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-...

The bending of bilayer plates is a mechanism which allows for large deformations via small externally induced lattice mismatches of the underlying materials. Its mathematical modeling, discussed herein, consists of a nonlinear fourth order problem with a pointwise isometry constraint. A discretization based on Kirchhoff quadrilaterals is devised and its Γ-convergence is proved. An iterative met...

We find self-accelerating beams in highly nonlocal nonlinear optical media, and show that their propagation dynamics is strongly affected by boundary conditions. Specifically for the thermal optical nonlinearity, the boundary conditions have a strong impact on the beam trajectory: they can increase the acceleration during propagation, or even cause beam bending in a direction opposite to the in...

The dynamics of beams that undergo large displacements is analyzed in frequency domain and comparisons between models derived by isogeometric analysis and p-FEM are presented. The equation of motion is derived by the principle of virtual work, assuming Timoshenko’s theory for bending and geometrical type of nonlinearity. As a result, a nonlinear system of second order ordinary differential equa...

Self-action effects such as self-defocusing and self-bending are well-known nonlinear optical phenomenon dating back to the 1960s. Until recently the so-called blooming or lensing effect of a symmetric beam has been a main topic of investigation. A smaller number of experiments using asymmetric beams were reported (see, for example Khoo, Golub, and Swartzlander.) Whereas many early experiments ...

Nonlinear resonant ultrasound spectroscopy (NRUS) consists of evaluating one or more resonant frequency peak shifts while increasing excitation amplitude. NRUS exhibits high sensitivity to global damage in a large group of materials. Most studies conducted to date are aimed at interrogating the mechanical damage influence on the nonlinear response, applying bending, or longitudinal modes. The s...

This paper deals with boundary value problems for nonlinear monotone potential operators. An analysis of the nonlinear (monotone potential) Sturm–Liouville operator Au := − ( k((u′)2)u′(x) )′+q(x)u(x), x ∈ (a, b) shows that the potential of this operator as well as the potential of related boundary value problems play an important role not only for solvability of these problems, but also for li...