Vibration reduction in beam bridge under moving loads using nonlinear smooth and discontinuous oscillator

Abstract

The coupled system of smooth and discontinuous absorber and beam bridge under moving loads is constructed in order to detect the effectiveness of smooth and discontinuous absorber. It is worth pointing out that the coupled system contains an irrational restoring force which is a barrier for conventional nonlinear techniques. Hence, the harmonic balance method and Fourier expansion are used to obtain the approximate solutions of the system. The first and the second kind of generalized complete elliptic integrals are introduced. Furthermore, using power flow approach, the performance of smooth and discontinuous absorber in vibration reduction is estimated through the input energy, the dissipated energy, and the damping efficiency. It is interesting that only depending on the value of the smoothness parameter, the efficiency parameter of vibration reduction is optimized. Therefore, smooth and discontinuous absorber can adapt itself to effectively reducing the amplitude of the vibration of the beam bridge, which provides an insight to the understanding of the applications of smooth and discontinuous oscillator in engineering and power flow characteristics in nonlinear system.

A Novel Dynamic Absorber with Variable Frequency and Damping

“…According to equations (1) and (2), the relationship between the spring's deformation δ and the shear strain c is…”

“…Due to its geometric nonlinearity, the restoring force yielded the irrational nonlinear form, which made its frequency vary depending on the smoothness parameter α. In recent years, the applications of SD oscillator for the vibration reduction have been studied [2,3], which showed that the desired effect of the vibration reduction can be achieved by adjusting the smooth parameter α. However, in these papers, how to change α to realize the frequency conversion is barely mentioned.…”

Vibration reduction of vehicle-bridge-coupled system using smooth-and-discontinuous absorber

“…As is given in Tian et al, 20 SD oscillator is an example of a conservative system whose natural frequency can be changed depending on the parameter a = l 0 =l (see Figure 1). In fact, from Figure 1, we know that if the springs of SD absorber are vertical and a = 0, SD absorber can be regarded as a linear absorber (TMD).…”

“…In a complicated real system, frequency often shifts from one mode to another, which involves a versatile dynamic absorber which can lead itself to linear dynamic dampers or nonlinear one to meet reduction demands. As is given in Tian et al, 20 SD oscillator is an example of a conservative system whose natural frequency can be changed depending on the parameter a = l 0 =l (see Figure 1). In fact, from Figure 1, we know that if the springs of SD absorber are vertical and a = 0, SD absorber can be regarded as a linear absorber (TMD).…”

“…It happened to be coincided with the characteristics of smooth-and-discontinuous (SD) oscillator whose natural frequency can be changed depended on the value of the smoothness parameter. [17][18][19] Based on SD oscillator, we constructed SD absorber and used it to reduce the vibration of the 2-degree-of-freedom coupled system of vehicle and bridge in Tian et al 20 In this article, we focus on the 3-degree-of-freedom coupled system in which moving vehicles are simplified as moving spring masses and the effectiveness of SD absorber with parameter variation in this case.…”