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In this paper, the dynamics of a two-degree-of-freedom block-on-belt system subjected to both dry friction and external excitations is studied. The dry friction in the system follows the classical Coulomb's law, and the external excitations consist of two harmonic forces with different frequencies. In the study, a new two-dimensional (2-D) map is developed, which reduces the system without losing its essential dynamic features and greatly simplifies the investigation. On the basis of the 2-D map, bifurcation analysis and the computation of Poincaré sections and Lyapunov exponents can be carried out straightforwardly. Numerical simulations are performed, in which the proposed 2-D map is proved to be very effective and provide a powerful tool to understand the dynamical behavior of the system. Numerical results show that the system possesses rich dynamics characterized by periodic, quasi-periodic and chaotic attractors. Furthermore, it is found that the two-frequency excitation has significant influence on the dynamical behavior of the system.

An improved aerothermoelastic flutter model of an infinitely long isotropic panel is proposed to investigate the complex dynamic behaviors of panel structures in supersonic flow. Considering the history effects of aerodynamic heating, a new model suitable for numerical computation of the temperature distribution in the panel is presented and proved mathematically. Then, the internal force and moment in the panel induced by thermal stress are accurately introduced into the existing panel flutter model. Finally, some numerical analyses based on the Galerkin procedure are presented, in combination with the presented aerothermoelastic model which is based on von Karman large deflection plate theory. From the numerical results, it is found that the effects of the aerodynamic heating and its history are significant and complicated, since they can induce, intensify, or change the oscillation behaviors of the panel. Furthermore, a rich variety of nonlinear dynamic behaviors, such as instabilities and chaos in the panel flutter model, are captured and analyzed, by bifurcation analysis and the maximum Lyapunov exponent in nonlinear dynamics. As a conclusion, it can be drawn that the model presented could be used to study the aerothermoelastic dynamics accurately and feasibly.

The main aim of this paper is to focus on analysis of the dynamic properties of the electromechanical system with an impact element. This model is constructed with three degrees of freedom in the mechanical oscillating part, two translational and one rotational, and is completed with an electric circuit. The mathematical model of the system is represented by three mutually coupled second-order ordinary differential equations. Here, the most important nonlinearities are: stiffness of the support spring elements and internal impacts. Several important results were obtained by means of computational simulations. The impacts considerably increase the number of resonance peaks of the frequency response characteristic. Character of the system motion strongly depends on the width of clearances between the impact body and the rotor frame and changes from simple periodic to close to chaotic or to periodic with a large number of ultraharmonic components. For a suitably chosen system parameters, a significant damping effect of the impact element was observed.

The present contribution deals with the prediction of diffuse necking in the context of forming and stretching of metal sheets. For this purpose, two approaches are investigated, namely bifurcation and the maximum force principle, with a systematic comparison of their respective ability to predict necking. While the bifurcation approach is of quite general applicability, some restrictions are shown for the application of maximum force conditions. Although the predictions of the two approaches are identical for particular loading paths and constitutive models, they are generally different, which is even the case for elasticity, confirming the distinct nature of the two concepts. Closed-form expressions of the critical stress and strain states are derived for both criteria in elasto-plasticity and rigid-plasticity for a variety of hardening models. The resulting useful formulas in rigid-plasticity are shown to also accurately represent the elasto-plastic critical states for small ratios of the hardening modulus with respect to Young's modulus. Finally, the well-known expression of Swift's diffuse necking criterion, whose foundations are attributed in the literature to the maximum force principle, is shown here to originate from the bifurcation approach instead, providing a sound justification for it.

A transducer is a system that couples two loads. For example, an electromechanical transducer couples a mechanical force and an electrical voltage. A two-load, nonlinear system can exhibit rich behavior of bifurcation, which can be displayed in a three-dimensional space, with the horizontal plane representing the two loads, and the vertical axis representing the state of the system. In this three-dimensional space, a state of equilibrium at fixed loads corresponds to a point on a surface. The surface is smooth, but its projection to the load plane results in singularities of two types: fold and cusp. Here we identify the fold and cusp for a dielectric elastomer transducer by a combination of experiment and calculation. We conduct two kinds of experiment: electrical actuation under a constant force and mechanical pulling under a constant voltage. The theory and the experiment agree well. The fold and cusp are essential in the design of loading paths to avoid or harness the bifurcation.

When a hyperelastic tube is inflated, the inflation pressure has a maximum for almost all rubber material models, but has no maximum for commonly used arterial models. It is generally believed that the pressure having a maximum is a necessary condition for localized bulging to occur, and therefore aneurysms cannot be modeled as a mechanical bifurcation phenomenon. However, recent theoretical studies have shown that if the axial stretch is fixed during inflation, localized bulging may still occur even if a pressure maximum does not exist in uniform inflation. In this paper, numerical simulations are conducted to confirm this theoretical prediction. It is also demonstrated that if the axial pre-stretch is not sufficiently large, unloading near the two ends can reduce the axial stress to a value close to zero and Euler-type buckling then occurs.

In this paper, the incremental equilibrium equations and corresponding boundary conditions for the isotropic, hyperelastic and incompressible shells are derived and then employed in order to analyze the behavior of spherical and cylindrical shells subjected to external pressure. The generalized differential quadrature (GDQ) method is utilized to solve the eigenvalue problem that results from a linear bifurcation analysis. The results are in full agreement with the previously obtained results and the effects of thickness and mode number are studied on the shell’s stability. For the spherical and cylindrical shells of arbitrary thickness which are subjected to external hydrostatic pressure, the symmetrical buckling takes place at a value of ${\alpha }_1$ which depends on the geometric parameter $A_1/A_2$ and the mode number $n$, where $A_1$ and $A_2$ are the undeformed inner and outer radii, respectively, and ${\alpha }_1$ is the ratio of the deformed inner radius to the undeformed inner radius.

Responsive polymeric materials have attracted extensive research attention due to their capabilities in response to external stimuli such as electric field, magnetic field, temperature, pH, light, and chemicals while maintaining their unique features. However, with the existence of external stimuli, such materials are also susceptible to stimuli-induced instabilities and bifurcations that limit the functionalities of their applications. This paper aims to provide an overview on the state of the art of analytical and numerical methodologies for characterizing those stimuli-induced behaviors, including incremental approach, finite element method, and tension field theory. The general formulations and simulation procedures adopted in the analysis techniques are briefly introduced, and the advantages and limitations of each method are identified. Some research gaps and prospective directions are also discussed, which is expected to provide guidance for better design and applications of responsive polymeric materials in future studies.

In this paper, we demonstrate the potential functionalization of inherent nonlinearities associated with electrostatic MEMS resonators for low air pressure applications, with operating ranges as low as 0.65-295 mbar. The proposed pressure sensor is made of a polysilicon microplate subject to electrostatic actuation via an underneath electrode and attached to two cantilever microbeams. The pressure sensing mechanism relies on the motion-induced current method, a transduction mechanism that converts the dynamic alteration of the microplate due to pressure variations into an electrical signal detected via a lock-in amplifier. The experimental study showed evidence of the possible tunability of the pressure sensor via the deployment of different detection mechanisms to achieve superior performance in terms of sensitivity and low pressure operating range. These mechanisms rely on nonlinear dynamic features that result from the strong coupling between the microplate and the surrounding fluid along with the electrostatic actuation. These include dynamic pull-in instability, bifurcation and softening behavior associated with the elastic effect of the squeeze-film damping. The experimental results revealed that tracking the bifurcation frequency allows for the detection of low pressure levels, in the range of a few millibars. This capability is not provided by the resonance frequency shift method, which, while offering higher sensitivity, does not achieve the same low-pressure detection.