Thickness-shear vibrations of a plate is one of the most widely used functioning modes of quartz crystal resonators. For an analysis of vibrations, the Mindlin and Lee plate theories based on the displacement expansion of the thickness coordinate have been used as the linear theories. However, due to lacking of available method and complexity of the problem, the nonlinear thickness-shear vibrat...

Asymptotic behaviour of eigenvalues and eigenfunctions of a stiff problem is described in the case of the fourth-order ordinary differential operator. Considering the stiffness coefficient that depends on a small parameter ε and vanishes as ε → 0 on a subinterval, we prove the existence of low and high frequency resonance vibrations. The low frequency vibrations admit the power series expansion...

Roughly 20 years ago Valentino Braitenberg published a book on vehicles—a treatment of the amazingly complex behavior of a variety of very simple machines (Braitenberg 1984). This approach was inspired by the “law of uphill analysis and downhill invention.” Accordingly it is easier to design a mechanism to do something from scratch than to figure out just how nature has contrived to do it. Alth...