in this paper, a simple and efficient method for modeling and solving the equations of a rotor with any number of disks, bearings and mass unbalances is presented using the assumed modes method. this model consists of a continuous shaft, arbitrary number of mass unbalances in any axial location and phase angle, and any number of rigid disks and bearings. this arrangement is extensively used in ...

An accurate solution procedure based on the three-dimensional elasticity theory for the free vibration analysis of Functionally Graded Sandwich (FGS) plates is presented. Since no assumptions on stresses and displacements have been employed, it can be applied to the free vibration analysis of plates with arbitrary thickness. The two-constituent FGS plate consists of ceramic and metal graded thr...

This article deals with the free in-plane vibration analysis of a frame with four arbitrary inclined members by differential transform method. Based on four differential equations and sixteen boundary and compatibility conditions, the related structural eigenvalue problem will be analytically formulated. The frequency parameters and mode shapes of the frame will be calculated for various values...

The aim of this paper is to conduct experimental modal analysis and numerical simulation to verify the structural characteristics of a deployable-retractable wing for aircraft and spacecraft. A modal impact test was conducted in order to determine the free vibration characteristics. Natural frequencies and vibration mode shapes were obtained via measurement in LMS Test. Lab. The frequency respo...

In this article, the free vibration behavior of nanoscale FG rectangular plates is studied within the framework of the refined plate theory (RPT) and small-scale effects are taken into account. Using the nonlocal elasticity theory, the governing equations are derived for single-layered FG nanoplate. The Navier’s method is employed to obtain closed-form solutions for rectangular nanoplates assum...

In this study, analytical solution is presented to calculate the free vibration frequencies of nonuniform microbeams. Scale effects are modelled using modified couple stress theory and the microbeam is assumed to be thin while Poisson's ratio effects are also taken into account. Nonuniformity is presented by exponentially varying width among the microbeam while the thickness remains constant. R...

Optimization concept in the context of shear deformation theories was born for the development of accurate models to study the bending problem of structures. The present study seeks to extend such an approach to the dynamic analysis of plates. A compact and unified formulation with non-polynomial shear strain shape functions (SSSFs) is employed to develop a static and free vibration analysis of...

In this paper, homotopy perturbation and modified Lindstedt-Poincare methods are employed for nonlinear free vibrational analysis of simply supported and double-clamped beams subjected to axial loads. Mid-plane stretching effect has also been accounted in the model. Galerkin's decomposition technique is implemented to convert the dimensionless equation of the motion to nonlinear ordinary differ...

A finite element analysis is presented for sloshing and impulsive motion of liquid-filled conical tanks during lateral anti-symmetric excitation. The performed analyses led to the development of a number of charts which can be used to identify the natural frequency, the mode shapes of conical tanks for both fundamental and the cos(θ)-modes of vibration. Conical tank geometry was described with ...