The open profile thin elastic wavy shell natural oscillations problem is considered. proposed method for determining the numerical values of lowest frequencies and corresponding forms vibrations shells with a complicated shape based on Rayleigh-Ritz energy method. results calculation rigidly pinched lower contour are presented.

Using  principle  of  minimum  total  potential  energy  approach  in conjunction  with  Rayleigh-Ritz  method,  the  electro-thermo- mechanical  axial  buckling  behavior  of  piezoelectric  polymeric cylindrical  shell  reinforced  with  double-walled  boron-nitride nanotube  (DWBNNT)  is  investigated. Coupling  between  electrical and mechanical  fields  are  considered  according  to  ...

The A-gradient minimization of the Rayleigh quotient allows to construct robust and fastconvergent eigensolvers for the generalized eigenvalue problem for (A,M) with symmetric and positive definite matrices. The A-gradient steepest descent iteration is the simplest case of more general restarted Krylov subspace iterations for the special case that all step-wise generated Krylov subspaces are tw...

The Rayleigh quotient is unarguably the most important function used in the analysis and computation of eigenvalues of symmetric matrices. The Rayleigh-Ritz method finds the stationary values of the Rayleigh quotient, called Ritz values, on a given trial subspace as optimal, in some sense, approximations to eigenvalues. In the present paper, we derive upper bounds for proximity of the Ritz valu...

Using principle of minimum total potential energy approach in conjunction with Rayleigh-Ritz method, the electro-thermo-mechanical axial buckling behavior of piezoelectric polymeric cylindrical shell reinforced with double-walled boron-nitride nanotube (DWBNNT) is investigated. Coupling between electrical and mechanical fields are considered according to a representative volume element (RVE)-ba...

Power supply is a bottle-neck problem of wireless micro-sensors, especially where the replacement of batteries is impossible or inconvenient. Now piezoelectric material is being used to harvest vibration energy for self-powered sensors. However, the geometry of a piezoelectric cantilever beam will greatly affect its vibration energy harvesting ability. This paper deduces a remarkably precise an...

As a result of environmental and accidental actions, damage occurs in structures. The early detection of any defect can be achieved by regular inspection and condition assessment. In this way, the safety and reliability of structures can be increased. This paper is devoted to propose a new and effective method for detecting, locating, and quantifying beam-like structures. This method is based o...

In this paper at first introduced constituent equations for piezoelectric and then by the help of this equations, internal energy of hinged-hinged piezoelectric multilayer beam was computed. Then by the principle of minimum potential energy and Rayleigh -Ritz method the bending curvature equation of hinged-hinged piezoelectric multilayer beam under concentrated moment, concentrated force, unifo...