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- Lecture 19: Continuous Systems - University of Iowa
In continuous systems it is not possible to identify discrete masses, damping, or springs We must consider the continuous distribution of the mass, damping, and elasticity and assume that each of the infinite number of points of system can vibrate If a system is modeled as a discrete one, the governing equations are ODEs
- Introduction to Boundary Conditions and Continuous Systems of . . .
Importantly, we show that the boundary conditions of the fixed ends make the normal modes discrete < p><p> Then, we extend our analysis to continuous systems, as opposed to systems of discrete oscillators We do this by taking a continuous limit of the discrete-mass system, wherein the "mass" is substituted by a "mass per unit length" or
- Linear Chain Normal Modes Overview and Motivation - USU
where the integer n labels the (normal-mode) solution Now because any integer n in Eq (10) produces a value for φ that satisfies Eq (9), it looks like φn can take on an infinite number of values; this seems to imply an infinite number of normal modes Well, this can't be right because we know that there are only two normal modes for
- Boundary conditions and stability of a perfectly matched . . .
The normal mode analysis is used to study the stability and well-posedness of the resulting initial boundary value problem (IBVP) The result is that any linear well-posed boundary condition yielding an energy estimate for the elastic wave equation, without the PML, will also lead to a well-posed IBVP for the PML
- VIBRATION OF CONTINUOUS SYSTEMS Introduction - aucegypt. edu
As a result, the motion of continuous systems is governed by partial differential equations to be satisfied over the entire domain of the system, subject to boundary conditions and initial conditions Although discrete systems and continuous system may appear entirely different in nature, the difference is more in form than concept
- partial differential equations - Why are normal mode . . .
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