Dynamic Response of a Beam Structure Excited by Sequentially Moving Rigid Bodies

2020 ◽  
Vol 20 (08) ◽  
pp. 2050093
Author(s):  
Hao Gao ◽  
Bingen Yang
Keyword(s):  
Dynamic Response ◽  
Rigid Body ◽  
Parametric Resonance ◽  
Coupled System ◽  
Rigid Bodies ◽  
Coupled Systems ◽  
Solution Technique ◽  
Beam Structure ◽  
Dynamic Interactions ◽  
Contact Points

A coupled dynamic system consisting of a supporting beam structure and multiple passing rigid bodies is seen in various engineering applications. The dynamic response of such a coupled system is quite different from that of the beam structure subject to moving loads or moving oscillators. The dynamic interactions between the beam and moving rigid bodies are complicated, mainly because of the time-varying number and locations of contact points between the beam and bodies. Due to lack of an efficient modeling and solution technique, previous studies on these coupled systems have been limited to a beam carrying one or a few moving rigid bodies. As such, dynamic interactions between a supporting structure and arbitrarily many moving rigid bodies have not been well investigated, and parametric resonance induced by a sequence of moving rigid bodies, which has important engineering implications, is missed. In this paper, a new semi-analytical method for modeling and analysis of the above-mentioned coupled systems is developed. The method is based on an extended solution domain, by which the number of degrees of freedom of a coupled system is fixed regardless of the number of contact points between the beam and moving rigid bodies at any given time. This feature allows simple and concise description of flexible–rigid body interactions in modeling, and easy and effective implementation of numerical algorithms in solution. The proposed method provides a useful platform for thorough study of flexible–rigid body interactions and parametric resonance for coupled beam–moving rigid body systems. The accuracy and efficiency of the proposed method in computation is demonstrated in several examples.

Dynamic Analysis and Parametric Excitation of a Multi-Span Beam Structure Coupled With a Sequence of Moving Rigid Bodies

2018 ◽  
Author(s):  
Hao Gao ◽  
Bingen Yang
Keyword(s):  
Rigid Body ◽  
Dynamic Analysis ◽  
Parametric Resonance ◽  
Degrees Of Freedom ◽  
Coupled System ◽  
Rigid Bodies ◽  
Time Varying ◽  
Beam Structure ◽  
Assumed Mode Method ◽  
Mode Method

Dynamic analysis of a multi-span beam structure carrying moving rigid bodies is essentially important in various engineering applications. With many rigid bodies having different speeds and varying inter-distances, number of degrees of freedom of the coupled beam-moving rigid body system is time-varying and the beam-rigid body interaction is thus complicated. Developed in this paper is a method of extended solution domain (ESD) that resolves the issue of time-varying number of degrees and delivers a consistent mathematical model for the coupled system. The governing equation of the coupled system is derived with generalized assumed mode method through use of exact eigenfunctions and solved via numerical integration. Numerical simulation shows the accuracy and efficiency of the proposed method. Moreover, a preliminary study on parametric resonance on a beam structure with 10 rigid bodies provides guidance for future development of conditions on parametric resonance induced by moving rigid bodies, which can be useful for operation of certain coupled structure systems.

Dynamic Analysis and Parametric Resonance of a Fast Projection System

2019 ◽  
Author(s):  
Hao Gao ◽  
Bingen Yang
Keyword(s):  
Dynamic Response ◽  
Parametric Resonance ◽  
Coupled System ◽  
Rigid Bodies ◽  
Time Varying ◽  
Dynamic Coupling ◽  
Projection System ◽  
System Parameters ◽  
Gun Barrel ◽  
Systematic Solution

Abstract Fast projection systems are seen in various engineering applications, including weaponry systems. This work is concerned with the vibration of coupled gun barrel-bullet systems. The vibration of the muzzle end of a gun barrel (launching structure) is critical to shooting accuracy and launching safety. Under a rapid and repeated launching process, the launching structure may experience parametric resonance that is induced by accelerating projectiles. In this paper, a mathematical model of the coupled gun barrel-bullet is developed. In the development, the gun barrel is modeled by a cantilever beam; the projectiles are modeled as moving rigid bodies with time-varying velocities; and the dynamic coupling between the gun barrel and projectiles are described by pairs of springs and dampers. With this model, the dynamic response of the coupled system is determined through use of an extended solution domain (ESD) technique, which facilitates systematic solution of the dynamic response of the coupled beam-rigid body system. Numerical results show that parametric resonance can be induced in the launching structure, which is highly dependent on system parameters and projectile launching rate.

Rigid body collisions with friction

1990 ◽  
Vol 431 (1881) ◽  
pp. 169-181 ◽  
Keyword(s):  
Energy Dissipation ◽  
Rigid Body ◽  
Rigid Bodies ◽  
Consistent Theory ◽  
Contact Points ◽  
Collision Processes ◽  
Inconsistent Theory ◽  
The Impact ◽  
Impact Hypothesis ◽  
Alternative Theories

An energetically consistent theory is presented for dynamics of partly elastic collisions between somewhat rough rigid bodies with friction that opposes slip. This theory is based on separately accounting for frictional and non-frictional sources of dissipation. Alternative theories derived from Newton’s impact law or Poisson’s impact hypothesis are shown to be valid only for central (collinear) or non-frictional collisions; generally the latter theories yield erroneous energy dissipation if small initial slip stops during collision between eccentric bodies. Collision processes are complex when small slip is stopped by friction; then either the direction of slip reverses or contact points roll without slip. An inconsistent theory based on Newton’s impact law can yield erroneous energy increases when slip stops during collision; the consistent theory always dissipates energy. The impact law that specifies a simple proportionality between normal components of contact velocity for incidence and rebound is not applicable in any range of incident velocities with small slip if the collision is non-collinear with friction. In Percussion the force or Impetus whereby one body is moved may cause another body against which it strikes to be put in motion, and withal lose some of its strength or swiftness. (J. Wallis, 1668)

scholarly journals Dynamic Response of a Bridge–Embankment Transition with Emphasis on the Coupled Train–Track–Subgrade System

2020 ◽  
Vol 10 (17) ◽  
pp. 5982
Author(s):  
Ping Hu ◽  
Chunshun Zhang ◽  
Wei Guo ◽  
Yonghe Wang
Keyword(s):  
Dynamic Response ◽  
Rigid Body ◽  
Dynamic Performance ◽  
Coupled System ◽  
Transition System ◽  
Differential Settlement ◽  
Train Track ◽  
Transition Section ◽  
Energy Variation ◽  
Driving Speed

Dynamic response of a bridge–embankment transition is determined by, and therefore an indicator of, the coupled train–track–subgrade system. This study aims to investigate the approach of coupling the train–track–subgrade system to determine the dynamic response of the transition. The coupled system is established numerically based on the weak energy variation, the overall Lagrange format of D’Alembert’s principle and dynamics of the multi-rigid body, which is verified by in-site measurements. With this model, the influence of rail bending, differential settlement and other factors on the dynamic performance of the transition system is analyzed. The results show that when the train driving speed is 350 km/h, basic requirements should be satisfied. These requirements include that the irregularity bending of the bridge–embankment transition section should be less than 1/1000, the rigidity ratio should be controlled within 1:6, and the length of the transition section should be more than 25 m. In addition, the differential settlement should not exceed 5 mm. Among these factors, the differential settlement and the bending of the rail surface are the main ones to cause the severe dynamic irregularity of the transition section. Our analysis also indicates a requirement to strengthen the 18 m and 25–30 m distance from the abutment tail and the bed structure.

Effect of Differential Ballast Settlement on Dynamic Response of Vehicle–Track Coupled Systems

2018 ◽  
Vol 18 (07) ◽  
pp. 1850091 ◽  
Author(s):  
Yu Sun ◽  
Yu Guo ◽  
Zaigang Chen ◽  
Wanming Zhai
Keyword(s):  
Dynamic Response ◽  
Ride Comfort ◽  
Coupled System ◽  
Coupled Systems ◽  
Track Structure ◽  
Static Deflection ◽  
The Finite Element Method ◽  
Dynamics Model ◽  
Running Safety ◽  
Bed Changes

An improved vehicle-track coupled dynamics model that takes into account the differential ballast settlement is presented in this paper. Central to this formulation is an iterative method for acquiring the mapping relationship between the ballast settlement and the deflection of rail and sleepers. The proposed method is validated by comparing the results obtained with those of the finite element method (FEM) and the equilibrium state calculated for the track with the ballast settlement. Using the proposed method and dynamic model, numerical analyses have been performed for the static deflection of the rail and sleepers and for the dynamic response of the vehicle-track coupled system. The results indicate that the upper track structure will settle along with the ballast bed, and sleepers are likely to become unsupported when the settlement amplitude is large or when the settlement wavelength is small. The contact between the sleeper and the ballast bed changes dynamically when the vehicle passes through the settlement area. The ballast settlement has a significant effect on the deformation of the track and sleepers, thereby deteriorating the running safety and ride comfort of the vehicle.

Velocity and Acceleration Analysis of Contact Between Three-Dimensional Rigid Bodies

1996 ◽  
Vol 63 (4) ◽  
pp. 974-984 ◽  
Author(s):  
N. Sankar ◽  
V. Kumar ◽  
Xiaoping Yun
Keyword(s):  
Rigid Body ◽  
Relative Motion ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
Local Surface ◽  
Contact Points ◽  
Pure Rolling ◽  
Acceleration Analysis ◽  
Rigid Body Motions ◽  
Two Bodies

During manipulation and locomotion tasks encountered in robotics, it is often necessary to control the relative motion between two contacting rigid bodies. In this paper we obtain the equations relating the motion of the contact points on the pair of contacting bodies to the rigid-body motions of the two bodies. The equations are developed up to the second order. The velocity and acceleration constraints for contact, for rolling, and for pure rolling are derived. These equations depend on the local surface properties of each contacting body. Several examples are presented to illustrate the nature of the equations.

Modeling of Wheeled Mobile Robot on Rough Terrain

2003 ◽  
Author(s):  
Meihua Tai
Keyword(s):  
Kinematic Model ◽  
Rigid Bodies ◽  
The Body ◽  
Rough Terrain ◽  
Robotic Platform ◽  
Dynamic Interactions ◽  
Kinematic Constraints ◽  
The Road ◽  
Contact Points ◽  
External Forces

This paper presents kinematic and dynamic modeling of a wheeled mobile robotic platform for rough terrain operations. In the model, the body of the robot and each wheel set are considered as rigid bodies translating and rotating in space. For robots navigating on the ground, the external forces to the system are all coming from the road-tire interactions. In the kinematic model, it is assumed that the ground can provide whatever forces required to satisfy kinematic constraints at contact points, and in the dynamic model, the dynamic interactions between the tires and the terrain are considered.

Dynamic Response of Coupled Tanks and Piping Systems Under Seismic Loading

2015 ◽  
Author(s):  
Oreste S. Bursi ◽  
Giuseppe Abbiati ◽  
Luca Caracoglia ◽  
Vincenzo La Salandra ◽  
Rocco Di Filippo ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Seismic Loading ◽  
Coupled System ◽  
Coupled Systems ◽  
Piping System ◽  
Axial Loads ◽  
Industrial Plants ◽  
Piping Systems ◽  
Uncertain Boundary

Dynamic analysis is an integral part of seismic risk assessment of industrial plants. Such analysis often neglects actual boundary conditions or proper coupling between structures of coupled systems, which introduces uncertainty into the system and may lead to erroneous results, e.g., an incorrect fragility curve, in comparison with the actual behaviour of the analyzed structure. Hence, it is important to study the effect of uncertainties on the dynamic characteristics of a system, when coupling effects are neglected. Along this line, this paper investigates the effects of uncertain boundary conditions on the dynamic response of coupled tank-piping systems subjected to seismic loading. In particular, to take into account the presence of the tank as boundary condition for the piping system, two sources of uncertainty were considered: the tank aspect ratio and the piping-to-tank attachment height ratio. Moreover, to model the seismic input, a Filtered White Noise (FWN) characterized by a Kanai-Tajimi spectrum was used. Finally, to study the dynamic interaction of a set of coupled tank-piping systems, the non-intrusive stochastic collocation (SC) technique was applied. It allowed for calculating surface responses of stresses and axial loads of a pair of components of the coupled system with a reduced number of deterministic numerical simulations.

On Singularity of Rigid-Body Dynamics Using Quaternion-Based Models

2012 ◽  
Vol 79 (2) ◽  
Author(s):  
Homin Choi ◽  
Bingen Yang
Keyword(s):  
Dynamic Response ◽  
Rigid Body ◽  
Dynamic Modeling ◽  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Applied Torque ◽  
Body Dynamics

It is well known that use of quaternions in dynamic modeling of rigid bodies can avoid the singularity due to Euler rotations. This paper shows that the dynamic response of a rigid body modeled by quaternions may become unbounded when a torque is applied to the body. A theorem is derived, relating the singularity to the axes of the rotation and applied torque, and to the degrees of freedom of the body in rotation. To avoid such singularity, a method of equivalent couples is proposed.

Velocity and Acceleration Analysis of Contact Between Three-Dimensional Rigid Bodies

1994 ◽  
Author(s):  
Nilanjan Sarkar ◽  
Vijay Kumar ◽  
Xiaoping Yun
Keyword(s):  
Rigid Body ◽  
Relative Motion ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
Local Surface ◽  
Contact Points ◽  
Pure Rolling ◽  
Acceleration Analysis ◽  
Rigid Body Motions ◽  
Two Bodies

Abstract During manipulation and locomotion tasks encountered in robotics, it is often necessary to control the relative motion between two contacting rigid bodies. In this paper we obtain the equations relating the motion of the contact points on the pair of contacting bodies to the rigid body motions of the two bodies. The equations are developed up to the second order. The velocity and acceleration constraints for contact, for rolling, and for pure rolling are derived. These equations depend on the local surface properties of each contacting body. Several examples are presented to illustrate the nature of the equations.

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