Combined dynamic response of primary and multiply connected cascaded secondary subsystems

Abstract

SUMMARYA method is proposed for the deterministic and stochastic non-stationary analysis of linear composite systems with cascaded secondary subsystems subjected to a seismic input. This method makes it possible to evaluate, by means of a unitary formulation, the deterministic and non-stationary stochastic response of both classically and non-classically damped subsystems and of secondary subsystems multiply supported on the primary one, as well as the ground. The proposed procedure is very efficient from a computational point of view, because of the Kronecker algebra systematically employed. Indeed, by using this algebra, it is possible to obtain in a very compact and elegant form the eigenproperties of the composite system as a function of the eigenproperties of the two subsystems taken separately. Moreover, it is possible to write the first order differential equations governing the evolution of the second order moments of the response and to solve them in a simple way.

Spectral analysis of systems with non‐classical damping using classical mode superposition technique

“…The power spectral density function of base acceleration is assumed as the Kanai-Tajimi spectrum expressed as where wg = 20 rad/sec, to = 0. 4 and So = l.0m2/(sec3 rad).…”

Response of Linear and Non-Linear Structural Systems under Gaussian or Non-Gaussian Filtered Input

“…(93) it is possible to proceed in two ways (see e.g. [37] (120) where 9r<~t) is the fundamental matrix of differential Eq. (95c) and…”

“…(90) By using the properties of Kronecker product we can write Eq. (93) in explicit form as follows [37] where…”

“…(164) and (165) it is possible to evaluate the statistical moments until the s-th order. Notice that the inverse matrices which appear in these equations can be easily evaluated by using the eigenproperties of the structural system and of the filter [37].…”

Damage Detection of a Bridge by Parametric Statistical Moment Method

“…The differential equations describing the time evolution of the vector ,2 () t Z m can be written as follows [13] ,2 2 ,2 2…”