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Full Description
This monograph is devoted to construction of novel theoretical approaches of m- eling non-homogeneous structural members as well as to development of new and economically ef?cient (simultaneously keeping the required high engineering ac- racy)computationalalgorithmsofnonlineardynamics(statics)ofstronglynonlinear behavior of either purely continuous mechanical objects (beams, plates, shells) or hybrid continuous/lumped interacting mechanical systems. In general, the results presented in this monograph cannot be found in the - isting literature even with the published papers of the authors and their coauthors. We take a challenging and originally developed approach based on the integrated mathematical-numerical treatment of various continuous and lumped/continuous mechanical structural members, putting emphasis on mathematical and physical modeling as well as on the carefully prepared and applied novel numerical - gorithms used to solve the derived nonlinear partial differential equations (PDEs) mainly via Bubnov-Galerkin type approaches. The presented material draws on the ?elds of bifurcation, chaos, control, and s- bility of the objects governed by strongly nonlinear PDEs and ordinary differential equations (ODEs),and may have a positive impact on interdisciplinary ?
elds of n- linear mechanics, physics, and applied mathematics. We show, for the ?rst time in a book, the complexity and fascinating nonlinear behavior of continual mechanical objects, which cannot be found in widely reported bifurcational and chaotic dyn- ics of lumped mechanical systems, i. e. , those governed by nonlinear ODEs.
Contents
Theory of Non-homogeneous Shells.- Static Instability of Rectangular Plates.- Vibrations of Rectangular Shells.- Dynamic Loss of Stability of Rectangular Shells.- Stability of a Closed Cylindrical Shell Subjected to an Axially Non-symmetrical Load.- Composite Shells.- Interaction of Elastic Shells and a Moving Body.- Chaotic Vibrations of Sectoria Shells.- Scenarios of Transition from Harmonic to Chaotic Motion.- Dynamics of Closed Flexible Cylindrical Shells.- Controlling Time-Spatial Chaos of Cylindrical Shells.- Chaotic Vibrations of Flexible Rectangular Shells.- Determination of Three-layered Non-linear Uncoupled Beam Dynamics with Constraints.- Bifurcation and Chaos of Dissipative Non-linear Mechanical Systems of Multi-layer Sandwich Beams.- Nonlinear Vibrations of the Euler-Bernoulli Beam Subjected to Transversal Load and Impact Actions.
