Buckling and nonlinear dynamics of elastically coupled double-beam systems

Abstract

a b s t r a c tThis paper deals with damped transverse vibrations of elastically coupled double-beam system under even compressive axial loading. Each beam is assumed to be elastic, extensible and supported at the ends. The related stationary problem is proved to admit both unimodal (only one eigenfunction is involved) and bimodal (two eigenfunctions are involved) buckled solutions, and their number depends on structural parameters and applied axial loads. The occurrence of a so complex structure of the steady states motivates a global analysis of the longtime dynamics. In this regard, we are able to prove the existence of a global regular attractor of solutions. When a finite set of stationary solutions occurs, it consists of the unstable manifolds connecting them.

Dynamic responses of a damaged double Euler–Bernoulli beam traversed by a ‘phantom’ vehicle

“… 40 , 41 Stojanović et al 30 have provided closed‐form solutions for Timoshenko and Rayleigh models (Stojanović and Kozić 26 and Zhao et al 24 ), as has been by Škec et al 42 for brittle and quasi‐brittle surfaces. For composites, similar work exist (Liu and Yang 22 and Rezaiee‐Pajand and Hozhabrossadati 28 ), including buckling (Bochicchio et al 43 and Deng et al 25 ). Stability of such systems due to random forces has been investigated by Pavlović et al 27 For non‐linear multilevel beams, a harmonic balance method 29 has been observed to be effective.…”

“…For lower range of velocities around (1-30) km/h, the control of RMS of displacement for the primary beam, secondary beam and the vehicle is not significant using either single or multiple TMDs. For velocity range of around (30)(31)(32)(33)(34)(35)(36)(37)(38)(39)(40)(41)(42)(43)(44)(45) km/h, the TMDs detune in this region and adversely effect the displacement response by around 2%. The TMDs start performing better for higher range of velocity around (60-180) km/h where the displacement response control is around 4% using multiple TMDs and around 1% for a single TMD.…”

“…Figure 23 shows the velocity range where the TMDs are failing to control the acceleration response of the vehicle. In a narrow range of (38)(39)(40)(41)(42)(43)(44)(45) km/h, the TMDs adversely effect the primary system and increase the responses by approximately 0.5%.…”

Vibrations of complex composite double-column system by extended Laplace transform method

“…A specific configuration of the double-beam system (with identical beams) under the impact of a moving load or oscillator was studied by Gao (2015, 2016) by the linear transform method. From the mathematical perspective, Bochicchio et al (2016) explored the mechanism of nonlinear vibration and buckling of the double-beam system under compressive axial forces. and investigated the free and forced vibrations of the double-beam/column system using the method proposed by Seelig and Hoppmann (1964) and Seelig et al (1963).…”