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Time domain simulation of a piano. Part 1: model description

J. Chabassier, A. Chaigne, P. Joly (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The purpose of this study is the time domain modeling of a piano. We aim at explaining the vibratory and acoustical behavior of the piano, by taking into account the main elements that contribute to sound production. The soundboard is modeled as a bidimensional thick, orthotropic, heterogeneous, frequency dependent damped plate, using Reissner Mindlin equations. The vibroacoustics equations allow the soundboard to radiate into the surrounding air, in which we wish to compute the complete acoustical...

Úlohy o kloboucích

Matúš Proner, Antonín Slavík (2022)

Pokroky matematiky, fyziky a astronomie

Článek přináší výběr některých úloh, ve kterých trpaslíci hádají barvy svých klobouků a snaží se za pomoci matematiky najít optimální strategii.

Uniform L 1 error bounds for semi-discrete finite element solutions of evolutionary integral equations

Lin, Qun, Xu, Da, Zhang, Shuhua (2012)

Applications of Mathematics 2012

In this paper, we consider the second-order continuous time Galerkin approximation of the solution to the initial problem u t + ∫ 0 t β ( t - s ) A u ( s ) d s = 0 , u ( 0 ) = v , t > 0 , where A is an elliptic partial-differential operator and β ( t ) is positive, nonincreasing and log-convex on ( 0 , ∞ ) with 0 ≤ β ( ∞ ) < β ( 0 + ) ≤ ∞ . Error estimates are derived in the norm of L t 1 ( 0 , ∞ ; L x 2 ) , and some estimates for the first order time derivatives of the errors are also given.

Use of a differential evolution algorithm for the optimization of the heat radiation intensity

Mlýnek, Jaroslav, Knobloch, Roman, Srb, Radek (2015)

Application of Mathematics 2015

This article focuses on the heat radiation intensity optimization on the surface of an aluminium shell mould. The outer mould surface is heated by infrared heaters located above the mould and the inner mould surface is sprinkled with a special PVC powder. This is an economic way of producing artificial leathers in the automotive industry (e.g. the artificial leather on car dashboards). The article includes a description of a mathematical model that allows us to calculate the heat radiation intensity...

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