Nonlinear Vibrations in Homogeneous Nonprismatic Timoshenko Cantilevers

Nonlinear Vibrations of Timoshenko Beams Carrying a Concentrated Mass

Transverse vibrations of Timoshenko type beams carrying a concentrated mass have been investigated. Both ends of this mass-beam system have simply supports. Hamilton Principle has been used in order to derive equation of motion . For this coupled differential equations, approximately solutions have been searched by means of Method of Multiple Scales(a perturbation method). These solutions consi...

Dynamic state switching in nonlinear multiferroic cantilevers

We demonstrate read-write-read-erase cyclical mechanical-memory properties of all-thin-film multiferroic heterostructured cantilevers when a high voltage is applied on the PbðZr0:52Ti0:48ÞO3 piezo-film. The device state switching process occurs due to the presence of a hysteresis loop in the piezo-film frequency response. The reference frequency at which the strain-mediated Fe0:7Ga0:3 based mul...

Dynamic Analysis of a Nonlinear Timoshenko Equation

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...

Linear and nonlinear photoinduced deformations of cantilevers.

Glassy and elastomeric nematic networks with dye molecules present can be very responsive to illumination, huge reversible strains being possible. If absorption is appreciable, strain decreases with depth into a cantilever, leading to bend that is the basis of micro-opto-mechanical systems (MOMS). Bend actually occurs even when Beer's law suggests a tiny penetration of light into a heavily dye-...

Mildly dissipative nonlinear Timoshenko systems — global existence and exponential stability