Dependency of critical damping on various parameters of tapered bidirectional graded circular plates rested on Hetenyi medium

In industrial machinery and automobiles the critical damping plates are used as shock absorbers to dampen system and return rest position, in the shortest period of time. The paper is focused on the effects of various parameters on critical damping of a complicated system including a tapered bidirectional graded circular plate subjected to radially variable in-plane pre-load and rested on visco-Hetenyi elastic medium with semi-rigid restraint. By employing a Chebyshev-Ritz method, dependency of critical damping is investigated for the first time on various parameters including bidirectional arbitrary material gradation, variable in-plane pre-load, Hetenyi elastic medium parameters, tapering, semi-rigid restraint and Poisson’s ratio. For the Chebyshev-Ritz method developed here, the proper scale factor and orthogonal shifted Chebyshev polynomials of the first kind without auxiliary function requirement are used. The conventional rule of mixture and Mori-Tanaka homogenization scheme are used to model transverse gradation. The characteristic equation is calculated by vanishing determinant of the total potential energy Hessian. An equivalent ABAQUS model is introduced to eliminate necessity of complicated modeling of original structure.

Exact determination of critical damping in multiple exponential kernel-based viscoelastic single-degree-of-freedom systems

In this paper, exact closed forms of critical damping manifolds for multiple-kernel-based nonviscous single-degree-of-freedom oscillators are derived. The dissipative forces are assumed to depend on the past history of the velocity response via hereditary exponential kernels. The damping model depends on several parameters, considered variables in the context of this paper. Those parameter combinations which establish thresholds between induced overdamped and underdamped motion are called critical damping manifolds. If such manifolds are represented on a coordinate plane of two damping parameters, then they are named critical curves, so that overdamped regions are bounded by them. Analytical expressions of critical curves are deduced in parametric form, considering certain local nondimensional parameters based on the Laplace variable in the frequency domain. The definition of the new parameter (called the critical parameter) is supported by several theoretical results. The proposed expressions are validated through numerical examples showing perfect fitting of the determined critical curves and overdamped regions.

EFFECT OF VISCOUS DAMPING IN NUMERICAL CALCULATION OF CABLE-MEMBRANE STRUCTURES BY THE METHOD OF DYNAMIC RELAXATION

The aim of this article is to assess the speed of convergence of numerical calculation of cable-membrane structures using dynamic relaxation method in the process of finding critical damping pre-calculated on undamped system. The procedure is tested on four different constructions in six numerical cases. The variety of examples is as large as possible to demonstrate the greatest versatility of the test procedure. The efficiency of the procedure is evaluated based on the number of iterations.