In this paper, vibration analysis of multiple-stepped Bernoulli-Euler and Timoshenko beams carrying point masses is presented analytically for various boundary conditions. Each attached element is considered to have both translational and rotational inertias. The method of solution is “transfer matrix method” which is based on the changes in the vibration modes at the vicinity of any discontinu...

A class of identities satisfied by both Bernoulli and Euler polynomials is established. Recurrence relations for Bernoulli and Euler numbers are derived.

The optimal position and minimum support stiffness of a vibrating Timoshenko beam are investigated to maximize the fundamental frequency. Finite element method is employed. intermediate support's ideal minimal for wide variety slenderness proportions were achieved after validating finite model with Euler-Bernoulli model's analytical solution. It was observed that its sensitive ratio. According ...

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

This article proposes a method to estimate the axial force in a bar based on local vibration measurements. The method assumes Timoshenko beam theory and in addition accounts for the rotational inertia of the bar and the mass of the sensors. A major advantage of the proposed method is its generality. Assuming at least five sensors along the length of the bar, no information on the connection of ...

Mechanical metamaterials are man-made rationally-designed structures that present unprecedented mechanical properties not found in nature. One of the most well-known is auxetics, which demonstrates negative Poisson’s ratio (NPR) behavior very beneficial several industrial applications. In this study, a specific type auxetic metamaterial structure namely idealized 3D re-entrant studied analytica...

in this paper effects of fractured sleepers on rail track vibration under moving wheelset have been investigated. two parallel rails of the track have been modeled as euler-bernoulli beams on elastic points as rail pads. also sleepers have been modeled as visco-elastic euler-bernoulli beams. it is assumed that, some sleepers under the rail track have been fractured and modeled by two beams. the...

Active vibration control is an important problem in structures. The objective of active vibration control is to reduce the vibrations of a system by automatic modification of the system’s structural response. In this paper, the modeling and design of a fast output sampling feedback controller for a smart flexible beam system embedded with shear sensors and actuators for SISO system using Timosh...