Impact of a Mass on a Damped Elastically Supported Beam

1948 ◽  
Vol 15 (2) ◽  
pp. 125-136
Author(s):  
W. H. Hoppmann
Keyword(s):  
Differential Equation ◽  
Elastic Foundation ◽  
Forced Vibration ◽  
Numerical Solutions ◽  
Coefficient Of Restitution ◽  
Tabular Form ◽  
Single Degree Of Freedom ◽  
Simply Supported ◽  
Single Degree ◽  
Elastically Supported

Abstract In this paper a study is made of the problem of the central impact of a mass on a simply supported beam on an elastic foundation with considerations of internal and external damping. The differential equation for the forced vibration of the beam is developed. It is solved for the case in which the force is a function of time and is concentrated at the center of the beam. Formulas are obtained for the deflections. An expression is developed for the coefficient of restitution which is essential in determining the deflections and the strains. Criteria are devised for determining the cases in which the beam may be considered as a single-degree-of-freedom system when damping and an elastic foundation are considered. The importance of these criteria is discussed. A numerical example illustrating the theory developed in the paper is worked out in detail. Results of computations for several numerical solutions are given in tabular form.

The Dynamics of a Nonharmonically Excited System Having Rigid Amplitude Constraints

1992 ◽  
Vol 59 (3) ◽  
pp. 693-695 ◽  
Author(s):  
Pi-Cheng Tung
Keyword(s):  
Dynamic Response ◽  
Bifurcation Analysis ◽  
Piecewise Linear ◽  
Coefficient Of Restitution ◽  
Degree Of Freedom ◽  
Linear Oscillator ◽  
Chaotic Motions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Excited System

We consider the dynamic response of a single-degree-of-freedom system having two-sided amplitude constraints. The model consists of a piecewise-linear oscillator subjected to nonharmonic excitation. A simple impact rule employing a coefficient of restitution is used to characterize the almost instantaneous behavior of impact at the constraints. In this paper periodic and chaotic motions are found. The amplitude and stability of the periodic responses are determined and bifurcation analysis for these motions is carried out. Chaotic motions are found to exist over ranges of forcing periods.

On the Motion of Lineal Bodies Subject to Linear Damping

1997 ◽  
Vol 64 (1) ◽  
pp. 227-229 ◽  
Author(s):  
M. F. Beatty
Keyword(s):  
Differential Equation ◽  
Dynamical Systems ◽  
Rigid Body ◽  
General Class ◽  
Plane Motion ◽  
Rigid Bodies ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Linear Damping

Wilms (1995) has considered the plane motion of three lineal rigid bodies subject to linear damping over their length. He shows that these plane single-degree-of-freedom systems are governed by precisely the same fundamental differential equation. It is not unusual that several dynamical systems may be formally characterized by the same differential equation, but the universal differential equation for these systems is unusual because it is exactly the same equation for the three very different systems. It is shown here that these problems belong to a more general class of problems for which the differential equation is exactly the same for every lineal rigid body regardless of its geometry.

Forced Vibration of Systems With Nonlinear, Nonsymmetrical Characteristics

1957 ◽  
Vol 24 (3) ◽  
pp. 435-439
Author(s):  
S. Mahalingam
Keyword(s):  
Approximate Solution ◽  
Linear System ◽  
Nonlinear Vibration ◽  
Forced Vibration ◽  
Free Vibrations ◽  
Frequency Function ◽  
Vibration Absorber ◽  
Single Degree Of Freedom ◽  
Nonlinear Vibration Absorber ◽  
Single Degree

Abstract A one-term approximate solution is given for the amplitudes of steady forced vibration of a single-degree-of-freedom system with a nonlinear (nonsymmetrical) spring characteristic. The method is similar to that of Martienssen (1), but the construction uses a modified curve (or “frequency function”) in place of the actual spring characteristic, the curve being so chosen that it gives the correct frequency for free vibrations. The method is extended to deal with a nonlinear vibration absorber fitted to a linear system.

The Active Control of Forced Vibration Produced by Arbitrary Disturbances

1985 ◽  
Vol 107 (1) ◽  
pp. 33-37 ◽  
Author(s):  
J. S. Burdess ◽  
A. V. Metcalfe
Keyword(s):  
Vibration Control ◽  
Active Control ◽  
Forced Vibration ◽  
Disturbance Observer ◽  
Degree Of Freedom ◽  
Experimental Results ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Impact Forces ◽  
Mass Spring

This paper considers the vibration control of a single degree of freedom mass-spring-damper system when subjected to an arbitrary, unmeasurable disturbance. The idea of a disturbance observer is introduced and it is shown how an estimate of the excitation can be derived and used to generate a control, which reduces the vibration. This control is shown to be robust with respect to the parameters describing the behavior of the system. Experimental results are presented which show the efficacy of the method when the system is excited by periodic, random, and impact forces. Comments are made on the application of the method.

scholarly journals Dynamic Response of Breasting Dolphin Moored with 40,000 DWT Ship due to Parallel Passing Ship Phenomenon

2018 ◽  
Vol 147 ◽  
pp. 05003
Author(s):  
Heri Setiawan ◽  
Muslim Muin
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Dynamic Response ◽  
Computer Program ◽  
Lateral Force ◽  
Degree Of Freedom ◽  
Hydrodynamic Interactions ◽  
Single Degree Of Freedom ◽  
Sdof System ◽  
Single Degree

When a ship is moving through another ship moored nearby, hydrodynamic interactions between these ships result in movements of the moored vessel. The movement may occur as surge, sway, and/or yaw. When a ship is passing a moored vessel parallelly, this effect will give a dominant lateral force on the moored ship and response from this phenomenon will appear in a certain time. Only dynamic response due to sway force is considered in this study, the sway force shall be absorb by the breasting dolphin. 40,000 DWT shall be moored to the breasting dolphin. Three passing ships size are considered, the breasting dolphin shall be modeled as a single degree of freedom model. This model will be subjected to a force caused by parallel passing ship. The model is assumed to be in a state of quiet water, this assumption is taken so that the fluid does not provide additional force on the model. The SDOF system shall be analyzed using a computer program designed to solve an ordinary differential equation.

SDOF Models for RC and FRC Circular Plates under Blast Loads

2011 ◽  
Vol 82 ◽  
pp. 440-445 ◽  
Author(s):  
Matteo Colombo ◽  
Paolo Martinelli
Keyword(s):  
Reinforced Concrete ◽  
Shock Tube ◽  
Pressure Wave ◽  
Fibre Reinforced Concrete ◽  
Circular Plates ◽  
Blast Loads ◽  
Single Degree Of Freedom ◽  
Simply Supported ◽  
Single Degree ◽  
Slabs On Ground

This work presents simplified models, in the form of single degree of freedom (SDOF)elasto-plastic systems, for the dynamic analysis of traditional reinforced concrete (RC) and fibre-reinforced concrete (FRC) circular plates under blast loads. Two cases have been examined inthis study: simply supported and resting on Winkler-type soil plates. Both cases intend toprovide a simplified tool for predicting the response respectively for specimens subjected toblast pressure wave inside shock-tube facilities and for slabs on ground under blast loads. Thesecond case also represents the loading conditions inside a new shock tube facility specificallyintended for the investigation of underground tunnel lining subjected to blast loads.

Single Degree of Freedom Forced Vibration System

2021 ◽  
pp. 41-79
Keyword(s):  
Forced Vibration ◽  
Influence Factor ◽  
Initial Conditions ◽  
Degree Of Freedom ◽  
Transient Solution ◽  
Vibration System ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Damped System ◽  
Arbitrary Loading

This chapter concerns the study of forced vibration of a single degree of freedom system, treating undamped and damped system under harmonic, periodic, and arbitrary loading with different cases and examples. Passing by all components of the general solution of an undamped forced system, which are a transient solution, depends only on initial conditions, transient solution due to the load at the end the stationary solution. In this chapter, a study of the dynamic influence factor depends on the ration between load frequency and structure one is presented.

Nonlinear Analysis of Concrete-Filled Steel Tubular Columns under Blast Loading

2014 ◽  
Vol 941-944 ◽  
pp. 765-769
Author(s):  
Xue Ye Cao ◽  
Yan Li ◽  
Jun Hai Zhao
Keyword(s):  
Integration Method ◽  
Blast Load ◽  
Strength Theory ◽  
Single Degree Of Freedom ◽  
Unified Strength Theory ◽  
Simply Supported ◽  
Tubular Columns ◽  
Single Degree ◽  
Distributed Load ◽  
Ultimate Moment

The plastic ultimate moment of concrete-filled steel tubular and the ultimate displacement of the simply supported beam under uniformly distributed load is established based on unified strength theory. Considered nonlinear impact of mass and stiffness changed in the process of the reaction, the dynamic response of concrete-filled steel tubular columns under blast load were analyzed by the equivalent single degree of freedom model and step by step integration method. Compared the results of this method with relevant literatures, the consequence is good. It can be seen that from the results, this method was satisfied for the requirement of the analytical precision, it can be referred for the research and the safety of concrete-filled steel tubular columns under blast load.

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