From the bond-graph model of a dynamic system, the state equations can be obtained. When the system contains only energy storing elements in integral causality, the system of state equations is immediately and directly determined. When the model contains at least one energy storing element in derivative causality, the resulted system of differential-algebraic equations arises some difficulties in finding the final form of the system of state equations. The work presents a new method of deducing the state equations in case of bond-graph models with one, or several energy storing elements in derivative causality. This method is based on the kinetic energy of the system and offers the possibility to avoid a difficult mathematical calculus for the transition from a system of differential algebraic equations to the system of state equations.
The bond-graph method is used for finding the equations which describe the systems dynamics, by analysing the way of power transmission from the source to the working elements. When the energy storage elements I and C are in integral causality, the number of state equations equals the number of these elements. If there are also energy storage elements in derivative causality, the system contains a number of differential equations equal to the number of energy storage elements in integral causality and a number of algebraic equations equal to the number of energy storage elements in derivative causality. The work presents a new method for finding the system of differential equations for mechanical systems with one degree of freedom, starting from the original system which contains both algebraic and differential equations.
Abstract. The bond-graph method for the analysis of systems dynamics is very widespread in engineering and, because of its simplicity and its advantages, it has been developed a lot in the last decades. The bond graph model is a diagram which describes the manner of transmitting and transforming the power in a system, starting from the source up to the final elements. One of the most preferred ways of using the bond-graph diagram is the construction of the block diagram, appropriate for an adequate soft, the most frequently used one being MATLAB-SIMULINK. The block diagram model has a wide range of application in the study of systems dynamics because of its great advantages in case of numerical simulations. The manner of obtaining the block diagram from the bond-graph diagram is left at researcher choice, because there are no clear and well-defined procedures. The work presents a systematic procedure which contains several well-defined steps that lead to an exact and unitary approach of this problem.
The vibrations coming from outer sources can cause, in the most cases, important disturbances in mechanical systems functioning. For this reason, solutions for the mitigation of these negative effects are sought, one of them being the use of vibration dynamic absorbers.
In the present work, a damped vibrating mechanical system is considered and a dynamic absorber with damping attached to it. The mechanical system is acted by a sinusoidal force. The mechanical system behavior is modeled by a system of four state-space equations, having as input data the outer force and as output data the elongations of the vibrating motions for the two masses, corresponding to the original system and to the dynamic absorber, respectively. In this paper, the analytical steady state solution for system functioning is determined.
The absorber effect can be optimized by using this solution. For this purpose, a soft in MATLAB environment is conceived, soft which offers the possibility of computing the mass, the spring elastic constant and the absorber coefficient of viscous friction, so that the amplitude of the original system oscillations, caused by the input force, to be minimal.
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