Finite-time stability results for fractional damped dynamical systems with time delays

This paper is explored with the stability procedure for linear nonautonomous multiterm fractional damped systems involving time delay. Finite-time stability (FTS) criteria have been developed based on the extended form of Gronwall inequality. Also, the result is deduced to a linear autonomous case. Two examples of applications of stability analysis in numerical formulation are described showing the expertise of theoretical prediction.

Some possible Lagrangians for the quadratically damped system

In this paper, some possible Lagrangians for the quadratically damped systems are investigated. The corresponding classical Hamiltonians are investigated with Hamilton equations. The quantum Hamiltonians are also constructed so that they may be Hermitian. As an example, the quantum mechanics for the harmonic oscillator with a small quadratic damping is discussed.

Passing through resonance of the unbalanced rotor with self-balancing device

The slow dynamics of unbalanced rotors with a passive self-balancing system are investigated considering the interaction of the mechanical system with a limited power engine. The slow dynamics equations are obtained using the averaging technique for partially strongly damped systems. Stationary system configurations, different types of nonstationary solutions while passing through resonance, and areas of stability and attraction are investigated.

A Simplified Matrix Analysis Approach to Multi-story Buildings Involving a Friction Damper

Damping through friction tends to be one of the most efficient methods to suppress damage to structures from earthquakes. Realizing robust structures is therefore highly dependent on designing for the dynamic forces of friction-damped structures and exploring their reliability against natural disasters. This paper presents a simplified matrix analysis algorithm for multi-story friction- damped buildings. The behavior of friction-damped systems has analyzed more accurately by modeling the master-slave degree of freedom of the joints. First, the formulation of the problem is discussed, and a condensed general equation is derived. Then, an end-to-end solution is proposed to find the responses of structures. The displacement response of each story has been carried out in both condensed and non-condensed general equations, and the results clearly show the accuracy of the proposed method. The numerical analysis and the results of the simulation of various friction-damped structures depicts the proposed approach consists with the commercial finite element method and is applicable for the analysis various types of structures. It is noted that the acceleration and displacement responses of the structures investigated under the proposed method and the traditional finite element method are so consistent that only a 1.5% difference is observed. Moreover, as a result of the proper allocation of degrees of freedom during the analysis, this method yields a reduction in computational costs especially in large buildings.

A Simplified Matrix Analysis Approach to Multi Storey Buildings Involving a Friction Damper

Damping through friction tends to be one of the most efficient methods to suppress damage to structures from earthquakes. Realizing robust structures is therefore highly dependent on designing for the dynamic forces of friction- damped structures and exploring their reliability against natural disasters. This paper presents a simplified matrix analysis algorithm for multi-storey friction- damped buildings. We have analyzed the behavior of friction- damped systems more accurately by modeling the master-slave degree of freedom of the joints. First, the formulation of the problem is discussed, and a condensed general equation is derived. Then, an end- to- end solution is proposed to find the responses of structures. The displacement response of each storey has been carried out in both condensed and non-condensed general equations, and the results clearly show the accuracy of the proposed method. The numerical analysis and the results of the simulation of various friction- damped structures depicts the proposed approach consists with the commercial finite element method and is applicable for the analysis various types of structures. It is noted that the acceleration and displacement responses of the structures investigated under the proposed method and the traditional finite element method are so consistent that only a 1.5% difference is observed. Moreover, as a result of the proper allocation of degrees of freedom during the analysis, this method yields a reduction in computational costs especially in large buildings.

Study the Effects of Mass in a Simple Damped Harmonic Motion of a Mass-spring System Using Simulation

The effect of mass on the behavior of oscillatory systems in a damped spring-mass system was studied using simulation. It was found that the mass affects the amplitude and displacement in the case of an undamped oscillatory system. In critically damped systems, the mass affects the displacement exponentially, and the system doesn’t oscillate. In the case of an overdamped system, there is also no oscillatory motion, and an increase in the mass was not affected, since the system gets to rest very quickly. The study shows that simulation can be a very helpful tool to study the behavior of oscillatory physical systems. Keywords: Simple harmonic motion damped mass-Spring system, simulation