Theoretical Investigation of Propagation of Laser Beam and Ultrashort Pulsed Beam;

By starting from the paraxial wave equation,the analytical expression of the ultrashort Hyperbolic Secant pulsed beam are deduced.

By using slowly-varying envelope approximation, a family of solutions of the paraxial wave equation are found in theory, which represents a new family of ultrashort pulsed beams called ultrashort pulsed complex argument Sinc-Gaussian beams.

Laser peen forming (LPF) is a process that elongates the peened metal surface and bends the overall shape with a shockwave,which is formed by a pulsed laser beam shocking the metal surface,penetrates the metal and introduces a residual impress stress field in the surface and inside.

By means of the impulse response matrix method, dy namic responses of multi DOF syste ms and their sensitivity with resp ect to design variables are expres sed in the form of integration, wi thout the conditions of proportion al damping and symmetric mass, dam ping and stiffness matrices.