterials by considering a shunted inductor energy harvesting circuit. For a chain of a finite number of metamaterial units, the coupled equation of motion of the system is deduced using generalized Bloch’s theorem. Successively, the backward substitution method is applied to compute harvested power and the transmissibility of the system. Additionally, through the extensive non-dimensional study of this system, the proposed metamaterial band structure is investigated to perceive locally resonant mechanical and electromechanical bandgaps. The results explicate that the insertion of the piezoelectric material in the resonating unit provides better tun-ability for vibration attenuation and harvested energy.

Simultaneous energy harvesting and vibration attenuation in piezo-embedded negative stiffness metamaterial

2020 ◽  
Vol 31 (8) ◽  
pp. 1076-1090 ◽  
Author(s):  
Ankur Dwivedi ◽  
Arnab Banerjee ◽  
Bishakh Bhattacharya
Keyword(s):  
Energy Harvesting ◽  
Negative Stiffness ◽  
Engineering Properties ◽  
Mechanical Metamaterials ◽  
Analytical Simulation ◽  
Vibration Attenuation ◽  
Unit Cells ◽  
Parametric Studies ◽  
A Chain ◽  
Bloch’S Theorem

Mechanical metamaterials are uniquely engineered form of periodically arranged unit cells that exhibit interesting frequency-dependent physical properties like negative effective mass, Young’s modulus and Poisson’s ratio. These extreme engineering properties are beyond the natural properties of a material, which can modulate the propagation of wave. In this article, a mechanical realization of one of these uncommon properties called negative stiffness is emulated through analytical simulation. Wave propagation in metamaterials is contingent on frequency, which in turn results in transmission and attenuation bands. Simultaneous vibration control and energy harvesting can be executed by embedding energy harvesting smart material within the resonating units of the metamaterial. However, this needs careful design studies to outline the range of parameters. In this work, first, the band structure of a piezo-embedded negative stiffness metamaterial is studied using generalized Bloch’s theorem. Subsequently, harvested power along with the transmissibility is computed for a chain of finite number of metamaterial units by using backward substitution method. The results of the parametric studies elucidate that piezo-embedded negative stiffness metamaterial can enhance the performance in terms of vibration attenuation and harvested energy.

Parametric Study on Rectangular Sonic Crystal

2012 ◽  
Vol 152-154 ◽  
pp. 281-286 ◽  
Author(s):  
Arpan Gupta ◽  
Kian Meng Lim ◽  
Chye Heng Chew
Keyword(s):  
Band Gap ◽  
Periodic Structure ◽  
Parametric Study ◽  
Sound Propagation ◽  
Periodic Structures ◽  
Sound Attenuation ◽  
Experimental Results ◽  
Center Frequency ◽  
Sonic Crystal ◽  
Sonic Crystals

Sonic crystals are periodic structures made of sound hard scatterers which attenuate sound in a range of frequencies. For an infinite periodic structure, this range of frequencies is known as band gap, and is determined by the geometric arrangement of the scatterers. In this paper, a parametric study on rectangular sonic crystal is presented. It is found that geometric spacing between the scatterers in the direction of sound propagation affects the center frequency of the band gap. Reducing the geometric spacing between the scatterers in the direction perpendicular to the sound propagation helps in better sound attenuation. Such rectangular arrangement of scatterers gives better sound attenuation than the regular square arrangement of scatterers. The model for parametric study is also supported by some experimental results.

scholarly journals Periodic structures stiffness topology optimization

2019 ◽  
Author(s):  
Joao Victor Watanabe Nunes ◽  
Renato Pavanello
Keyword(s):  
Topology Optimization ◽  
Boundary Conditions ◽  
Periodic Structures ◽  
Computational Costs ◽  
Evolutionary Structural Optimization ◽  
Low Weight ◽  
Uniform Medium ◽  
Refined Meshes ◽  
Optimum Topology ◽  
Periodic Materials

Stiffness topology optimization aims to determine the best material arrangement, capable of conciliating high structural stiffness and low weight, which handles certain loading conditions subjected to predefined boundary conditions. The imposed periodic constrain is fundamented on the fact that structures made of periodic materials behave as a homogeneous continuum, because the macro-structure cells are modeled as a uniform medium composed by periodic material. The optimization algorithm used in this work is the BESO (Bi-directional Evolutionary Structural Optimization), which analyzes the structure, under its loadings and boundary conditions, and generates the optimum topology through addition and removal of material. However, in order to reduce the high computational costs of this method when applied to very refined meshes, which is the case with most periodic structures, emphasis was placed on the integration between Matlab and Ansys softwares, with promising results.

scholarly journals Negative and positive stiffness in auxetic magneto-mechanical metamaterials

2018 ◽  
Vol 474 (2215) ◽  
pp. 20180003 ◽  
Author(s):  
K. K. Dudek ◽  
R. Gatt ◽  
M. R. Dudek ◽  
J. N. Grima
Keyword(s):  
Theoretical Model ◽  
Experimental Testing ◽  
Vibration Damping ◽  
Negative Stiffness ◽  
Poisson's Ratio ◽  
Fundamental Importance ◽  
Practical Applications ◽  
Mechanical Metamaterials ◽  
Wide Range ◽  
Negative Poisson's Ratio

This work discusses the concept of allowing the control of the stiffness of a particular class of re-entrant auxetic magneto-mechanical metamaterials through the introduction of magnets to the system. It is shown, through experimental testing backed up by a theoretical model, that the appropriate insertion of magnets in such a system will alter its stiffness, possibly even making it exhibit ‘negative stiffness’. This leads to a completely different behaviour of the structure in terms of stability. It is also reported that the investigated mechanical metamaterials may exhibit both negative stiffness and negative Poisson's ratio at the same time. Moreover, it is shown that the effect which magnets have on the stiffness of the system may be fine-tuned upon replacing magnets with electromagnets. Such systems have the potential to be used in a wide range of practical applications such as vibration damping devices where achieving a negative stiffness is of fundamental importance.

Novel multidirectional negative stiffness mechanical metamaterials

2019 ◽  
Vol 29 (1) ◽  
pp. 015037 ◽  
Author(s):  
Xiaojun Tan ◽  
Bing Wang ◽  
Shaowei Zhu ◽  
Shuai Chen ◽  
Kaili Yao ◽  
...  
Keyword(s):  
Negative Stiffness ◽  
Mechanical Metamaterials

scholarly journals Exploring the dynamics of hourglass shaped lattice metastructures

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Vivek Gupta ◽  
Sondipon Adhikari ◽  
Bishakh Bhattacharya
Keyword(s):  
Building Block ◽  
Vibration Suppression ◽  
Mechanical Performance ◽  
Wave Attenuation ◽  
Experimental Testing ◽  
Nonlinear Behaviour ◽  
Engineering Structures ◽  
Mechanical Metamaterials ◽  
Wide Range ◽  
Specific Frequency

AbstractContinuous demand for the improvement of mechanical performance of engineering structures pushes the need for metastructures to fulfil multiple functions. Extensive work on lattice-based metastructure has shown their ability to manipulate wave propagation and producing bandgaps at specific frequency ranges. Enhanced customizability makes them ideal candidates for multifunctional applications. This paper explores a wide range of nonlinear mechanical behavior that can be generated out of the same lattice material by changing the building block into dome shaped structures which improves the functionality of material significantly. We propose a novel hourglass shaped lattice metastructure that takes advantage of the combination of two oppositely oriented coaxial domes, providing an opportunity for higher customizability and the ability to tailor its dynamic response. Six new classes of hourglass shaped lattice metastructures have been developed through combinations of solid shells, regular honeycomb lattices and auxetic lattices. Numerical simulation, analytical modelling, additive layer manufacturing (3D printing) and experimental testing are implemented to justify the evaluation of their mechanics and reveal the underlying physics responsible for their unusual nonlinear behaviour. We further obtained the lattice dependent frequency response and damping offered by the various classes of hourglass metastructures. This study paves the way for incorporating hourglass based oscillators to be used as building block of future mechanical metamaterials, leading to a new class of tunable metamaterial over a wide range of operating frequencies. The proposed class of metastructure will be useful in applications where lightweight and tunable properties with broadband vibration suppression and wave attenuation abilities are necessary.

scholarly journals Optimal electromechanical bandgaps in piezo-embedded mechanical metamaterials

2021 ◽  
Author(s):  
Ankur Dwivedi ◽  
Arnab Banerjee ◽  
Sondipon Adhikari ◽  
Bishakh Bhattacharya
Keyword(s):  
Energy Harvesting ◽  
Band Structure ◽  
Physical Properties ◽  
Piezoelectric Material ◽  
Periodic Structures ◽  
Physical Parameters ◽  
Negative Mass ◽  
Mechanical Metamaterials ◽  
Vibration Attenuation ◽  
Unit Cells

AbstractElastic mechanical metamaterials are the exemplar of periodic structures. These are artificially designed structures having idiosyncratic physical properties like negative mass and negative Young’s modulus in specific frequency ranges. These extreme physical properties are due to the spatial periodicity of mechanical unit cells, which exhibit local resonance. That is why scientists are researching the dynamics of these structures for decades. This unusual dynamic behavior is frequency contingent, which modulates wave propagation through these structures. Locally resonant units in the designed metamaterial facilitate bandgap formation virtually at any frequency for wavelengths much higher than the lattice length of a unit. Here, we analyze the band structure of piezo-embedded negative mass metamaterial using the generalized Bloch theorem. For a finite number of the metamaterial units coupled equation of motion of the system is deduced, considering purely resistive and shunted inductor energy harvesting circuits. Successively, the voltage and power produced by piezoelectric material along with transmissibility of the system are computed using the backward substitution method. The addition of the piezoelectric material at the resonating unit increases the complexity of the solution. The results elucidate, the insertion of the piezoelectric material in the resonating unit provides better tunability in the band structure for simultaneous energy harvesting and vibration attenuation. Non-dimensional analysis of the system gives physical parameters that govern the formation of mechanical and electromechanical bandgaps. Optimized numerical values of these system parameters are also found for maximum first attenuation bandwidth. Thus, broader bandgap generation enhances vibration attenuation, and energy harvesting can be simultaneously available, making these structures multifunctional. This exploration can be considered as a step towards the active elastic mechanical metamaterials design.

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