Nonlinear dynamics of contact interaction of a size-dependent plate supported by a size-dependent beam.

A mathematical model of complex vibrations exhibited by contact dynamics of size-dependent beam-plate constructions was derived by taking the account of constraints between these structural members. The governing equations were yielded by variational principles based on the moment theory of elasticity. The centre of the investigated plate was supported by a beam. The plate and the beam satisfied the Kirchhoff/Euler-Bernoulli hypotheses. The derived partial differential equations (PDEs) were reduced to the Cauchy problems by the Faedo-Galerkin method in higher approximations, whereas the Cauchy problem was solved using a few Runge-Kutta methods. Reliability of results was validated by comparing the solutions obtained by qualitatively different methods. Complex vibrations were investigated with the help of methods of nonlinear dynamics such as vibration signals, phase portraits, Fourier power spectra, wavelet analysis, and estimation of the largest Lyapunov exponents based on the Rosenstein, Kantz, and Wolf methods. The effect of size-dependent parameters of the beam and plate on their contact interaction was investigated. It was detected and illustrated that the first contact between the size-dependent structural members implies chaotic vibrations. In addition, problems of chaotic synchronization between a nanoplate and a nanobeam were addressed.

On the iterative methods of linearization, decrease of order and dimension of the Karman-type PDEs.

Iterative methods to achieve a suitable linearization as well as a decrease of the order and dimension of nonlinear partial differential equations of the eighth order into the biharmonic and Poisson-type differential equations with their simultaneous linearization are proposed in this work. Validity and reliability of the obtained results are discussed using computer programs developed by the authors.

Non-invasive stimulation of the vibrissal pad improves recovery of whisking function after simultaneous lesion of the facial and infraorbital nerves in rats.

We have recently shown that manual stimulation of target muscles promotes functional recovery after transection and surgical repair to pure motor nerves (facial: whisking and blink reflex; hypoglossal: tongue position). However, following facial nerve repair, manual stimulation is detrimental if sensory afferent input is eliminated by, e.g., infraorbital nerve extirpation. To further understand the interplay between sensory input and motor recovery, we performed simultaneous cut-and-suture lesions on both the facial and the infraorbital nerves and examined whether stimulation of the sensory afferents from the vibrissae by a forced use would improve motor recovery. The efficacy of 3 treatment paradigms was assessed: removal of the contralateral vibrissae to ensure a maximal use of the ipsilateral ones (vibrissal stimulation; Group 2), manual stimulation of the ipsilateral vibrissal muscles (Group 3), and vibrissal stimulation followed by manual stimulation (Group 4). Data were compared to controls which underwent surgery but did not receive any treatment (Group 1). Four months after surgery, all three treatments significantly improved the amplitude of vibrissal whisking to 30° versus 11° in the controls of Group 1. The three treatments also reduced the degree of polyneuronal innervation of target muscle fibers to 37% versus 58% in Group 1. These findings indicate that forced vibrissal use and manual stimulation, either alone or sequentially, reduce target muscle polyinnervation and improve recovery of whisking function when both the sensory and the motor components of the trigemino-facial system regenerate.

Manual stimulation of forearm muscles does not improve recovery of motor function after injury to a mixed peripheral nerve.

Transection and re-anastomosis of the purely motor facial nerve leads to poor functional recovery. However, we have recently shown in rat that manual stimulation (MS) of denervated vibrissal muscles reduces the number of polyinnervated motor endplates and promotes full recovery of whisking. Here, we examined whether MS of denervated rat forearm muscles would also improve recovery following transection and suture of the mixed (sensory and motor) median nerve (median-median anastomosis, MMA). Following MMA of the right median nerve, animals received no postoperative treatment, daily MS of the forearm muscles or handling only. An almost identical level of functional recovery, measured by the force of grip in grams, was reached in all animals by the sixth postoperative week and maintained till 3 months following surgery regardless of the postoperative treatment. Also, we found no differences among the groups in the degree of axonal sprouting, the extent of motor endplate polyinnervation and in the soma size of regenerated motoneurons. Taken together, we show that while MS is beneficial following motor nerve injury, combined strategies will be required for functional recovery following mixed nerve injury.