On the Existence of Normal Modes of Damped Discrete-Continuous Systems
نویسندگان
چکیده
In this paper we investigate a class of combined discrete-continuous mechanical systems consisting of a continuous elastic structure and a nite number of concentrated masses, elastic supports and linear oscillators of arbitrary dimension. After the motion equations for such combined systems are derived, they are formulated as an abstract evolution equation on an appropriately deened Hilbert space. Our main objective is to ascertain conditions under which the combined systems have classical normal modes. Using the sesquilinear form approach, we show that unless some matching conditions are satissed, the combined systems cannot have normal modes even if Kelvin-Voigt damping is considered.
منابع مشابه
Non-homogeneous continuous and discrete gradient systems: the quasi-convex case
In this paper, first we study the weak and strong convergence of solutions to the following first order nonhomogeneous gradient system $$begin{cases}-x'(t)=nablaphi(x(t))+f(t), text{a.e. on} (0,infty)\x(0)=x_0in Hend{cases}$$ to a critical point of $phi$, where $phi$ is a $C^1$ quasi-convex function on a real Hilbert space $H$ with ${rm Argmin}phineqvarnothing$ and $fin L^1(0...
متن کاملGenerating Discrete Trace Transition System of a Polyhe-dral Invariant Hybrid Automaton
Supervisory control and fault diagnosis of hybrid systems need to have complete information about the discrete states transitions of the underling system. From this point of view, the hybrid system should be abstracted to a Discrete Trace Transition System (DTTS) and represented by a discrete mode transition graph. In this paper an effective method is proposed for generating discrete mode trans...
متن کاملTime-Varying Modeling of Systematic Risk: using High-Frequency Characterization of Tehran Stock Exchange
We decompose time-varying beta for stock into beta for continuous systematic risk and beta for discontinuous systematic risk. Brownian motion is assumed as nature of price movements in our modeling. Our empirical research is based on high-frequency data for stocks from Tehran Stock Exchange. Our market portfolio experiences 136 days out of 243 trading days with jumps which is a considerable rat...
متن کاملSystem identification of a beam with frictional contact
The nonlinear system becomes an area with numerous investigations over the past decades. The conventional modal analysis could not be applied on nonlinear continuous system which makes it impossible to construct the reduced order models and obtain system response based on limited number of measurement points. Nonlinear normal modes provide a useful tool for extending modal analysis to nonlinea...
متن کاملExistence and blow-up of solution of Cauchy problem for the sixth order damped Boussinesq equation
In this paper, we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation. Moreover, the finite-time blow-up of the solution for the equation is investigated by the concavity method.
متن کامل