In this paper, transverse vibration analysis of rotating micro-beam is investigated based on the modified couple stress theory. The simply-supported modeled utilizing Euler-Bernoulli and Timoshenko beam theories. system around a fixed axis perpendicular to axial direction beam. For first time, displacement filed introduced as coupled field translational field. other words, mentioned rotational ...

In this paper, we study a semilinear Timoshenko system having two damping effects. The observation that two damping effects might lead to smaller decay rates for solutions in comparison to one damping effect is rigorously proved here in providing optimality results. Moreover the global well-posedness for small data in a low regularity class is presented for a larger class of nonlinearities than...

We study the asymptotic behavior of Timoshenko systems with memory, where the memory is given by a non-dissipative kernel and is acting only on one equation of the system. We show that the exponential stability depends on conditions regarding the decay rate of the kernel and a nice relationship between the coefficients of the system. Moreover, with full-memory effect in the system, we will show...

and Applied Analysis 3 Here, S t denotes the corresponding semigroup on H, generated by problem 1.1 , and ·, · 2 is the inner product in L2 Ω . The following energy equation holds: E0 E t ∫ t 0 δ‖v τ ‖λdτ, 2.3 where E t ≡ E u t , v t ≡ 1 2 ‖v t ‖2 J u t , 2.4 J u ≡ 1 2 a u 1 2 ( γ 1 )c u − 1 r b u , 2.5 with a u ≡ ‖u‖B, b u ≡ μ‖u‖r , c u ≡ β‖∇u‖ γ 1 2 . 2.6 Here, E0 ≡ E u0, v0 is the initial en...