scholarly journals Euler-Maclaurin Closed Form Finite State Space Model for a String Applied to Broadband Plate Vibrations

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Michael J. Panza
Keyword(s):  
Closed Form ◽  
State Space ◽  
State Space Model ◽  
Closed Form Solution ◽  
String Model ◽  
Form Solution ◽  
Space Model ◽  
Function Solution ◽  
Plate Vibrations ◽  
Finite State

The Euler-Maclaurin sun formula is applied to the infinite series Green's function solution in the space-time Laplace transform domain for the one dimensional wave equation for a string fixed at each end. The resulting approximate closed form solution is used to derive a single third order input-output ordinary differential equation to model the string dynamics. The average modal density of a plate is shown to be comparable to a string. A finite three state-space model is developed for the string and applied to the vibrations of a plate subjected to broadband random and impulse inputs. The applications include the direct problem of determining the response to a disturbance input and the inverse problem of identifying the disturbance input with a finite state observer based on the finite string model. Numerical simulations using many plate modes are obtained in the time and frequency domains and are used to compare the multimodal plate model to the finite string based model and to demonstrate how the finite string based model can be used to represent the multimodal vibrations of the plate.

scholarly journals A Finite State Space Model for Representing the Broadband Infinite Series for Acoustic Reverberation between Parallel Reflecting Planes

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Michael J. Panza
Keyword(s):  
Transfer Function ◽  
Closed Form ◽  
State Space ◽  
Infinite Series ◽  
State Space Model ◽  
Closed Form Expression ◽  
Space Model ◽  
Finite State ◽  
Acoustic Reverberation ◽  
Finite State Space

The acoustic reverberation between two parallel reflecting planes can be represented by an infinite series of the images caused by the planes. To provide a more useful model for analysis and control, the infinite series version of the Green’s function is converted into a finite state space model that retains the high frequency character that enables broadband noise inputs to be examined. The infinite series is first summed into a very accurate, approximate closed form expression in the time domain in terms of a radical function. The radical is then transformed into an expression containing exponentials which have exact Laplace transforms that lead to an overall closed form transfer function for the system. The system transfer function is transformed into a third-order state space model that theoretically contains all of the frequency characteristics of the infinite series representation. The accuracy of the state space model is examined by comparing it to the infinite series solution for three typical types of acoustical inputs: exponential for impulse noise, single frequency sine for harmonic noise, and a multifrequency Schroeder phased harmonic sequence for random noise.

Modeling and Control of Surface Quality in Chemical Mechanical Planarization (CMP)

2017 ◽  
Author(s):  
Pavan Poosarla ◽  
Hamid Emadi ◽  
Abhijit Chandra ◽  
Sourabh Bhattacharya
Keyword(s):  
State Space ◽  
Control Strategies ◽  
Chemical Mechanical Planarization ◽  
State Space Model ◽  
Closed Form Solution ◽  
Surface Profile ◽  
Open Loop ◽  
Form Solution ◽  
Machining Process ◽  
Loop Control

Obtaining uniform surface finish across large length scales is extremely important in Chemical Mechanical Planarization (CMP). Existing control strategies use results from model simulations to propose open-loop control strategies to reduce the step height on surfaces being polished. In the present work, we propose a strategy to control the surface profile of substrate during CMP process. The evolution of the surface profile is predicted using the state space model of the polishing process. The resulting state space equation is solved and a closed form solution of the surface profile is obtained as a function of time. Based on the solution, we provide a fundamental limitation for the machining process in terms of the extent of planarization that can be achieved for a given material budget.

PMCMC for Term Structure of Interest Rates under Markov Regime Switching and Jumps

2020 ◽  
Vol 8 (2) ◽  
pp. 159-169
Author(s):  
Xiangdong Liu ◽  
Xianglong Li ◽  
Shaozhi Zheng ◽  
Hangyong Qian
Keyword(s):  
Parameter Estimation ◽  
Interest Rates ◽  
Closed Form ◽  
State Space ◽  
Term Structure ◽  
Regime Switching ◽  
State Space Model ◽  
Gaussian State ◽  
Space Model ◽  
Non Gaussian

AbstractA parameter estimation method, called PMCMC in this paper, is proposed to estimate a continuous-time model of the term structure of interests under Markov regime switching and jumps. There is a closed form solution to term structure of interest rates under Markov regime. However, the model is extended to be a CKLS model with non-closed form solutions which is a typical nonlinear and non-Gaussian state-space model(SSM) in the case of adding jumps. Although the difficulty of parameter estimation greatly prevents from researching models, we prove that the nonlinear and non-Gaussian state-space model has better performances in studying volatility. The method proposed in this paper will be implemented in simulation and empirical study for SHIBOR. Empirical results illustrate that the PMCMC algorithm has powerful advantages in tackling the models.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations
Sign in / Sign up

Export Citation Format

Share Document