We establish a homogenization result and a corrector result for a vibration problem of elasticity. We assume that the data depend in a periodic way on a small parameter ε. We assume also that the Lamé coefficients take possibly high values in a periodical set of disconnected inclusions and take values of the order ε2 elsewhere. In the fibered case, torsional vibrations take place at an infinite...

An analysis is presented of the torsional vibration of a rigid disc embedded to the surface of a transversely isotropic elastic half space. By using Hankel transform the mixed boundary value problem transform into a dual integral equation, which then transform to a Fredholm integral equation. After reduction to a Fredholm’s integral equation of second kind, solutions to the problem are obtained...

in this study, nonlocal nonlinear instability and the vibration of a double carbon nanotube (cnt) system have been investigated. the visco-pasternak model is used to simulate the elastic medium between nanotubes, on which the effect of the spring, shear and damping of the elastic medium is considered. both of the cnts convey a viscose fluid and a uniform longitudinal magnetic field is applied t...

In this paper a new element for analysis of thin-walled structures is presented, and the effects of secondary shear stresses on longitudinal displacements are examined. Since the Interpolation Functions are based on non-uniform torsional differential equations, the analysis of stiffness matrix is facilitated. Therefore, its ability to produce accurate results with the least number of elements i...

Several types of microfabricated mechanical filters are analyzed for RF communications applications and their advantages over the traditional SAW or FBAR filters are described. GHz frequency operation requires sub-micron dimensions. This work focuses on the modeling of a filter with torsional mode vibration. Ansys finite element simulation has been performed to make comparison with the analytic...

this study introduces the differential transform method (dtm) to analyse the free vibration response of a rotating, closed section, composite, timoshenko beam which features material coupling between flapwise bending and torsional vibrations due to ply orientation. the governing differential equations of motion are derived using hamilton’s principle and solved by applying dtm. the natural frequ...

This study introduces the Differential Transform Method (DTM) in the analysis of the free vibration response of a rotating closed section composite, Timoshenko beam, which features material coupling between flapwise bending and torsional vibrations due to ply orientation. The governing differential equations of motion are derived using Hamilton’s principle and solved by applying DTM. The natura...

We consider the dynamics of a thin liquid film in the attractive substrate potential and under the action of a longitudinal or a tilted vibration. Using a multiscale technique we split the film motion into the oscillatory and the averaged parts. The frequency of the vibration is assumed high enough for the inertial effects to become essential for the oscillatory motion. Applying the lubrication...

The coupled dynamic model of the intermediate and tail gearboxes’ spiral bevel gear-oblique shaft-laminated membrane coupling was established by employing hybrid modeling method finite element lumped mass. Among them, equation shaft constructed Timoshenko beam; gears were derived theoretically lumped-mass method, where effects time-varying meshing stiffness, transmission error, external imbalan...