Nonlinear Dynamics of a Dielectric Elastomer Membrane Under Compressive Loading

2020 ◽  
Author(s):  
Robert L. Lowe ◽  
Christopher G. Cooley
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Response ◽  
Frequency Response ◽  
Compressive Loading ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Dielectric Elastomer ◽  
Large Strains ◽  
Membrane Stretch ◽  
Wide Range

Abstract This paper investigates the nonlinear dynamics of square dielectric elastomer membranes under time-dependent, through-thickness compressive loading. The dielectric elastomer is modeled as an isotropic ideal dielectric, with mechanical stiffening at large strains captured using the Gent hyperelastic constitutive model. The equation of motion for the in-plane membrane stretch is derived using Hamilton’s principle. The static response of the membrane is first investigated, with equilibrium stretches calculated numerically for a wide range of compressive pre-loads and applied voltages. Snap-through instabilities are observed, with the critical snap-through voltage decreasing with increasing compressive pre-load. The dynamic response of the membrane is then investigated under forced harmonic excitation. Frequency response plots characterizing the steady-state vibration reveal primary, subharmonic, and superharmonic resonances. Near these resonances, two stable vibration states are possible, corresponding to upper and lower branches in the frequency response. Significant and practically meaningful differences in the dynamic response are observed when the system vibrates at a fixed frequency about the upper and lower branches, a feature not discussed in previous research.

scholarly journals Numerical Investigation of the Dynamic Response of Symmetric Laminated Composite Beams to Harmonic Excitations

2009 ◽  
Vol 18 (5) ◽  
pp. 096369350901800 ◽  
Author(s):  
Zeki Kıral
Keyword(s):  
Dynamic Response ◽  
Frequency Response ◽  
Flexural Rigidity ◽  
Plate Theory ◽  
Damping Ratio ◽  
Excitation Frequency ◽  
Laminated Composite ◽  
Harmonic Excitation ◽  
Numerical Results ◽  
Harmonic Response

The aim of this study is to investigate the dynamic response of a laminated composite beam subjected to a harmonic excitation by a numerical time integration method known as Newmark method. The finite element method based on the classical laminated plate theory is used in order to obtain structural stiffness. The structural damping is modelled as proportional damping which is referred to as Rayleigh damping and two different damping ratios are used. The effect of damping on the frequency response of the beam is investigated for a broad range of excitation frequency. The effect of excitation point on the harmonic response is also considered. Four different lay-up configurations namely [0]2s, [0/90]s, [45/-45]s and [90]2s are considered in order to show the effect of the stacking sequence on the frequency response of the beam. The numerical results presented in this study show that, the magnitude of the harmonic response of the beam reduces considerably as the damping ratio increases and [90]2s lay-up produces largest dynamic response due to the reducing flexural rigidity. Numerical results also show that the location and frequency of the harmonic excitation has important role on the dynamic response of the beam.

scholarly journals Dynamic Electromechanical Response of a Viscoelastic Dielectric Elastomer under Cycle Electric Loads

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Junjie Sheng ◽  
Yuqing Zhang
Keyword(s):  
Dynamic Response ◽  
Dynamic Stability ◽  
Relaxation Times ◽  
Excitation Frequency ◽  
Dielectric Elastomer ◽  
Time Dependent ◽  
Electric Load ◽  
Single Cycle ◽  
Set Up ◽  
Electric Loads

Dielectric elastomer (DE) is able to produce large electromechanical deformation which is time-dependent due to the viscoelasticity. In the current study, a thermodynamic model is set up to characterize the influence of viscoelasticity on the electromechanical and dynamic response of a viscoelastic DE. The time-dependent dynamic deformation, the hysteresis, and the dynamic stability undergoing viscoelastic dissipative processes are investigated. The results show that the electromechanical stability has strong frequency dependence; the viscoelastic DE can attain a larger stretch in the dynamic response than the quasistatic actuation. Furthermore, with the decreasing frequency of the applied electric load, the viscoelastic DE system will present dynamic stability evolution from an aperiodic motion to the quasiperiodic motion. The DE system may also experience a stability evolution from a single cycle motion to multicycle motion with the increasing relaxation times. The value and variation trend of the amplitude of the stretch are highly dependent on the excitation frequency and the relaxation time.

Nonlinear Dynamic Responses of Elastic Structures With Two Rectangular Liquid Tanks Subjected to Horizontal Excitation

2010 ◽  
Vol 6 (2) ◽  
Author(s):  
Takashi Ikeda
Keyword(s):  
Frequency Response ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Pitchfork Bifurcation ◽  
Harmonic Excitation ◽  
Dynamic Responses ◽  
Response Curves ◽  
Chaotic Vibrations ◽  
Tuned Liquid Dampers ◽  
Theoretical Results

Nonlinear vibrations of an elastic structure with two partially filled liquid tanks subjected to horizontal harmonic excitation are investigated. The natural frequencies of the structure and sloshing satisfy the tuning condition 1:1:1 when tuned liquid dampers are used. The equations of motion for the structure and the modal equations of motion for the first, second, and third sloshing modes are derived by using Galerkin’s method, taking into account the nonlinearity of the sloshing. Then, van der Pol’s method is employed to determine the frequency response curves. It is found in calculating the frequency response curves that pitchfork bifurcation can occur followed by “localization phenomenon” for a specific excitation frequency range. During this range, sloshing occurs at different amplitudes in the two tanks, even if the dimensions of both tanks are identical. Furthermore, Hopf bifurcation may occur followed by amplitude- and phase-modulated motions including chaotic vibrations. In addition, Lyapunov exponents are calculated to prove the occurrence of both amplitude-modulated motions and chaotic vibrations. Bifurcation sets are also calculated to show the influence of the system parameters on the frequency response. Experiments were conducted to confirm the validity of the theoretical results. It was found that the theoretical results were in good agreement with the experimental data.

Modelling of Multilayer Perforated Electrodes for Dielectric Elastomer Actuator Applications

MRS Advances ◽  
2020 ◽  
Vol 5 (14-15) ◽  
pp. 765-771 ◽  
Author(s):  
Seshadri Reddy Nagireddy ◽  
Karnati Kumar Sai Charan ◽  
Rishabh Bhooshan Mishra ◽  
Aftab M. Hussain
Keyword(s):  
Electric Fields ◽  
Spray Coating ◽  
Dielectric Elastomer ◽  
Large Strains ◽  
Maximum Output ◽  
Mechanical Stiffness ◽  
Coverage Area ◽  
Wide Range ◽  
Transfer Method ◽  
Electrode Coverage

AbstractDielectric elastomer actuators (DEAs), which are inherently complaint capacitors, are emerging as pseudo-muscular actuators with a wide range of applications. In order to achieve high stretchability for large DEA actuation, carbon nanotube (CNT) and other 1D materials-based electrodes are used to maintain conductance at large strains. These electrodes are typically fabricated using spray coating or filter transfer method and resemble a perforated electrode under high magnification. Hence, there can be a loss of field and stray capacitance when multiple layers of carbon nanotubes (CNTs)-based electrodes are used. This study investigates the effect of microscopic perforations on the nature of electric fields and on the capacitance of multi-layered CNT-based DEA structures with various dimensions and geometric properties of the electrodes. It has been found that the capacitance decreases with increase in the perforations however its effect is limited for a reasonable coverage. The change in normalized is found to be negligible (∼5%) for an electrode coverage area of over 90%, however, the maximum output work reduces by 18.2%. This analysis is important to develop robust and reliable CNT-based DEA structures, without using excessive CNTs which can lead to increased mechanical stiffness of the electrodes.

Bifurcation Modes of Periodic Solution in a Duffing System Under Constant Force as Well as Harmonic Excitation

2019 ◽  
Vol 29 (13) ◽  
pp. 1950173 ◽  
Author(s):  
Lei Hou ◽  
Xiaochao Su ◽  
Yushu Chen
Keyword(s):  
Frequency Response ◽  
Damping Ratio ◽  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Harmonic Excitation ◽  
Nonlinearity Parameter ◽  
Constant Force ◽  
Response Curves ◽  
Duffing System ◽  
Singularity Method

This paper focuses on the classification of the bifurcation modes of a Duffing system under the combined excitations of constant force and harmonic excitation. The Harmonic Balance method combined with the arc-length continuation is used to obtain the periodic solutions of the system, and the Floquet theory is employed to analyze the stability of the corresponding solutions. Accordingly, the frequency-response curves affected respectively by the constant force and the magnitude of the harmonic excitation are analyzed to show the basic dynamical properties of the system. Afterwards, the bifurcation investigations are carried out with the aid of the two-state variable singularity method. It is derived that there are a total of six different types of bifurcation modes due to the effects of the constant force and the magnitude of the harmonic excitation. At last, the effects of the nonlinearity parameter and the damping ratio on the bifurcation modes of the system are also discussed. The results obtained in this paper extend the findings in reference that the system can have markedly three types of frequency-response curves: with only one solution, or with maximum three or five solutions for a certain excitation frequency, and contribute to a better understanding of the significant influence of the constant force.

Nonlinear dynamics of mechanical system with external excitation

Open Physics ◽  
2005 ◽  
Vol 3 (1) ◽  
Author(s):  
Bogusław Ryczek
Keyword(s):  
Nonlinear Dynamics ◽  
Computer Simulation ◽  
Mechanical System ◽  
Dry Friction ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Friction Model ◽  
Lumped Mass ◽  
External Excitation ◽  
Transient Motion

AbstractThis paper attends to the problem of vibration of a self-excited mechanical system with a relatively complicated, history dependent dry friction model. The experimentally identified friction model allows description of various cases of stationary and transient motion. The system is composed of a lumped mass that interacts with a belt by means of dry friction. The system is additionally subjected to an external harmonic excitation through elastic element. The main objective of the experimental research has been focused on the analysis of the system behaviour for various values of the excitation frequency. This paper includes also computer simulation of the vibration of the considered system and comparison between the results of experimental and theoretical analysis. The comparison enables the assumed friction model for steel-polyester pair to be verified. It was another goal of the investigations.

Intrinsic Localized Modes of Principal Parametric Resonances in Pendulum Arrays Subjected to Vertical Excitation

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Takashi Ikeda ◽  
Yuji Harata ◽  
Chongyue Shi ◽  
Keisuke Nishimura
Keyword(s):  
Experimental Data ◽  
Theoretical Analysis ◽  
Frequency Response ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Localized Modes ◽  
Response Curves ◽  
Chaotic Motions ◽  
Intrinsic Localized Modes ◽  
Spring Constants

Intrinsic localized modes (ILMs) are investigated in an N-pendulum array subjected to vertical harmonic excitation. The pendula behave nonlinearly and are coupled with each other because they are connected by torsional, weak, linear springs. In the theoretical analysis, van der Pol's method is employed to determine the expressions for frequency response curves for the principal parametric resonance, considering the nonlinear restoring moment of the pendula. In the numerical results, frequency response curves for N = 2 and 3 are shown to examine the patterns of ILMs, and demonstrate the influences of the connecting spring constants and the imperfections of the pendula. Bifurcation sets are also calculated to show the excitation frequency range and the conditions for the occurrence of ILMs. Increasing the connecting spring constants results in the appearance of Hopf bifurcations. The numerical simulations reveal the occurrence of ILMs with amplitude modulated motions (AMMs), including chaotic motions. ILMs were observed in experiments, and the experimental data were compared with the theoretical results. The validity of the theoretical analysis was confirmed by the experimental data.

A Multi-Point Loaded Piezocomposite Beam: Mechanics and Response to Harmonic Excitation

2018 ◽  
Author(s):  
Patrick S. Heaney ◽  
Onur Bilgen
Keyword(s):  
Experimental Data ◽  
Dynamic Response ◽  
Natural Frequency ◽  
Harmonic Excitation ◽  
Wide Range ◽  
Cantilevered Beam ◽  
Inertial Loading ◽  
Tip Mass ◽  
Configuration Changes ◽  
Beam Mechanics

In this paper a multi-segment beam, in what is called an inertial four-point loaded configuration, is proposed and its dynamic response is analyzed. In this configuration, two symmetrical overhanging free segments extend beyond the pinned supports, and two tip masses are attached to these free segments yielding symmetrical inertial loading at the tips. By varying the configuration parameters of this multi-segment beam, such as support locations and tip loading, the dynamic response of the system can be significantly altered. The harmonically excited transverse vibration of a piezocomposite beam with four-point loaded boundary conditions is analyzed as a function of the support location and tip mass. Experimental data for several support locations is presented for validation of the analytical model and the predicted relationship between the system natural frequency, support locations, and tip masses. Comparisons are also made between the multi-point loaded cases and a reference cantilevered beam. The analytical and experimental results demonstrate that the natural frequency of a multi-point loaded beam can be continuously adjusted in a relatively wide range using the configuration changes investigated.

Localization Phenomena in Pendulum Arrays Subjected to Vertical Excitation

2014 ◽  
Author(s):  
Takashi Ikeda ◽  
Yuji Harata ◽  
Chongyue Shi ◽  
Keisuke Nishimura
Keyword(s):  
Experimental Data ◽  
Theoretical Analysis ◽  
Frequency Response ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Response Curves ◽  
Chaotic Motions ◽  
Vertical Excitation ◽  
Parametric Resonances ◽  
Spring Constants

Localization phenomena, also referred to as intrinsic localized modes (ILMs), are investigated in an N-pendulum array subjected to vertical harmonic excitation. The pendula behave nonlinearly and are connected with each other by weak linear springs. In the theoretical analysis, van der Pol’s method is employed to determine the expressions for frequency response curves for the principal parametric resonances, considering the nonlinear restoring moment of the pendula. In the numerical results, frequency response curves for N=2 and 3 are shown to examine the patterns of ILMs, and the influences of the connecting spring constants and the imperfections of the pendula. Bifurcation sets are also calculated to show the excitation frequency range and the conditions for the occurrence of ILMs. Increasing the connecting spring constant results in the appearance of Hopf bifurcation. The numerical simulations reveal the occurrence of ILMs with amplitude modulated motions (AMMs) including chaotic motions. ILMs were observed in experiments, and the experimental data were compared with the theoretical results. The validity of the theoretical analysis was confirmed by the experimental data.

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