Solid-state Raman lasers are known as important sources at normally difficult to access wavelengths, and our recent studies have shown that they also form the basis of a class of wavelength selectable lasers. This paper summarizes our recent studies in wavelength selectable Raman lasers in the visible (532-650nm) and ultraviolet (266-321 nm).

Analyzing the NONLINEAR vibration of beams is one of the important issues in structural engineering. According to this, an impressive analytical method which is called modified iteration perturbation method (MIPM) is used to obtain the behavior and frequency of a cantilever beam with geometric NONLINEAR. This new method is combined by the Mickens and iteration methods. Moreover, this method does not require small parameter in the equation which is difficult to be found for NONLINEAR oscillation. The accuracy of the solution that is obtained by the use of MIPM has been shown graphically and compared with exact solution. Comparison shows that good adaptation is obtained and MIPM as a powerful method for solving the vibrational behavior of structures analytically.

The disordered fibrous networks provide load-bearing and main structural to different biological materials such as soft tissues. These networks display a highly NONLINEAR stress-strain relationship behavior when subjected to mechanical loads. This NONLINEAR strain-stiffening behavior is dependent on the network microstructure and properties of constituting fiber. We conduct a comprehensive computational study to characterize the importance of material properties of individual fibers as well as the local connectivity or coordination number and bending rigidity in the overall NONLINEAR mechanical response of a 3D random fiber network. The presented model shows the NONLINEAR stiffening with increasing applied shear strain more than critical shear strain. We determine the amount of strain-stiffening as a function of network microstructure parameters and the amount of NONLINEARity of the fibers. The results show that the constitutive behavior of fibers displays much more strain-stiffening than networks made up of linear fibers. We find that the importance of the NONLINEAR reaction of individual fiber materials in the general mechanical behavior of networks becomes more important with increasing network connectivity. Furthermore, the amount of stress created in the network under shear increases with the enhanced connectivity of the network due to an increase in the network stiffness. Our model points to the important role of the mechanical response of individual fiber as well as the microstructure of the network in determining the overall mechanical properties of the 3D random network, which could be used to design and better understand the complex biomimetic network systems such as biological tissues and artificial engineering networks.

We want to study the dynamics of a simple linear harmonic micro spring which is under the influence of the quantum Casimir force/pressure and thus behaves as a (an) NONLINEAR (anharmonic) Casimir oscillator. Generally, the equation of motion of this NONLINEAR micromechanical Casimir oscillator has no exact solvable (analytical) solution and the turning point(s) of the system has (have) no fixed position(s); however, for particular values of the stiffness of the micro spring and at appropriately well-chosen distance scales and conditions, there is (are) approximately sinusoidal solution(s) for the problem (the variable turning points are collected in a very small interval of positions). This, as a simple and elementary plan, may be useful in controlling the Casimir stiction problem in micromechanical devices.

In this paper, the continuse Legendre wavelets constructed on the interval [0, 1] are used to solve the NONLINEAR Fredholm integro-differential equation. The NONLINEAR part of integro-differential is ap- proximated by Legendre wavelets, and the NONLINEAR integro-differential is reduced to a system of NONLINEAR equations. We give some numerical examples to show applicability of the proposed method.

In this paper, we first introduce the concepts of an equilibrium region and a stable equilibrium region. Then, we state and prove conditions under which a NONLINEAR autonomous system has a stable equilibrium region. It will be shown that these concepts and stability conditions are generalizations of the corresponding concepts of equilibrium points and asymptotical stable equilibrium points and their stability conditions. Using these conditions and Poincare-Bendixson theorem, we discuss conditions for the existence of periodic solutions in a NONLINEAR system of ordinary differential equations.

In this paper, NONLINEAR vibration control of a plate is investigated using a NONLINEAR modified positive position feedback method that is applied through a piezoelectric layer on the plate. Based on the classical theory of displacement and strain relations with von Karman, intended equations of motion for the smart plate have been obtained. In this model, transverse vibrations are studied and stimulations are performed for the primary resonance. Boundary conditions of the smart plate are simply supported. The plate is thickness symmetrical. Using the Galerkin method the temporal NONLINEAR equations governing the system have been found. Then, the free and forced vibrations of the structure with the NONLINEAR modified positive position feedback controller have been solved using the Method of Multiple Scales to obtain an analytical solution. Results show that this controller reduces the amplitude of the vibration by inducing an increase in the damping coefficient. In addition, this provides a higher level of suppression in the overall frequency domain response by increasing the compensator gain. Finally, the results of the analytical solution for the closed-loop NONLINEAR modified positive position feedback controller are presented and compared with the result of the conventional positive position feedback controller and NONLINEAR integral resonant controller. The results show that the performance of the NONLINEAR modified positive position feedback controller is better than other controllers and significantly reduces the vibration amplitude.