This paper presents an analytical technique for the analysis of a stochastic dynamic system whose damping behavior is described by a fractional derivative of order 1/2. In this approach, an eigenvector expansion method proposed by Suarez and Shokooh is used to obtain the response of the system. The properties of Laplace transforms of convolution integrals are used to write a set of general Duha...

Abstract. A viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions on the relaxation function and with certain initial data and by adopting the perturbed energy method, we establish uniform decay rate of the solution energy in terms of the behavior of the relaxation function, which are not n...

where a, b > 0, p > 2, m ≥ 1, and Ω is a bounded domain of R (n ≥ 1), with a smooth boundary ∂Ω. In the absence of the viscoelastic term (g = 0), the problem has been extensively studied and results concerning existence and nonexistence have been established. For a = 0, the source term bu |u|p−2 causes finite time blow up of solutions with negative initial energy (see [2], [8]). For b = 0, the ...

A viscoelastic rod model which includes damping has been used to simulate the spinal column mathematically. This one-dimensional rod was subjected to a ramp input acceleration and the theoretical acceleration at the end of the rod was compared to the experimental head acceleration data from previously conducted cadaver t&s. The agreement between the experimental and theoretical results is bette...