Linearization and parametric vibration analysis of some applied problems in multibody systems

Abstract

The paper deals with the application of the Runge-Kutta method for calculating steady-state periodic vibrations of the parametric vibration systems governed by linearized differential equations. The numerical calculation is also demonstrated by two models of multibody systems and measurements on real objects. Good agreement is obtained between the numerical and experimental results. Consequently, the obtained results can also be applicable to investigate other complicated models of multibody systems which perform the steady-state motions.

Developing a Mathematical Model of a Horizontal Looper Taking into Account the Features of a Steel Strip

“…When analyzing systems with elasticities, it is usually assumed that the elastic links are weightless and are characterized by constant coupling rigidity, i.e., the proportionality coefficient between the moment (force) and deformation [6,7,8]. In other cases, it is assumed that the material has a constant mass, but can change its stiffness due to temperature changes [9,10].…”

“…The electric drive of the horizontal looper is a multimass system that cannot be reduced to a two-mass system [8,15,16]. When analyzing the electric drive system of a horizontal looper, it is necessary to take into account changing the rigidity of the strip as a distributed mechanical system with decreasing or increasing its length in the drive.…”

Parametric Vibration Analysis of Transmission Mechanisms Using Numerical Methods

“…To verify the calculating results using the numerical methods, the dynamic load moment of the mechanical adjustment unit was measured on the driving shaft (see also Figure 16). A typical record of the measured moment is plotted in Figure 20, together with the curves calculated from the dynamic model by using the WKB-method [18,34], the kinesto-static calculation and the proposed numerical procedures based on Newmark method and Runge-Kutta method. Comparing the curves displayed in this figure, it can be observed that the calculating result using the numerical methods is more closely in agreement with the experimental result than the results obtained by the WKB-method and the kinesto-static calculation.…”

Advances in Vibration Engineering and Structural Dynamics

“…Equations ( 31) represent a set of constraint conditions between the unknown (boundary) constants, a n , b n ,..., g n and h n , and the Fourier expansion coefficients A mn , B mn , and C mn ( m, n = 0, 1, 2,... ). The constraint equations (31a-h) can be rewritten more concisely, in matrix form, as = Ly Sx (34) Vibrations of Cylindrical Shells http://dx.doi.org/10.5772/51816…”

“…The one-dimensional extended rod theory for the transverse motion takes the coupled equations concerning v , ϕ , and u * , as given in Eqs. (32) to (34). Now consider the equation of motion expressed in terms with the lateral deflection.…”