Investigation of bar system modal characteristics using Dynamic Stiffness Matrix polynomial approximations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68378297%3A_____%2F17%3A00465280" target="_blank" >RIV/68378297:_____/17:00465280 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.sciencedirect.com/science/article/pii/S0045794916310495" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0045794916310495</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.compstruc.2016.10.015" target="_blank" >10.1016/j.compstruc.2016.10.015</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Investigation of bar system modal characteristics using Dynamic Stiffness Matrix polynomial approximations

Popis výsledku v původním jazyce

The aim of this study is an alternative approach to structure response or modal analysis. The structure consists of one-dimensional bars with continuously distributed mass and stiffness. The analysis is considered on an abstract basis as a problem of a differential system on an oriented graph. This graph is a geometric representation of the investigated mechanical system, where elements of the graph are individual bars of the system, recti- or curvilinear. The system as a whole is fixed through boundary conditions or interconnected with other sub-systems. Hence the paper can be taken as a follow up to earlier works presented at the CC2013 and CST2014 Conferences, where full mathematical background dealing with a general problem has been discussed. This paper is focused on the problem of dynamics of a system with straight prismatic bars with uniformly distributed mass. Dissipation of energy is omitted in order to keep the formulation in the real domain. The detailed assembly procedure of the Dynamic Stiffness Matrix (DSM) and transformation from local to global coordinates is outlined and demonstrated. Conventional way of eigenvalue searching by means of discrete alternative of the Newton-Raphson method is sketched out and later two possibilities based on polynomial and hyperbolic approximations of the DSM elements are pointed out. Lambda matrices as a tool are introduced together with a couple of application possibilities. The Wittrick-Williams algorithm is discussed and applied to localize and facilitate the eigenvalues searching on the whole frequency interval investigated. Finally, an illustrative example of the eigenvalue analysis of a structure is included. Strengths and shortcomings of the approach are discussed. Some open problems and orientation of further investigation are briefly outlined.

Název v anglickém jazyce

Investigation of bar system modal characteristics using Dynamic Stiffness Matrix polynomial approximations

Popis výsledku anglicky

The aim of this study is an alternative approach to structure response or modal analysis. The structure consists of one-dimensional bars with continuously distributed mass and stiffness. The analysis is considered on an abstract basis as a problem of a differential system on an oriented graph. This graph is a geometric representation of the investigated mechanical system, where elements of the graph are individual bars of the system, recti- or curvilinear. The system as a whole is fixed through boundary conditions or interconnected with other sub-systems. Hence the paper can be taken as a follow up to earlier works presented at the CC2013 and CST2014 Conferences, where full mathematical background dealing with a general problem has been discussed. This paper is focused on the problem of dynamics of a system with straight prismatic bars with uniformly distributed mass. Dissipation of energy is omitted in order to keep the formulation in the real domain. The detailed assembly procedure of the Dynamic Stiffness Matrix (DSM) and transformation from local to global coordinates is outlined and demonstrated. Conventional way of eigenvalue searching by means of discrete alternative of the Newton-Raphson method is sketched out and later two possibilities based on polynomial and hyperbolic approximations of the DSM elements are pointed out. Lambda matrices as a tool are introduced together with a couple of application possibilities. The Wittrick-Williams algorithm is discussed and applied to localize and facilitate the eigenvalues searching on the whole frequency interval investigated. Finally, an illustrative example of the eigenvalue analysis of a structure is included. Strengths and shortcomings of the approach are discussed. Some open problems and orientation of further investigation are briefly outlined.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20102 - Construction engineering, Municipal and structural engineering

Projekt

<a href="/cs/project/GA15-01035S" target="_blank" >GA15-01035S: Dynamická stabilita a post-kritické procesy v nekonzervativních a neholonomních stochastických soustavách s interakcemi</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Computers and Structures

ISSN

0045-7949

e-ISSN

—

Svazek periodika

180

Číslo periodika v rámci svazku

February

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

10

Strana od-do

3-12

Kód UT WoS článku

000393526800002

EID výsledku v databázi Scopus

2-s2.0-85006054037