Transverse vibrations analysis of a beam with degrading hysteretic behavior by using Euler-Bernoulli beam model

Abstract

The paper is based on the analytical and experimental results from [14], [15] and reveals, by mathematical methods, the degradation of ma- terial stifiness due to the decrease of the first natural frequency, when the driving frequency is slightly lower than the first natural frequency of the undegradated structure. By considering the vibration of the uni- form slender cantilever beam as an oscillating system with degrading hysteretic behavior the following equation is considered subjected to the boundary conditions To approximate the solution of the this problem, we use the method of Newton interpolating series (see [6]) and the Taylor series method (see [8]).

Study of Viscoelastic Rubber Mounts on Vehicle Suspensions with In-Wheel Electric Motors

“…Rubber mounts and bushings are extensively used as vibration isolation due to their viscoelastic nature. Viscoelasticity yields an intrinsic hysteretic behavior, which has been addressed by numerous research works [ 17 , 18 ].…”

New analytical method for dynamic response of thermoelastic damping in simply supported generalized piezothermoelastic nanobeam

“…Now, solving Equation ( 42) using the boundary conditions ( 33)-( 34) at = after taking dimensionless conditions defined by Equation (25)…”

“…Zenkour [11] studied the thermomechanical response of microbeams with Refined two-temperature MPL theory and the modified couple stress analysis. Also, some other researchers worked on the nanobeam with other theories of thermoelasticity as Sharma and Kaur [12], Abouelregal and Zenkour [13], Elaziz et al [14], Wu et al [15], Reddy and Cheng [16], Bhatti et al [17], Singh et al [18], Craciun et al [19], Sharma and Marin [20], Khisaeva and Ostoja-Starzewski [21], Singh et al [22], Sharma and Grover [23], Vlase et al [24], Groza et al [25], Nicolescu & Bobe [26], Golewski [27][28][29], Abbas [30], Lata and Kaur [31][32][33][34][35][36], Bhatti and Michaelides [37].…”

Mechanical Properties of a Chiral Cellular Structure with Semicircular Beams

“…In the studies of elastic properties of compliant cellular structures, analytical analysis is often employed to obtain theoretical models of structure’s elastic constants [ 50 ], and finite element analysis is usually utilized as verification for the theoretical models. In the theoretical modeling of the elastic constants, Euler–Bernoulli beam model considering the internal bending moment and axial force has been widely used [ 51 , 52 ]. In the finite element analysis, various novel finite element models have been proposed by scientists in exploring mechanics of structures [ 53 , 54 ].…”