By Jan Awrejcewicz (eds.)

The publication is a suite of contributions dedicated to analytical, numerical and experimental thoughts of dynamical structures, offered on the foreign convention on Dynamical platforms: idea and functions, held in Łódź, Poland on December 2-5, 2013. The stories provide deep perception into either the speculation and functions of non-linear dynamical platforms, emphasizing instructions for destiny learn. subject matters lined contain: restricted movement of mechanical structures and monitoring keep watch over; diversities within the inverse dynamics; singularly perturbed ODEs with periodic coefficients; asymptotic strategies to the matter of vortex constitution round a cylinder; research of the common and chaotic dynamics; infrequent phenomena and chaos in strength converters; non-holonomic constraints in wheeled robots; unique bifurcations in non-smooth platforms; micro-chaos; strength trade of coupled oscillators; HIV dynamics; homogenous modifications with purposes to off-shore slim buildings; novel ways to a qualitative learn of a dissipative process; chaos of postural sway in people; oscillators with fractional derivatives; controlling chaos through bifurcation diagrams; theories on the subject of optical choppers with rotating wheels; dynamics in specialist structures; taking pictures tools for non-standard boundary worth difficulties; computerized sleep scoring ruled through hold up differential equations; isochronous oscillations; the aerodynamics pendulum and its restrict cycles; limited N-body difficulties; nano-fractal oscillators and dynamically-coupled dry friction.

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**Example text**

For the WLLS with N D 4 and given parameters, the estimates for different numbers of active spikes a, a D 1; 2; 3, are plotted. As observed in previous simulations, the actual speed resulting from a certain gait frequency can slightly vary, due to the allowed error of . 18 and 0:31 ms 1 , the gait with a D 2 is advantageous; • for speeds higher than 0:31 ms 1 , the gait with a D 1 is superior. Remark 1. Consider driving a car as an analogy. A large value of a is equivalent to a low gear of the car.

Ru J. B. ru © Springer International Publishing Switzerland 2014 J. A. Krysko et al. Many researchers have applied the Bubnov–Galerkin methods (BGMs) in the Vlasov form as well as Ritz and FDM methods to solve problems of the stability of beams, plates, and shells subjected to the action of a constant transversal load and taking into account the geometric nonlinearities. The mentioned numerical approaches yield reliable and validated results regarding a wide class of both stationary and nonstationary problems of mathematical physics.

Pinned support of arc slices w D 0; @2 w v @w D 0; C @r 2 r @r F D 0; @F D 0: @r (13) 2. A. Krysko et al. Fig. 2 Mesh of a sector shell 3. Sliding clamping of arc slices @w D 0; @r w D 0; F D 0; @F D 0: @r (15) F D 0; @2 F D 0: @Â 2 (16) 4. 1 Finite Difference Method In order to reduce the continuous system governed by (12)–(17) to a lumped system by the FDM with the approximation O. 2 / versus spatial coordinates r and Â (Fig. 2), the following difference operators are applied: . w/ C 2 rr w. rÂ w .