## Drgania belek i płyt wywołane uderzeniami

### Zofia Kozyra

#### Abstract

This dissertation aims to present methods to determine structure elements vibrations under impact. Vibrations of Bernoulli-Euler beam, Timoshenko beam, Kirchhoff plate and Hencky-Bolle middle thickness plate are analysed. Impact problem is discussed in several ways, mostly, as the transient load with finite time of action or infinite, as impulse obtained as a result of the time tends to zero, as a force or velocity Dirac impulse. Impact of particle on the above structure elements is considered. In this issue it is necessary to formulate differential equations which describe structure vibrations and correct initial conditions which will allow to fulfil principle of conservation of momentum and in case of elastic impact also energy conservation law. In literature there are formulas with velocity initial conditions, which don’t meet these principles. Functions of dynamic loads are described and partial differential equations are solved by dividing space and time variables. Additional difficulty of this part of work was that impact problems are defined by partial differential equations with variable coefficients which can be distributions. In case of Timoshenko beam and Hencky-Bolle plate, Laplace transform was used to solve function dependent on time. There are presented figures of displacement and time changes with different loads and compared obtained results.Diploma type | Doctor of Philosophy | ||||

Author |
Zofia Kozyra (FCE / ICE)
Zofia Kozyra
| ||||

Title in Polish | Drgania belek i płyt wywołane uderzeniami | ||||

Language | pl polski | ||||

Certifying Unit | Faculty of Civil Engineering (FCE) | ||||

Discipline | construction / (technology domain) / (technological sciences) | ||||

Defense Date | 17-09-2010 | ||||

Supervisor |
Wacław Szcześniak (FCE / IRB)
Wacław Szcześniak
| ||||

Internal reviewers |
Grzegorz Eugeniusz Jemielita (FCE / ICE)
Grzegorz Eugeniusz Jemielita
Roman Bogacz (FACME / IAE)
Roman Bogacz
| ||||

Pages | 153 | ||||

Keywords in English | xxx | ||||

Abstract in English | This dissertation aims to present methods to determine structure elements vibrations under impact. Vibrations of Bernoulli-Euler beam, Timoshenko beam, Kirchhoff plate and Hencky-Bolle middle thickness plate are analysed. Impact problem is discussed in several ways, mostly, as the transient load with finite time of action or infinite, as impulse obtained as a result of the time tends to zero, as a force or velocity Dirac impulse. Impact of particle on the above structure elements is considered. In this issue it is necessary to formulate differential equations which describe structure vibrations and correct initial conditions which will allow to fulfil principle of conservation of momentum and in case of elastic impact also energy conservation law. In literature there are formulas with velocity initial conditions, which don’t meet these principles. Functions of dynamic loads are described and partial differential equations are solved by dividing space and time variables. Additional difficulty of this part of work was that impact problems are defined by partial differential equations with variable coefficients which can be distributions. In case of Timoshenko beam and Hencky-Bolle plate, Laplace transform was used to solve function dependent on time. There are presented figures of displacement and time changes with different loads and compared obtained results. | ||||

Thesis file |
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Citation count* | 5 (2020-09-18) |

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