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This paper examines the effect of viscoelasticity on the periodic response of a lumped parameter viscoelastic von Mises truss. The viscoelastic system is described by a second-order equation that governs the mechanical motion coupled to a first-order equation that governs the time evolution of the viscoelastic forces. The viscoelastic force evolves at a much slower rate than the elastic oscillations in the system. This adds additional time scales and degrees of freedom to the system compared to its viscous counterparts. The focus of this study is on the system’s behavior under harmonic loading, which is expected to show both regular and chaotic dynamics for certain combinations of forcing frequency and amplitude. While the presence of chaos in this system has already been demonstrated, we shall concentrate only on the periodic solutions. The presence of the intrawell and interwell periodic oscillations is revealed using the Harmonic Balance method. The study also looks at the influence of parameter changes on the system’s behavior through bifurcation diagrams, which enable us to identify optimal system parameters for maximum energy dissipation. Lastly, we formulate an equivalent viscous system using an energy-based approach. We observe that a naive viscous model fails to capture the behavior accurately depending on the system and excitation parameters, as well as the type of excitation. This underscores the necessity to study the full-scale viscoelastic system. 

Abstract Inspired by the ancient Japanese art of kirigami, slitted plastic sheets, termed kirigami springs, were designed, fabricated, and characterized, utilizing the quasi-mechanism behavior of various slit patterns. Quasi-static tension tests determined the spring stiffness, and experimental transient responses were analyzed to infer system damping. A system of two parallel-connected kirigami springs, attached to a mass oscillating on a smooth track, was modeled as a 1 DOF Helmholtz-Duffing oscillator with nonlinear damping. The system's free and forced responses were compared to experimental and numerical results using asymptotically valid solutions derived via the Method of Multiple Time Scales. This approach provides an unprecedented degree of programmability in the constitutive relations for nonlinear oscillators and is straightforward to implement. 

Abstract A digitally encoded mechanical metamaterial utilizing selective insertion of rigid elements into an elastomeric matrix achieves programmable stiffness based on geometric patterns. Beyond the linear behavior, interests are developed towards the nonlinear stiffness region to extend the application of such metamaterials from vibration isolation to shock mitigation. A 12-unit-cell prototype is constructed and experimentally characterized under compression and drop tests, yielding the stress-strain curves and energy absorption capabilities of all independent geometric patterns identified, respectively, with validation by finite-element analysis. The versatility of the metamaterial is illustrated via a categorization of its pattern-dependent responses. 

Abstract High frequency excitation (HFE) is known to induce various nontrivial effects, such as system stiffening, biasing, and the smoothing of discontinuities in dynamical systems. These effects become increasingly pertinent in multi-stable systems, where the system’s bias towards a certain equilibrium state can depend heavily on the combination of forcing parameters, leading to stability in some scenarios and instability in others. In this initial investigation, our objective is to pinpoint the specific parameter ranges in which the bistable system demonstrates typical HFE effects, both through numerical simulations and experimental observations. To accomplish this, we utilize the method of multiple scales to analyze the interplay among different time scales. The equation of slow dynamics reveals how the excitation parameters lead to a change in stability of equilibrium points. Additionally, we delineate the parameter ranges where stabilizing previously unstable equilibrium configurations is achievable. We demonstrate the typical positional biasing effect of high-frequency excitation that leads to a shift in the equilibrium points as the excitation parameter is varied. This kind of excitation can enable the active shaping of potential wells. Finally, we qualitatively validate our numerical findings through experimental testing using a simplistic model made with LEGOs. 

Abstract Contact electrification in a gas medium is usually followed by partial surface charge dissipation caused by dielectric breakdown of the gas triggered during separation of the surfaces. It is widely assumed that such discharge obeys the classical Paschen’s law, which describes the general dependence of the breakdown voltage on the product of gas pressure and gap distance. However, quantification of this relationship in contact electrification involving insulators is impeded by challenges in nondestructive in situ measurement of the gap voltage. The present work implements an electrode-free strategy for capturing discrete discharge events by monitoring the gap voltage via Coulomb force, providing experimental evidence of Paschen curves governing nitrogen breakdown in silicone-acrylic and copper-nylon contact electrification. It offers an alternative approach for characterizing either the ionization energies of gases or the secondary-electron-emission properties of surfaces without the requirement of a power supply, which can potentially benefit applications ranging from the design of insulative materials to the development of triboelectric sensors and generators. 

Abstract This paper examines the effect of viscoelasticity on the dynamic behavior of a bistable dome-shaped structure represented as a lumped parameter viscoelastic von Mises truss. The viscoelastic system is governed by a third order jerk equation. The presence of viscoelasticity also introduces additional time scales and degrees of freedom into the problem when compared to their viscous counterparts, thus making the study of these systems in the presence of harmonic loading even more interesting. It is highly likely that the system would exhibit non-regular behavior for some combination of forcing frequency and forcing amplitude. With this motivation, we start by studying the dynamics of a harmonically forced von Mises truss in the presence of viscous damping only. This leads to a Duffing type equation with an additional quadratic non-linearity. We demonstrate some of the rich dynamic behavior that this system exhibits in some parameter ranges. This provides useful insight into the possible behavior of the viscoelastic system. The viscous damper is then replaced by a viscoelastic unit. We show that the system can exhibit both regular as well as chaotic behavior. The threshold limit for the chaotic motion has been determined using Melnikov’s criteria and verified through numerical simulations using the largest Lyapunov exponent. 

In this article we propose a theoretical investigation of the nonlinear dynamical response of a class of planar resonators dubbed the V-Shaped resonator. The resonators are intended for energy harvesting purpose and are designed to exhibit two-to-one internal resonance. In particular, we navigate the design space for the generalized V-shaped resonator to investigate the influence of shape parameters on the performance of the Vibration Energy Harvester. Notably, we introduce two metrics that help elucidating the role of the shape parameter in dictating the behavior of the system in terms of peak voltage and operational bandwidth width. For simplicity, we consider that the system is subjected to harmonic excitations near its primary resonances. 

Abstract Kirigami is defined as the ancient Japanese art of cutting and folding paper to create three-dimensional structures, which is a subset of the larger term. Recent developments in kirigami-based structures have sparked interest in the engineering community for the development of mechanical metastructures with customized behavior such as negative Poisson’s ratio, out-of-plane buckling, and soft robot locomotion. In this manuscript, nonlinear springs based on kirigami are developed; the springs can be used to create customized nonlinear oscillators and vibration suppression systems. A Helmholtz-Duffing oscillator with nonlinear damping is created by attaching a mass to a smooth track with the kirigami springs attached to it. Kirigami springs were made by strategically cutting plastic sheets in predetermined patterns and arranging them in a ring. Identification of the unknown system parameters is accomplished through the use of a two-step procedure. To determine the quasi-static behavior of the spring, it was first subjected to tensile testing. These parameters serve as the foundation for developing a strategy for determining the unknown energy loss parameters in a system. In the second step, the Method of Multiple Scales is used to develop an approximate solution for the transient response, which is then tested. This solution is coupled with an optimization routine that, by modifying the unknown model parameters, seeks to reduce the error between the experimental free oscillations and the developed analytical solution as closely as possible. 

Human–machine interactions (HMIs) describe how humans engage various systems, including those that are smart, autonomous, or both. Most HMIs either allow the human to control the machine (an instrument panel), allow the machine to obtain data (a heart monitor), or even both (a virtual reality setup). HMIs may be placed in three broad classes. In one class, the individual is active in the interaction—that is, the individual is the user or purchaser of a technology such as an automobile. In another class, the user is passive but consenting in the interaction—that is, the interaction occurs with their consent, such as the use of devices for medical diagnosis. There is also a class in which the user is passive and nonconsenting in the interaction, such as the use of facial recognition for law enforcement purposes.