performance of structures during recent earthquakes shows that the effect of vertical component of earthquake (vce) could be considered as one of the main causes of bridges collapse. in most of bridge design codes, for seismic analysis of bridges, vce is not taken into account or a distinguished method isn’t presented for assessment of vce. in the present work, the effect of vce on two existing...

In this article, the existence of spectrum (the eigenvalues) for nonlinear continuous operators acting in Banach spaces is investigated. For study question it used a different approach that allows studying all eigenvalues operator relative to another operator. Here we show case necessary seek given satisfying certain conditions. The examples, which can be found, are provided. Moreover, problems...

The goal of this work was to verify experimentally the applicability of the recently developed Time-Averaged Wave Envelope (TAWE) method [1] as a tool for fast prediction of pulsed nonlinear pressure fields from focused nonaxisymmetric acoustic sources in attenuating media. The experiments were performed in water at the fundamental frequency of 2.8 MHz for spherically focused (focal length F = ...

We investigate theoretically the optical response of the output field and the tunable slow and fast light in a nonlinear optomechanical cavity with a degenerate optical parametric amplifier (OPA) and a higher order excited atomic ensemble. Studies show that the higher-order-excitation atom which is similar to the degenerate OPA that acts as a nonlinear medium, induces an additional dip in absor...

A mathematical model of a cracked rotor and an asymmetric rotor with two disks representing a turbine and a generator is uti­ lized to study the vibrations due to imbalance and side load. Nonlinearities typically related with a “breathing” crack are included using a Mayes steering function. Numerical simulations demonstrate how the variations of rotor parameters affect the vibration response an...

Motivated by the study of certain nonlinear wave equations (in particular, the Camassa–Holm equation), we introduce a new class of generalized indefinite strings associated with differential equations of the form −u′′ = z uω + zuυ on an interval [0, L), where ω is a real-valued distribution in H−1 loc [0, L), υ is a non-negative Borel measure on [0, L) and z is a complex spectral parameter. Apa...

In this paper, the first-order shear deformation theory is used to derive theoretical formulations illustrating the nonlinear dynamic response of functionally graded porous plates under thermal and mechanical loadings supported by Pasternak’s model of the elastic foundation. Two types of porosity including evenly distributed porosities (Porosity-I) and unevenly distributed porosities (Porosity-...