On the compact wave dynamics of tensegrity beams in multiple dimensions

Abstract

This work presents a numerical investigation on the nonlinear wave dynamics of tensegrity beams in 1D, 2D and 3D arrangements. The simulation of impact loading on a chain of tensegrity prisms and lumped masses allows us to apply on a smaller scale recent results on the propagation of compression solitary waves in 1D tensegrity metamaterials. Novel results on the wave dynamics of 2D and 3D beams revealfor the first time -the presence of compact compression waves in two-and three-dimensional tensegrity lattices with slender aspect ratio. The dynamics of such systems is characterized by the thermalization of the lattice nearby the impacted regions of the boundary. The portion of the absorbed energy moving along the longitudinal direction is transported by compression waves with compact support. Such waves emerge with nearly constant speed, and slight modifications of their spatial shape and amplitude, after collisions with compression waves traveling in opposite direction. The analyzed behaviors suggest the use of multidimensional tensegrity lattices for the design and additive manufacturing of novel sound focusing devices.

Design and Testing of Bistable Lattices with Tensegrity Architecture and Nanoscale Features Fabricated by Multiphoton Lithography

“…Figure 11 conveys this characteristic quiddity of ten bistable prisms clamped at one end. Numerical results on the wave dynamics of such a system, which have been obtained through the procedures diffusely illustrated in [15][16][17][18]54,55], show that they support the formation of compression waves with compact support when subjected to an impulsive load at the free end. Figure 11 shows some snapshots of the motion of the examined tensegrity column, which is impacted with initial vertical speed v 0 and initial angular speed ω 0 of the top base, so as to activate the bistable mechanism of the first unit.…”

“…Another peculiar property of a tensegrity system exhibiting a single soft mode is that the deformation process associated with the internal mechanism can be regarded as a "breathing," or pumping motion, which can be efficiently employed to design novel types of bistable pumps at multiple scales [61]. Such a feature of bistable structures can also be exploited to design systems that support the transport of mechanical energy through compact solitary waves, which is a subject receiving growing interest in the area of nonlinear mechanical metamaterials [15][16][17][18]49]. Figure 11 conveys this characteristic quiddity of ten bistable prisms clamped at one end.…”

“…The examined experimental behaviors lead us to conclude that the fabrication of multistable metamaterials using MPL is highly feasible. They pave the way to the future studies on the application of the systems studied in this work as novel mechanical actuators and sensor, to be employed for the focusing of mechanical waves in narrow regions of space [15][16][17][18], and the development of a new paradigm for non-destructive evaluation and structural health monitoring of materials and structures [49]. ,e,f) Examples of prestress-stable systems with one seflstress state and one mechanism: (c) A two-dimensional system displaced along its mechanism; (d) triangular tensegrity prism; (e) expanded octahedron or tensegrity icosahedron; (f) an irregular xtower.…”

“…Metamaterials comprised of lattice members are spatial periodic structures with unprecedented physical properties, mainly derived from the architecture of the repeated substructure, rather than the nature of the constituent materials. It is worth noting that extraordinary strength-to-weight and stiffness-to-weight ratios, frequency bandgaps, negative overall elastic moduli, negative mass density, auxeticity and solitary wave propagation represent characteristic and unconventional properties of such systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], as well as a multistable mechanical response [19][20][21][22][23][24][25][26][27][28]. However, the additive manufacturing of multi-cell realizations of mechanical metamaterials remains a challenge at present, due to the difficulty of reproducing the desired behaviors at small scales [8,9,[29][30][31][32].…”

“…Tensegrity structures exhibit different types of nonlinear static and dynamic responses, depending on their connectivity, geometry and state of selfstress [33][34][35]. Due to the complex nonlinear response of such structures, they have been employed to obtain different mechanical systems endowed with peculiar static and dynamic behaviors [15][16][17][18][36][37][38]. Some tensegrity modules can transcend from one stable state to two other stable states, either by changing the lengths of their elements or by changing the selfstress level [39].…”