By Jan Awrejcewicz,Vadim A Krysko,Irina V Papkova,Anton V Krysko
This ebook specializes in the computational research of nonlinear vibrations of structural individuals (beams, plates, panels, shells), the place the studied dynamical difficulties could be lowered to the honour of 1 spatial variable and time. The aid is performed in keeping with a proper mathematical technique geared toward lowering the issues with countless size to finite ones. the method additionally incorporates a transition from governing nonlinear partial differential equations to a suite of finite variety of traditional differential equations.
Beginning with an summary of the new effects dedicated to the research and keep watch over of nonlinear dynamics of structural contributors, putting emphasis on balance, buckling, bifurcation and deterministic chaos, easy chaotic platforms are in brief mentioned. subsequent, bifurcation and chaotic dynamics of the Euler–Bernoulli and Timoshenko beams together with the geometric and actual nonlinearity in addition to the elastic–plastic deformations are illustrated. regardless of the hired classical numerical research of nonlinear phenomena, many of the wavelet transforms and the 4 Lyapunov exponents are used to discover, video display and doubtless keep watch over chaos, hyper-chaos, hyper-hyper-chaos and deep chaos exhibited by way of oblong plate-strips and cylindrical panels.
The ebook is meant for post-graduate and doctoral scholars, utilized mathematicians, physicists, academics and academics of universities and firms facing a nonlinear dynamical procedure, in addition to theoretically vulnerable engineers of mechanical and civil engineering.