This paper reports an analytical method to show the effect of electrostatic and Casimir forces on the pull-in instability and vibration of single nano-plate (SNP) carrying a moving nanoparticle. Governing equations for nonlocal forced vibration of the SNP under a moving nanoparticle considering electrostatic and Casimir forces are derived by using Hamilton’s principle for the case when two ends...

Three problems in simple vibration theory are treated, the longitudinal vibration of a prismatic bar, the lateral vibration of a beam, and the vibration of a circular plate, each with arbitrarily placed discrete loads. It is shown that with the appropriate definition of an inner product on a Hilbert space the spatial differential operator may be made selfadjoint with all of the formal advantage...

This paper presents results of numerical simulations on reduction of sound pressure radiated from a square plate using different types of piezo actuators. For this purpose a FEM model was developed using ANSYS software with said steel plate with a hemisphere of air on one side of the plate. There are two criteria by which the reduction is measured: minimising vibrations of plate area and minimi...

this deals with the harmonic forced vibration of a circular plate surface bonded by two piezoelectric layers, based on the kirchhoff plate model. the form of electric potential field in the piezoelectric layer is assumed such that the maxwell static electricity equation is satisfied. the differential equations of motion are solved analytically for clamped edge boundary condition of the plate. t...

The free and forced in-plane vibrations of axially moving plates are investigated in this work. The plate possesses an internal damping of which the constitutive relation obeys the Kelvin-Voigt model, and the excitations are arbitrarily distributed on two opposite edges. First, the equations of motion and the boundary conditions of the axially moving plate are derived. Then, the extended Ritz m...

The mining chute is an important equipment in the process of coal transportation and coal screening preparation. During the working process, the mining chute will generate a lot of vibration and noise because of constantly friction and impact of gangue and coal blocks. In order to reduce the vibration and noise during the operation of the chute, a new type of foam aluminum laminated structure i...

Abstract—The effect of non-homogeneity on the free transverse vibration of thin rectangular plates of bilinearly varying thickness has been analyzed using generalized differential quadrature (GDQ) method. The non-homogeneity of the plate material is assumed to arise due to linear variations in Young’s modulus and density of the plate material with the in-plane coordinates x and y . Numerical re...

This paper deals with the finite element approximation of the vibration modes of a laminated plate modeled by the Reissner-Mindlin equations; DL3 elements are used for the bending terms and standard piecewise linear continuous elements for the in-plane displacements. An a priori estimate of the regularity of the solution, independent of the plate thickness, is proved for the corresponding load ...

In this study, free vibration of functionally graded rectangular plates for various types of boundary conditions has been presented . The properties of the plate are assumed as power- law form along the thickness direction , while poisson's ratio is kept constant. the linear vibration equations of functionally graded rectangular plates are derived based on first order shear deformation theory b...