CN109505228B

CN109505228B - Damping vibration damper for overhanging beam

Info

Publication number: CN109505228B
Application number: CN201811395296.6A
Authority: CN
Inventors: 刘灿昌; 刘文晓; 孔维旭; 李磊; 秦志昌
Original assignee: Shandong University of Technology
Current assignee: Shandong University of Technology
Priority date: 2018-11-22
Filing date: 2018-11-22
Publication date: 2020-11-24
Anticipated expiration: 2038-11-22
Also published as: CN109505228A

Abstract

The beam damping vibration attenuation device and the control method are provided, the damping vibration absorbers are used for controlling the bending moment of the beam, the vibration amplitude of the beam is reduced, and the fatigue damage of the bridge caused by vibration is reduced. The damping vibration attenuation device consists of a simply supported beam system and a damping bending moment control system. The simple supporting beam system consists of a beam, a fixed hinge support and a rolling support. The damping bending moment control system consists of a fixed end, a time-lag controller, a damping controller and a control beam. The damping vibration absorber of the bridge overhanging structure is used for controlling the bending moment of the bridge, and the controller occupies small space and is easy to install.

Description

Damping vibration damper for overhanging beam

Technical Field

A bridge bending moment control device, in particular to a bridge damping vibration attenuation device, belongs to the field of bridge bending moment control.

Background

When the delivery vehicle passes through the bridge, the bridge structure not only bears the static force effect, but also bears the action of the moving load and the bridge vibration inertia force, so that the vibration of the bridge is caused, and the vibration of the bridge structure can cause the structural member to generate fatigue, so that the strength and the stability of the structural member are reduced. When the vibration frequency of the vehicle passing through the bridge is equal to or close to the self-vibration frequency of the bridge span structure, the dynamic response of the axle is aggravated by the caused resonance, and the operation safety and the stability of the vehicle on the bridge can be influenced or even damaged by the overlarge vibration amplitude of the bridge. The bridge is subjected to vibration control by installing the modulation damper, so that a good effect is obtained, but the structure of the bridge cannot reserve a space for installing the modulation damper, and the modulation damper is difficult to be effectively applied to damping vibration attenuation of the bridge. Aiming at the phenomenon, the invention provides a damping vibration attenuation device for an overhanging structure of a bridge, which is used for controlling the bending moment of the bridge, reducing the vibration amplitude of the bridge and reducing the fatigue damage of the bridge caused by vibration.

Disclosure of Invention

Aiming at the defects of the bridge vibration control prior art, the invention provides a bridge damping vibration attenuation device, which comprises a simply supported beam system and a damping bending moment control system.

The simple supporting beam system consists of a beam, a fixed hinge support and a rolling support. The left end of the beam is connected with the fixed hinge support, the right end of the beam is connected with the rolling support, and the rolling support is connected with the control beam. The damping bending moment control system consists of a fixed end, a time-lag controller, a damping controller and a control beam. At the right end of the control beam, the control beam is fixedly connected with the upper end of the time-lag controller, the lower end of the time-lag controller is hinged with the upper end of the damping controller, and the lower end of the damping controller is hinged with the fixed end.

The beam vibration deflection value controlled by the damping vibration absorber is

In the formula, the beam vibration response amplitude

Beam vibration response phase

First order natural circular frequency of beam

Damping ratio of beam vibration

Equivalent force excitation amplitude acting on beam

The cross-sectional area S of the beam is bh, and the cross-sectional moment of inertia I of the beam is bh³12, w is the beam vibration deflection, b is the beam width, h is the beam height, ρ is the beam density, c is the beam damping coefficient, c is the beam vibration deflection₁For damping controller spring coefficient, s is the outrigger length, omega is the concentrated force excitation frequency, omega₀The first-order natural circular frequency of the beam, t is a time variable, f is an excitation amplitude acting on the beam, a is a distance from a concentrated force to the fixed hinge support, E is an elastic modulus of the beam, l is the length of the beam, x is a position coordinate of the beam, tau is a time lag of the time lag controller, and pi is a circumferential rate.

Compared with the prior art, the invention has the following advantages:

1. the damping vibration absorber of the bridge overhanging structure is used for controlling the bending moment of the bridge, and the controller occupies small space and is easy to install.

Drawings

FIG. 1 is a schematic view of a beam overhang damping vibration attenuation control device.

In the figure: 1. beam, 2, concentrated force, 3, control beam, 4, time lag controller, 5, damping controller, 6, rolling support, 7 and fixed hinge support

Detailed Description

Hereinafter, specific embodiments of the present invention will be described in detail. Well-known structures or functions may not be described in detail in the following embodiments in order to avoid unnecessarily obscuring the details. Approximating language, as used herein in the following examples, may be applied to identify quantitative representations that could permissibly vary in number without resulting in a change in the basic function. Unless defined otherwise, technical and scientific terms used in the following examples have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

The invention is further illustrated with reference to figure 1:

the simply supported beam system consists of a beam 1, a fixed hinge support 7 and a rolling support 6. The left end of the beam 1 is connected with a fixed hinge support 7, the right end of the beam 1 is connected with a rolling support 6, and the rolling support 6 is connected with the control beam 3. The self-adaptive damping bending moment control system consists of a fixed end, a time lag controller 4, a damping controller 5 and a control beam 3. At the right end of the control beam 3, the control beam 3 is fixedly connected with the upper end of a time-lag controller 4, the lower end of the time-lag controller 4 is hinged with the upper end of a damping controller 5, and the lower end of the damping controller 5 is hinged with a fixed end.

The vibration deflection value of the beam 1 controlled by the damping vibration absorber is

In which the amplitude of the vibration response of the beam 1

Beam 1 vibration response phase

First order natural circular frequency of beam 1

Beam 1 vibration damping ratio

Equivalent excitation amplitude acting on the beam 1

The cross-sectional area S of the beam 1 is bh, and the cross-sectional moment of inertia I of the beam 1 is bh³12, w is the beam 1 vibration deflection, b is the beam 1 width, h is the beam 1 height, ρ is the beam 1 density, c is the beam 1 damping coefficient, c₁The damping controller 5 has elastic coefficient, s is the length of the control beam 3, omega is the excitation frequency of the concentrated force 2₀The first-order natural circular frequency of the beam 1 is shown, t is a time variable, f is an excitation amplitude acting on the beam 1, a is a distance from the concentrated force 2 to the fixed hinge support 7, E is an elastic modulus of the beam 1, l is the length of the beam 1, x is a position coordinate of the beam 1, tau is a time lag of the time lag controller 4, and pi is a circumferential rate.

Example 1:

the width b of the beam 1 is 0.5m, the height h of the beam 1 is 0.04m, and the density p of the beam 1 is 7800kg/m³The damping coefficient c of the beam 1 is 100Ns/m, and the damping coefficient of the damping controller 5 is 2 x 10³Nm/s, the length s of the control beam 3 is 2m, the excitation frequency omega of the concentration force 2 is 20rad/s, and the excitation amplitude f of the concentration force 2 acting on the beam 1 is 5 x 10⁴N and E are the elastic modulus of the beam 1 of 200GPa, l is the length of the beam 1 of 10m, x is the position coordinate of the beam 1 of 5m, and the time lag of the time lag controller 4 is a quarter period of the excitation period. The calculated vibration amplitude of the rear beam 1 after the damping shock absorber 5 is damped is 0.0199m, the vibration amplitude of the beam 1 without the damping control of the damping shock absorber 5 is 0.0305m, the vibration damping amplitude is 0.0106m, and the vibration damping amplitude is 34.75%.

The above description is only for the preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A damping vibration attenuation device of an overhanging beam comprises a simply supported beam system and a damping bending moment control system; the simple supporting beam system consists of a beam (1), a fixed hinge support (7) and a rolling support (6); the left end of the beam (1) is connected with a fixed hinge support (7), the right end of the beam (1) is connected with a rolling support (6), and the rolling support (6) is connected with the control beam (3); the damping bending moment control system consists of a fixed end, a time lag controller (4), a damping controller (5) and a control beam (3); at the right end of the control beam (3), the control beam (3) is fixedly connected with the upper end of a time-lag controller (4), the lower end of the time-lag controller (4) is hinged with the upper end of a damping controller (5), and the lower end of the damping controller (5) is hinged with a fixed end;

the vibration deflection value of the beam (1) controlled by the damping vibration absorber corresponding to the beam damping vibration attenuation device is

，

In which the beam (1) has a vibration response amplitude

Beam (1) vibration response phase

First order natural circular frequency of beam (1)

Vibration damping ratio of beam (1)

Equivalent excitation amplitude acting on the beam (1)

The cross-sectional area S of the beam (1) is bh, and the cross-sectional inertia moment I of the beam (1) is bh³12, w is the vibration deflection of the beam (1), b is the width of the beam (1), h is the height of the beam (1), ρ is the density of the beam (1), c is the damping coefficient of the beam (1), c₁Is the elastic coefficient of the damping controller (5), s is the length of the control beam (3), omega₀Is the first-order natural circular frequency of the beam (1), omega is the excitation frequency of the concentrated force (2), t is the time variable, f is the excitation amplitude acting on the beam (1), a is the concentrated force (2) to the solidThe distance of the fixed hinge support (7), E is the elastic modulus of the beam (1), I is the section moment of inertia of the beam (1), l is the length of the beam (1), x is the position coordinate of the beam (1), tau is the time lag of the time lag controller (4), and pi is the circumferential rate.