Search

The nonlinear periodic response of viscoelastic laminated composite plates subjected to harmonic excitation is carried out in time domain using the generalized Maxwell model in the form of a Boltzmann integral. The integral form of the viscoelastic constitutive relation is converted to the incremental form for the finite element formulation based on the Reissner–Mindlin plate theory incorporating von Karman geometric nonlinearity. The recursive relations are developed to compute the current time-step solution using only the previous time-step solution. The periodic response is obtained using shooting technique coupled with Newmark's time integration and arc length continuation method. The implementation of the shooting technique for the Boltzmann Integral based viscoelasticity done for the first time in this study involves derivation of a number of additional recursive relations and initial conditions at the beginning of each shooting cycle. The nonlinear periodic vibration characteristics such as frequency response, damping factor, steady-state response history, phase plane plots, and frequency spectra are presented for viscoelastic plates with different boundary conditions and lamination schemes. Further, the influence of relaxation time and number of Maxwell elements on the frequency response characteristics are investigated. It is seen that the shooting technique is capable of predicting periodic responses of viscoelastic dynamical systems directly from the second-order equations of motion and is more efficient than the direct time integration method. The nonlinear response of viscoelastic plates predicted using the equivalent elastic model with Rayleigh proportional damping (having same linear frequency response) is found to be significantly different from the one predicted using viscoelastic constitutive model. • Geometrically nonlinear periodic response using generalized Maxwell model. • Shooting technique with Newmark's time integration and arc length continuation method. • Incremental constitutive relation for stress/moment resultants and recursive relations. • Responses of viscoelastic and elastic plates with Rayleigh damping are compared. [ABSTRACT FROM AUTHOR]

Existing studies on electro-active polymers (EAP) have largely ignored the unequal-biaxial deformation instability, focusing instead on the equi-biaxial deformation instability of such a material class. The present study develops the first thermo-electrostrictive unequal-biaxial deformation instability model for particle-reinforced EAP composites filled with suitably added filler, which enhances its performance. The model first calibrates the particle-reinforced electromechanical material-oriented data in conjunction with previously released experiments. Later, the model demonstrates several unstable failure modes of the composites, namely thermal absorption, tension loss, electrical breakdown, electromechanical instability, and stretch rupture. Analytical findings of the model solution also manifest the stable and unstable zones of studied polymeric composites undergoing thermo-electromechanical unequal-biaxial deformation in conjunction with all unstable failure modes. Such findings of the proposed model have significant implications for soft robotics, particularly in forecasting the behavior of EAP-based smart composites used in the design of more advanced and efficient soft robotic systems. • An overlooked thermo-electrostrictive unequal-biaxial deformation instability model for EAP composites is developed. • A second law of thermodynamics-based continuum mechanics approach is followed. • Several unstable failure modes of EAP composites are demonstrated. • The stable working areas of EAP composites undergoing thermo-electrostrictive unequal-biaxial deformation are displayed. [ABSTRACT FROM AUTHOR]

Actuation devices made of smart polymers typically show various instabilities, which can adversely affect their performance and lead to device failure. In general, smart polymers exhibit wrinkling instability when subjected to an electric or magnetic field. At the same time, wrinkles can be used constructively in certain applications demanding a controlled alternation of the surface morphology. Critical factors influencing thin films' pull-in and wrinkling instabilities are discovered concerning the anisotropic taut domains with an applied electro-magneto-mechanical field control. A continuum mechanics-based electro-magneto-mechanical model is developed for predicting the thresholds on the taut domains in the plane of principal stretches. Also, the concept of natural width under simple tension is implemented to derive the coupled nonlinear equation that evaluates the associated taut domains. The findings of the model solution indicate that the extent of taut domains can be controlled by modifying the level and the principal direction of the transverse isotropy. Additionally, the taut domain for a particular level of applied electromagnetic field increases with an increase in the anisotropy parameter, while it depleted with an increase in the fiber orientations from 0 ° to 90 ° for an applied level of electromagnetic loading. • A taut domains model of electro-magneto-active smart thin membrane is developed. • The concept of natural width in tension is applied to derive the governing equation. • The proposed model is validated with an energy-based model of dielectric membrane. • The effect of anisotropy and fiber orientations on the taut domains is investigated. [ABSTRACT FROM AUTHOR]

Electro-magneto-active (EMA) polymers-based smart actuators suffer from electro-magneto-mechanical instability (EMMI) phenomena arising due to the positive feedback between the applied electric and magnetic fields and reduction in the polymer thickness. This work presents a theoretical investigation of EMMI phenomena of an EMA polymeric actuator in both static and DC dynamic modes of operation. A physics-based non-affine material model is adopted here for capturing the effect of the polymer chain entanglements and crosslinks on the instability phenomena. Simultaneously, a computationally efficient energy approach for obtaining the DC dynamic instability parameters is constructed, which depends on the energy balance at the position of maximal overshoot in an oscillation cycle. The findings from the current study illustrate the trends of variation in the deformation, electric field, and magnetic field at the onset of static and dynamic EMMI with the polymeric entanglements and crosslinks parameters. It is observed that large entanglements and crosslinks in polymer chains improve the stable operation travel range, which positively impacts the actuator performance. [ABSTRACT FROM AUTHOR]

Abstract: A semi-analytical procedure for obtaining stability conditions for strongly non-linear single degree of freedom system (SDOF) subjected to random excitations is presented using stochastic averaging technique. The method is useful for finding stability conditions for systems having highly irregular non-linear functions which cannot be integrated in closed form to yield analytical expressions for averaged drift and diffusion coefficients. In spite of numerical methods available for finding stability of SDOF system by determining Lyapunov exponent, the proposed technique may have to be adopted (i) when the excitation is non-white; and (ii) when numerical integration fails due to convergence problem. The method is developed in such a way that it lends itself to a numerical computational scheme using FFT for obtaining numerical values of drift and diffusion coefficients of Its differential equation and the corresponding FPK equation for the system. These values of averaged drift and diffusion coefficients are then fit into polynomial form using curve fitting technique so that polynomials can be used for stability analysis. Two example problems are solved as illustrations. The first one is the Van der Pol oscillator having non-linearities which can be treated purely analytically. The example is considered for the validation of the proposed method. The second one involves non-linearities in the form of signum function for which purely analytical solution is not possible. The results of the study show that the proposed method is useful and efficient for performing stability analysis of dynamic systems having any type of non-linearities. [Copyright &y& Elsevier]