Shock Reduction Technique on Thin Plate Structure by Wave Refraction Using an Elastic Patch

In general, bending waves transfer the largest portion of shock energy in a plate-like structure. This study proposes a new shock reduction method using an elastic patch designed to defocus the bending waves through the refraction of the waves so that it is possible to effectively reduce the propagating shock for a certain target area. Elastic patches of three different shapes were considered. The shock reduction performance of these patches was analytically, numerically, and experimentally investigated and compared. All results consistently showed that attached patches can effectively reduce passing waves for areas behind patches. Therefore, utilizing the proposed methods, we can reduce the transient shock response at certain target areas of various practical structures without degradation of structural stiffness or strength simply by bonding with an elastic patch.

Analytically Solvable Models and Physically Realizable Solutions to Some Problems in Nonlinear Wave Dynamics of Cylindrical Shells

The axially symmetric propagation of bending waves in a thin Timoshenko-type cylindrical shell, interacting with a nonlinear elastic Winkler medium, is herein studied. With the help of asymptotic integration, two analytically solvable models were obtained that have no physically realizable solitary wave solutions. The possibility for the real existence of exact solutions, in the form of traveling periodic waves of the nonlinear inhomogeneous Klein–Gordon equation, was established. Two cases were identified, which enabled the development of the modulation instability of periodic traveling waves: (1) a shell preliminarily compressed along a generatrix, surrounded by an elastic medium with hard nonlinearity, and (2) a preliminarily stretched shell interacting with an elastic medium with soft nonlinearity.

Artificial flexible sperm-like nanorobot based on self-assembly and its bidirectional propulsion in precessing magnetic fields

Sperm cells can move at a high speed in biofluids based on the flexible flagella, which inspire novel flagellar micro-/nanorobots to be designed. Despite progress in fabricating sperm-type robots at micro scale, mass fabrication of vivid sperm-like nanorobots with flagellar flexibility is still challenging. In this work, a facile and efficient strategy is proposed to produce flexible sperm-like nanorobots with self-assembled head-to-tail structure, and its bidirectional propulsion property was studied in detail. The nanorobots were composed of a superparamagnetic head and a flexible Au/PPy flagellum, which were covalently linked via biotin-streptavidin bonding with a high yield. Under precessing magnetic fields, the head drove the flexible tail to rotate and generated undulatory bending waves propagating along the body. Bidirectional locomotion was investigated, and moving velocity as well as direction varied with the actuating conditions (field strength, frequency, direction) and the nanorobot’s structure (tail length). Effective flagellar propulsion was observed near the substrate and high velocities were attained to move back and forth without U-turn. Typical modelling based on elastohydrodynamics and undulatory wave propagation were utilized for propulsion analysis. This research presents novel artificial flexible sperm-like nanorobots with delicate self-assembled head-to-tail structures and remarkable bidirectional locomotion performances, indicating significant potentials for nanorobotic design and future biomedical application.

Artificial Flexible Sperm-like Nanorobot Based on Self-assembly and Its Magnetically Actuated Propulsion Property

Sperm cells can move at a high speed in biofluids based on the flexible flagella, which inspire novel flagellar micro-/nanorobots to be designed. However, mass fabrication of vivid sperm-like nanorobots with flagellar flexibility is still challenging. In this work, a facile and efficient strategy is proposed to produce flexible sperm-like nanorobots with self-assembled head-to-tail structure. The nanorobots were composed of a superparamagnetic head and a flexible Au/PPy flagellum, which were covalently linked via biotin-streptavidin bonding. Under a precessing magnetic field, the head drove the flexible tail to rotate and generated undulatory bending waves propagating along the body. Bidirectional locomotion of the nanorobot was investigated, and moving velocity as well as direction varied with the actuating conditions (field strength, frequency, direction) and the nanorobot’s structure (tail length). Effective flagellar locomotion was observed near the substrate and high velocities were attained in both forward and backward directions. Typical modelling based on elastohydrodynamics and undulatory wave propagation were utilized for propulsion analysis. This research presents novel artificial flexible sperm-like nanorobots with delicate self-assembled head-to-tail structures and remarkable bidirectional locomotion performances, indicating significant potentials for nanorobotic design and future biomedical application.

Reconstruction of the three-dimensional beat pattern underlying swimming behaviors of sperm

The eukaryotic flagellum propels sperm cells and simultaneously detects physical and chemical cues that modulate the waveform of the flagellar beat. Most previous studies have characterized the flagellar beat and swimming trajectories in two space dimensions (2D) at a water/glass interface. Here, using refined holographic imaging methods, we report high-quality recordings of three-dimensional (3D) flagellar bending waves. As predicted by theory, we observed that an asymmetric and planar flagellar beat results in a circular swimming path, whereas a symmetric and non-planar flagellar beat results in a twisted-ribbon swimming path. During swimming in 3D, human sperm flagella exhibit torsion waves characterized by maxima at the low curvature regions of the flagellar wave. We suggest that these torsion waves are common in nature and that they are an intrinsic property of beating axonemes. We discuss how 3D beat patterns result in twisted-ribbon swimming paths. This study provides new insight into the axoneme dynamics, the 3D flagellar beat, and the resulting swimming behavior. Graphic abstract

A Wronskian method for elastic waves propagating along a tube

A technique involving the higher Wronskians of a differential equation is presented for analysing the dispersion relation in a class of wave propagation problems. The technique shows that the complicated transcendental-function expressions which occur in series expansions of the dispersion function can, remarkably, be simplified to low-order polynomials exactly, with explicit coefficients which we determine. Hence simple but high-order expansions exist which apply beyond the frequency and wavenumber range of widely used approximations based on kinematic hypotheses. The new expansions are hypothesis-free, in that they are derived rigorously from the governing equations, without approximation. Full details are presented for axisymmetric elastic waves propagating along a tube, for which stretching and bending waves are coupled. New approximate dispersion relations are obtained, and their high accuracy confirmed by comparison with the results of numerical computations. The weak coupling limit is given particular attention, and shown to have a wide range of validity, extending well into the range of strong coupling.

Body and Tail Coordination in the Bluespot Salamander (Ambystoma laterale) During Limb Regeneration

Animals are incredibly good at adapting to changes in their environment, a trait envied by most roboticists. Many animals use different gaits to seamlessly transition between land and water and move through non-uniform terrains. In addition to adjusting to changes in their environment, animals can adjust their locomotion to deal with missing or regenerating limbs. Salamanders are an amphibious group of animals that can regenerate limbs, tails, and even parts of the spinal cord in some species. After the loss of a limb, the salamander successfully adjusts to constantly changing morphology as it regenerates the missing part. This quality is of particular interest to roboticists looking to design devices that can adapt to missing or malfunctioning components. While walking, an intact salamander uses its limbs, body, and tail to propel itself along the ground. Its body and tail are coordinated in a distinctive wave-like pattern. Understanding how their bending kinematics change as they regrow lost limbs would provide important information to roboticists designing amphibious machines meant to navigate through unpredictable and diverse terrain. We amputated both hindlimbs of blue-spotted salamanders (Ambystoma laterale) and measured their body and tail kinematics as the limbs regenerated. We quantified the change in the body wave over time and compared them to an amphibious fish species, Polypterus senegalus. We found that salamanders in the early stages of regeneration shift their kinematics, mostly around their pectoral girdle, where there is a local increase in undulation frequency. Amputated salamanders also show a reduced range of preferred walking speeds and an increase in the number of bending waves along the body. This work could assist roboticists working on terrestrial locomotion and water to land transitions.