Analysis of a thermoelastic Timoshenko beam model

Stability of thermoelastic Timoshenko beam with suspenders and time-varying feedback

“…The damping structure in system (2.14)-(2.16) is sufficient enough to stabilize the system without any additional conditions on the coefficient parameters as it is the case with many Timoshenko beam systems in the literature. The result of the present paper generalizes the one established in Bochichio et al [6] and allows a large class of functions that satisfy condition (A 2 ). We also gave some examples to illustrate our theoretical finding.…”

“…The temperature dissipation here is assumed to be governed by the Fourier law of heat conduction. For a(t) ≡ 1, g 1 (s) ≡ s and γ 2 ≡ 0, g 2 ≡ 0 in system (1.1), Bochichio et al [6] proved a well-posedness and an exponential stability result. A number of works have been done on different thermoelastic Timoshenko models without suspenders (see [10,12,16,17,28] and references in them).…”

“…Motivated by the works in [3,6,29], in the current paper, we are concerned with the stability result for the thermoelastic Timoshenko system with suspension cables, timevarying internal feedback, and time-varying weight given in (1.1)-(1.3). The result in [6] is a particular case of our result in this paper.…”

Suspension bridge model with laminated beam

“…A laminated beam with friction damping was considered in [16]. The internal damping combined with thermoelastic damping given by Fourier lay was considered in [3] for the suspension bridge, modeled by the Timoshenko system, where the cable is supposed to be thermally insulated, and it was proved that the solution decays exponentially to zero.…”

Local linear Timoshenko rod

“…If it is assumed that the motion is locally linear, then a natural choice for shear and bending are the constitutive equations of the Timoshenko theory (see e.g. [13], [14], [5], [6], [7] and [15]). For the longitudinal strain Hooke's law in its simplest form is used.…”