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]

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]