By Jan Awrejcewicz,Vadim A Krysko,Irina V Papkova,Anton V Krysko
This e-book specializes in the computational research of nonlinear vibrations of structural contributors (beams, plates, panels, shells), the place the studied dynamical difficulties may be diminished to the honour of 1 spatial variable and time. The relief is conducted in keeping with a proper mathematical technique geared toward decreasing the issues with endless size to finite ones. the method additionally contains a transition from governing nonlinear partial differential equations to a collection of finite variety of usual differential equations.
Beginning with an summary of the hot effects dedicated to the research and regulate of nonlinear dynamics of structural participants, putting emphasis on balance, buckling, bifurcation and deterministic chaos, uncomplicated chaotic structures 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, a number of the wavelet transforms and the 4 Lyapunov exponents are used to discover, display screen and probably keep watch over chaos, hyper-chaos, hyper-hyper-chaos and deep chaos exhibited by means of oblong plate-strips and cylindrical panels.
The ebook is meant for post-graduate and doctoral scholars, utilized mathematicians, physicists, lecturers and teachers of universities and corporations facing a nonlinear dynamical procedure, in addition to theoretically vulnerable engineers of mechanical and civil engineering.
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