2-D lattice structures have gained considerable attention over the past few decades due to their high strengthto- weight ratio. Enormous studies have been conducted on various shapes of the 2D lattice structures. Different shapes of the 2-D lattices exhibit different Poisson's ratio values. The Poisson's ratio ranges from negative to positive values for conventional lattice structures such as honeycomb and auxetic honeycomb lattice structures. However, there exist such lattice structures that exhibit Zero Poisson's Ratio (ZPR). In this article, we propose a novel hourglass structure (HG) that exhibits Zero Poisson's Ratio (ZPR HG), studied dispersion behaviour, and compared with negative (Aux HG) and positive (Hcb HG) Poisson's Ratios. The emergence of the band structure in the HG-ZPR has been studied analytically and compared with the conventional hourglass structures that exhibit positive/ negative Poisson's ratio. The dependency of the band structure on Poisson's ratio has been investigated. A significant variation in the band structure has been observed as the microstructure of the hourglass structure varies. This study intends to provide the necessary physical insights showing the dependency of the band structure on Poisson's ratio.
Low-frequency bandgaps are generally achieved by using locally resonant metamaterials at much higher wavelengths than the lattice constant. However, it remains a challenge to control wave propagation and vibration in these structures due to the limited number of conventional options available as periodic unit cell arrangements. This work investigates the band structure of flexural waves in a metamaterial sandwich beam with an hourglass lattice core using the transfer matrix method. The double dome-shaped hourglass unit cell is modelled with different non-dimensional geometric ratios. A sandwiched metamaterial beam model is then established using a periodic finite hourglass array, considered under the flexural wave propagation. The complete hourglass sandwiched system is further studied to obtain the bandgaps corresponding to the microstructure of the hourglass which is varied in the frequency domain. Subsequently, parametric analysis is performed using some specific non-dimensional geometric parameters that are found to be sensitive towards tailoring the mechanical properties of such unit cells. This study builds a foundation for modelling lightweight hourglass lattice sandwich beams with complex dome shape structures and presents guidelines for designing sandwich beams to control wave propagation.
Metamaterials have properties that are not usually found in conventional materials. Its unique periodic arrangement allows vibration suppression more successfully than most naturally occurring materials. In a Metamaterial beam, resonators with various designs can be attached in different configurations to obtain the bandgap according to the application requirement like vibration attenuation and waveguiding for aerospace, acoustics, or seismic isolators. This article proposes a cantilever beam with several spring-mass resonators periodically attached to it. The beam has been modelled as an Euler Bernoulli beam and is subjected to base excitation. The assumed modes method is employed to calculate the corresponding dynamic response of the structure in terms of its mode shapes. The transmissibility ratio is obtained as a function of the base excitation frequency. It is found that the transmissibility ratio is not only dependent on the excitation frequency but also the shape of the beam cross-section. Variation in the bandgap has been studied for different excitation frequencies and beam cross-sections, i.e., circular, triangular, rectangular and I-section, keeping the cross-sectional area and the mass of the beam constant. It has been observed that out of the four shapes, the I-section, rectangular and triangular or circular shapes are suitable for high, low, and intermediate frequency vibration attenuation, respectively. This study provides a basic framework to develop the metamaterial structures in an optimized manner.
Metamaterials have gained considerable attention in the past few decades due to their exceptional properties, such as negative mass, negative stiffness, and negative Poisson’s ratio. Much research has been conducted to understand how the band structure varies with unit cell designs for single and sandwich beam configurations. A few researchers have studied the variation in band structure in the graded metastructure considering single beam configuration. In this article, a new graded meta-sandwich beam has been studied that is constructed by repeating the unit cell, which consists of different combinations of translational and rotational springs. The band structure has been obtained by using the transfer matrix method along with Bloch-Floquet’s theorem. It has been noticed that a significant shifting and widening of the bandgaps has been noticed in the proposed graded meta-sandwich beam. Moreover, different configurations of metasandwich beams have also been studied. This study intends to provide the necessary physical insights to design a graded meta-sandwich beam for vibration attenuation applications.
2-D lattice structures have gained significant attention in the last few decades. Extensive analytical and experimental studies have been conducted to determine the elastic properties of the lattice structures. Further, the variation in the elastic properties of the passive lattice structures by changing various dimensional parameters and geometry have also been studied. However, once manufactured, it is impossible to vary the elastic properties of these lattice structures. A few studies have been conducted to understand the modulation of the elastic properties in symmetric hybrid lattice structures. This article proposes a geometrically asymmetric hybrid lattice structure having piezoelectric material on the opposite faces (top and bottom) of the consecutive inclined cell walls, respectively. The closed-form expressions have been derived by considering a bottom-up approach neglecting the axial deformation of the cell walls. Young’s modulus has emerged to be a function of externally applied voltage, warranting control of the elastic properties of the structure even after manufacturing. In contrast, Poisson’s ratio is independent of externally applied voltage. The transition from negative to positive values for Young’s modulus has also been observed at specific cell angle values and externally applied voltage to stress ratio. This study intends to provide the basic framework for voltage-dependent elastic properties in asymmetric lattice structures for potential use in various futuristic multi-functional structural systems and devices across different length scales.
Tensairity refers to a class of lightweight structure which has a wide range of interesting applications such as temporary bridges, inflatable kites, of unmanned aerial vehicle wings and mainsail in sailing boats. A Tensairity structure has three main components, namely tension element, compression element and air beam. The primary purpose of the air beam is to stabilise the compression element under loading. The combination of these elements results in a structure which has lightweight compared to conventional structures for the same strength and vice versa. In this study, we explore a new concept of meta tensairity beam. Air is modelled as spring, and an additional torsional spring has been used between the two beams and this structure has been repeated periodically. Both tension and compression elements have been modelled as Euler Bernoulli beam. The unwanted vibration which occurs in the tensairity structure can be attenuated by varying the stiffness of torsional spring. Band structure of meta tensairity beam has been obtained by using Bloch theorem and transfer matrix method. The phenomenon of frequency band attenuation has been incorporated in the Tensairity structure, and it gives rise to a new set of design potentials for lightweight structures. Real-time health monitoring of tensairity structures can also be done by harvesting energy from meta tensairity, which makes it a self-sustaining system.
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