Stochastic Stability of a Fractional Viscoelastic Plate Driven by Non-Gaussian Colored Noise

In this paper, the moment Lyapunov exponent and stochastic stability of a fractional viscoelastic plate driven by non-Gaussian colored noise is investigated. Firstly, the stochastic dynamic equations with two degrees of freedom are established by piston theory and Galerkin approximate method. The fractional Kelvin–Voigt constitutive relation is used to describe the material properties of the viscoelastic plate, which leads to that the fractional derivation term is introduced into the stochastic dynamic equations. And the noise is simplified into an Ornstein-Uhlenbeck process by utilizing the path-integral method. Then, via the singular perturbation method, the approximate expansions of the moment Lyapunov exponent are obtained, which agree well with the results obtained by the Monte Carlo simulations. Finally, the effects of the noise, viscoelastic parameters and system parameters on the stochastic dynamics of the viscoelastic plate are discussed.

Nonlinear oscillations of particle-reinforced electro-magneto-viscoelastomer actuators

This work presents the dynamic modeling and analysis of a particle-reinforced and pre-stressed electro-magneto-viscoelastic plate actuator. The actuator belongs to a smart actuator category and is made of an electro-magneto-active polymer filled with a particular volume fraction of suitable fillers. An energy-based electro-magneto-viscoelastic model is developed to predict the actuator response and interrogate the impact of particle reinforcement on the dynamic oscillations of a pre-stressed condition of the actuator. An Euler–Lagrange equation of motion is implemented to deduce the governing dynamic equation of the actuator. The findings of the model solutions provide preliminary insights on the alteration of the nonlinear behavior of the actuator excited by DC and AC dynamic modes of actuation. It is observed that the enrichment in the particle reinforcement characterized by the amount of fillers strengthens the polymer and depleted the associated level of deformation. Also, the depletion in the intensity of oscillation and enhancement in the frequency of excitation is perceived with an increase in the particle reinforcement. In addition, the time-history response, Poincare plots and phase diagrams are also plotted to assess the stability, periodicity, beating phenomenon, and resonant behavior of the actuator. In general, the current study provides initial steps toward the modern actuator designs for various futuristic applications in the engineering and medical field.

Dynamic Stability of Orthotropic Viscoelastic Rectangular Plate of an Arbitrarily Varying Thickness

The research object of this work is an orthotropic viscoelastic plate with an arbitrarily varying thickness. The plate was subjected to dynamic periodic load. Within the Kirchhoff–Love hypothesis framework, a mathematical model was built in a geometrically nonlinear formulation, taking into account the tangential forces of inertia. The Bubnov–Galerkin method, based on a polynomial approximation of the deflection and displacement, was used. The problem was reduced to solving systems of nonlinear integrodifferential equations. The solution of the system was obtained for an arbitrarily varying thickness of the plate. With a weakly singular Koltunov–Rzhanitsyn kernel with variable coefficients, the resulting system was solved by a numerical method based on quadrature formulas. The computational algorithm was developed and implemented in the Delphi algorithmic language. The plate’s dynamic stability was investigated depending on the plate’s geometric parameters and viscoelastic and inhomogeneous material properties. It was found that the results of the viscoelastic problem obtained using the exponential relaxation kernel almost coincide with the results of the elastic problem. Using the Koltunov–Rzhanitsyn kernel, the differences between elastic and viscoelastic problems are significant and amount to more than 40%. The proposed method can be used for various viscoelastic thin-walled structures such as plates, panels, and shells of variable thickness.