We consider a mathematical model of a linear vibrational system described by the second-order system of differential equations Mẍ +Dẋ+Kx = 0, where M, K and D are positive definite matrices, called mass, stiffness and damping, respectively. We are interested in finding an optimal damping matrix which will damp a certain part of the undamped eigenfrequencies. For this we use a minimization crite...

We describe a new class of propagation-invariant light beams with Fourier transform given by an eigenfunction of the quantum mechanical pendulum. These beams, whose spectra (restricted to a circle) are doubly periodic Mathieu functions in azimuth, depend on a field strength parameter. When the parameter is zero, pendulum beams are Bessel beams, and as the parameter approaches infinity, they res...

PURPOSE Flattening filter free (FFF) beams generated by medical linear accelerators are today clinically used for stereotactical and non-stereotactical radiotherapy treatments. Such beams differ from the standard flattened beams (FF) in the high dose rate and the profile shape peaked on the beam central axis. Definition of new parameters as unflatness and slope for FFF beams has been proposed b...

Piecewise-linear oscillators are often considered as finite degrees-of-freedom models of cracked elastic structures [1-3] but may also represent specifics of original systems. In many cases, the corresponding periodic solutions combine different pieces of linear solutions valid for two different subspaces of the configuration space [4,5]. It is always preferable though to deal with closed form ...

A new result enables direct calculation of thermoelastic damping in vibrating elastic solids. The mechanism for energy loss is thermal diffusion caused by inhomogeneous deformation, flexure in thin plates. The general result is combined with the Kirchhoff assumption to obtain a new equation for the flexural vibration of thin plates incorporating thermoelastic loss as a damping term. The thermal...

the aim of the present paper is to evaluate the influence of the soil- foundation- structure interaction (sfsi) effects on the component demand modifier factor of concrete gravity beams based on asce 41-06 standard. to this end, the beam on the nonlinear winkler foundation approach is employed which is a simple and efficient method. at first, four sets of 3-, 6-, 10- and 15-storey concrete mome...

Equations governing thermoelastic loss in vibrating thin plates are derived, generalizing Zener’s theory of thermoelastic loss in beams. The mechanism for the loss of mechanical energy is thermal diffusion caused by inhomogeneous deformation, flexure in thin plates. It is shown that a critical plate thickness, h∗, exists which separates two distinct types of response, which may be called therma...