Nonlinear Oscillations: Exact Solutions and their Approximations

Mechanics of dielectric elastomer structures: A review

This paper studies the nonlinear vibration of a dielectric elastomer balloon considering both the strain-stiffening and the second invariant of the Cauchy-Green deformation tensor. To this end, the Gent-Gent hyperelastic model is proposed. The ordinary differential equation governing the motion of the system is derived using the Euler-Lagrange energy method. Then, it is solved with the application of a time integration-based solver. The chaotic interval for critical system parameters is identified, with and without considering the influence of the second invariant. This identification is conducted by depicting bifurcation diagrams of Poincare sections and the largest Lyapunov exponent criteria. In order to better analyse different motions of the system, time histories, phase-plane diagrams, Poincare maps, and power spectral densities are illustrated. Based on the obtained results, the second invariant parameter of the Gent-Gent model could suppress the chaotic motion of the system. Increasing this parameter, a transition from the chaos to the quasiperiodic attractor would happen.

Nonlinear dynamics of dielectric elastomer balloons based on the Gent-Gent hyperelastic model

https://research-information.bris.ac.uk/ws/files/220610060/Nonlinear_dynamics_of_a_conical_dielectric_elastomer_oscillator_with_switchable_mono_to_bi_stability.pdf

Nonlinear dynamics of a conical dielectric elastomer oscillator with switchable mono to bi‐stability

Abstract This paper presents a critical review of the nonlinear dynamics of hyperelastic structures. Hyperelastic structures often undergo large strains when subjected to external time-dependent forces. Hyperelasticity requires specific constitutive laws to describe the mechanical properties of different materials, which are characterised by a nonlinear relationship between stress and strain. Due to recent recognition of the high potential of hyperelastic structures in soft robots and other applications, and the capability of hyperelasticity to model soft biological tissues, the number of studies on hyperelastic structures and materials has grown significantly. Thus, a comprehensive explanation of hyperelastic constitutive laws is presented, and different techniques of continuum mechanics, which are suitable to model these materials, are discussed in this literature review. Furthermore, the sensitivity of each hyperelastic strain energy density function to coefficient variation is shown for some well-known hyperelastic models. Alongside this, the application of hyperelasticity to model the nonlinear dynamics of polymeric structures (e.g., beams, plates, shells, membranes and balloons) is discussed in detail with the assistance of previous studies in this field. The advantages and disadvantages of hyperelastic models are discussed in detail. This present review can stimulate the development of more accurate and reliable models. 

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A review on the nonlinear dynamics of hyperelastic structures

Dielectric elastomers (DEs) are soft electromechanical devices, which operate under a high voltage. The majority of methods for calculating the nonlinear vibration of DEs are the numerical ones. However, the analytical methods may also be capable to achieve the reliable general and specific solutions for DEs. This paper investigates the vibration of a dielectric elastomer balloon (DEB) using the method of multiple scales (MMS). The equations of motion are derived by the method of Euler-Lagrange. Using the Taylor expansion , the governing equation of motion is transformed into a general form, then the MMS is applied to solve the problem. Two cases of voltage are considered; in the first one, the balloon is under a static voltage while in the second one the balloon is under a sinusoidal voltage . When the voltage is static, the time-history responses and the phase diagrams are depicted using the MMS and the Runge-Kutta numerical integration to verify the accuracy of the proposed method. For the sinusoidal voltage, the effect of jump phenomenon and variations of pressure and electrical potential difference (Voltage) on the frequency-response curves are studied. The results show that the MMS is in a good agreement with the Runge-Kutta numerical method. Moreover, with the presentation of various values of the pressure and the electrical potential difference, the softening behavior and the jump phenomenon are observed in the frequency response curves .

Analytical approximation solutions of a dielectric elastomer balloon using the multiple scales method

In this paper, nonlinear resonance characteristics of a dielectric elastomer actuator are investigated with special consideration on the thermal effects. A finite thermo-elasticity model based on t...

Nonlinear Resonance Analysis of Dielectric Elastomer Actuators Under Thermal and Isothermal Conditions

In this paper, an effort is made to study the chaotic motions of a dielectric elastomer (DE). The DE is activated by a time-dependent voltage (AC voltage), which is superimposed on a DC voltage. Th...

Chaotic Motion of a Parametrically Excited Dielectric Elastomer

This paper aims to investigate the chaotic and nonlinear resonant behaviors of a dielectric elastomer-based microbeam resonator, incorporating material and geometric nonlinearities. The von Karman ...

Amin Alibakhshi

Papers

Nonlinear dynamics of dielectric elastomer balloons based on the Gent-Gent hyperelastic model

Analytical approximation solutions of a dielectric elastomer balloon using the multiple scales method

Nonlinear Resonance Analysis of Dielectric Elastomer Actuators Under Thermal and Isothermal Conditions

Chaotic Motion of a Parametrically Excited Dielectric Elastomer

Nonlinear dynamic responses of electrically actuated dielectric elastomer-based microbeam resonators: