Coupled Beam System Research Articles

Mode localization and frequency loci veering in a disordered coupled beam system

Vibration mode localization and frequency loci veering in disordered coupled beam system are studied in this paper using finite element analysis. Two beams coupled with transverse and rotational springs are examined. Small disorders in the physical parameters such as Young`s modulus, mass density or span length of the substructure are introduced in the investigation of the mode localization and frequency loci veering phenomena. The effect of disorder in the elastic support on the mode localization phenomenon is also discussed. It is found that an asymmetric disorder in the weakly coupled system will lead to the occurrence of mode localization and frequency loci phenomena.

Study on Subdivision in Statistical Energy Analysis.

One of the main requirements for the successful use of Statistical Energy Analysis (SEA) is to divide a whole system into proper subsystems. It is assumed that the couplings between subsystems are weak in SEA. An SEA model without proper subsystems often provides unpleasant analytical results. This paper described a new method to judge whether the part on a system can be divided into two subsystems. On the basis of numerical study of a coupled beam system with Finite Element Method, an indicator for the judgment was defined as the ratio of initial slope of response on receiving subsystem to that on driven subsystem. The indicator was verified to be useful for determining the necessity of subdivision on two simple coupled beam, coupled plate systems and a complex floor panel of an automobile.

Mode Localization in a System of Coupled Flexible Beams with Geometric Nonlinearities

AbstractEs werden die begrenzten freien Schwingungen von zwei linear gekoppelten biegsamen Balken untersucht. Geometrische Nichtlinearitäten, die von der nichtlinearen Beziehung zwischen Krümmung und transversaler Verschiebung und longitudinaler Trägheit herrühren, werden betrachtet, die nichtlinearen partiellen Bewegungsdifferentialgleichungen werden diskretisiert unter Benutzung der Biegeschwingungen des linearisierten Systems, und eine Berechnung wird durchgefuhrt unter Benutzung der Methode der Vielfachmaßstäbe. Wenn die Balken in ihrer ersten Primärmode schwingen, werden lokalisierte Lösungen gefunden, welche von einer antisymmetrischen Mode abzweigen. Wenn die zweite und dritte Biegungsmode in die Betrachtung einbezogen wird, wirkt stark eine innere Resonanz von niedriger Ordnung auf das Lokalisationsphänomen, und es werden stabile Zweige der lokalisierten Lösungen gefunden, welche von einer symmetrischen Mode abzweigen. Wenn die Lage der gekoppelten Steife sich den Knoten der zweiten linearisierten Mode nähert, ergibt sich eine komplizierte Reihe von Bifurkationserscheinungen, wozu eine degenerierte destabilisierende Hamilton‐Hopf‐Verzweigung gehört.

Use of a generalized beam/spring element to analyze natural vibration of rail track and its application

This paper describes the formulation of a generalized beam/spring track element to obtain the natural vibration characteristics of a railway track modeled as a periodic elastically coupled beam system on a Winkler foundation. The rail/tie beams are described by either the Timoshenko beam theory or the Bernoulli-Euler beam theory. The rail beam is assumed to be discretely coupled to the cross-track ties through the coupling spring elements at the periodic rail/tie intersections. The generalized beam/spring element consists of a rail span beam segment, two adjacent tie beams, the coupling spring elements and the ultimate foundation stiffness. The entire track/beam system is then discretized into an assembly of periodic structural units. An equivalent frequency-dependent spring coefficient representing the resilient, flexural and inertial characteristics of the track substructure unit is formulated to establish the dynamic stiffness matrix of the generalized element. The eigenvalue problem of the track/beam system is solved by employing a comprehensive and efficient numerical routine. Solutions are provided for the natural frequencies of the track and the mode shapes of the rail/tie beams under transversely (cross-track) symmetric vibration. The natural vibration results are used to obtain the dynamic receptance response of a typical field track and to compare them with an existing model and field experimental data.

Modelling the dynamic response of railway track to wheel/rail impact loading

This paper describes the formulation and application of a dynamic model for a conventional rail track subjected to arbitary loading functions that simulate wheel/rail impact forces. The rail track is idealized as a periodic elastically coupled beam system resting on a Winkler foundation. Modal parameters of the track structure are first obtained from the natural vibration characteristics of the beam system, which is discretized into a periodic assembly of a specially-constructed track element and a single beam element characterized by their exact dynamic stiffness matrices. An equivalent frequency-dependent spring coefficient representing the resilient, flexural and inertial characteristics of the rail support components is introduced to reduce the degrees of freedom of the track element. The forced vibration equations of motion of the track subjected to a series of loading functions are then formulated by using beam bending theories and are reduced to second order ordinary differential equations through the use of mode summation with non-proportional modal damping. Numerical examples for the dynamic responses of a typical track are presented, and the solutions resulting from different rail/tie beam theories are compared.

Introduction to linear, parametric, and nonlinear vibrations

Part 1 Linear vibrations in mechanical engineering: classification of vibration problems fundamentals of vibrating mechanical systems the conservative single degree of freedom model the non-conservative single degree of freedom model practical uses for single degree of freedom models transients and impulses in single degree of freedom systems systems with more than one degree of freedom continuous systems. Part 2 Parametric vibrations in linear vibrating systems: stability considerations some simple physical systems analysis of governing equations further investigations into parametric phenomena. Part 3 Non-linear vibrations in forced and parametrically excited systems large deflection non-linearities material and structural configuration non-linearities. Part 4 Non-linear vibrations in autoparametric systems: two mode interaction in a coupled beam system application to vibration absorption multi-modal autoparametric interactions. Part 5 Phase plane concepts and chaotic vibrations: an introduction to the phase plane a summary of fundamental phase plane concepts chaos in vibrating systems.