Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
SOLUTION TO THE THERMOELASTIC PLATE VIBRATION PROBLEM IF THE THREE PLATE EDGES ARE SIMPLY SUPPORTED AND THE FOURTH ONE IS RIGIDLY FIXED
Operating conditions of uneven heating can cause changes in the physical and mechanical properties of materials. Awareness of the values and nature of thermal stresses are required for a comprehensive structural strength analysis. The authors propose their solution to the problem of identification of natural frequencies of vibrations of rectangular plates using a thermal factor. The introductory part of the paper covers the derivation of equations of (a) the thermoelastic vibration of a plate, (b) initial and boundary conditions. In the next part of the paper, the authors describe a method of frequency equation derivation for plates exposed to special boundary conditions, if the two opposite edges of the plate are simply supported, the temperature of the plate surface is equal to zero degrees Celsius, while the two other edges have an arbitrary type of fixation and an arbitrary thermal mode. The authors have derived a general solution for the above boundary conditions, and by altering the method of fixation of the two edges of a plate, the authors obtain transcendental trigonometric equations reducible to algebraic frequency equations by using expanding in series. Thus, derivation of frequency equations different from the general solution is feasible for various types of boundary conditions. The final part of the paper contains a derivation of the solution to the selected problem using the proposed method. The results demonstrate that the thermoelastic plate has four natural frequencies, two of them being equal to the frequencies of a plate free from the temperature influence, while the other two are close to the frequency of free vibrations of a plate.
SOLUTION TO THE THERMOELASTIC PLATE VIBRATION PROBLEM IF THE THREE PLATE EDGES ARE SIMPLY SUPPORTED AND THE FOURTH ONE IS RIGIDLY FIXED
Operating conditions of uneven heating can cause changes in the physical and mechanical properties of materials. Awareness of the values and nature of thermal stresses are required for a comprehensive structural strength analysis. The authors propose their solution to the problem of identification of natural frequencies of vibrations of rectangular plates using a thermal factor. The introductory part of the paper covers the derivation of equations of (a) the thermoelastic vibration of a plate, (b) initial and boundary conditions. In the next part of the paper, the authors describe a method of frequency equation derivation for plates exposed to special boundary conditions, if the two opposite edges of the plate are simply supported, the temperature of the plate surface is equal to zero degrees Celsius, while the two other edges have an arbitrary type of fixation and an arbitrary thermal mode. The authors have derived a general solution for the above boundary conditions, and by altering the method of fixation of the two edges of a plate, the authors obtain transcendental trigonometric equations reducible to algebraic frequency equations by using expanding in series. Thus, derivation of frequency equations different from the general solution is feasible for various types of boundary conditions. The final part of the paper contains a derivation of the solution to the selected problem using the proposed method. The results demonstrate that the thermoelastic plate has four natural frequencies, two of them being equal to the frequencies of a plate free from the temperature influence, while the other two are close to the frequency of free vibrations of a plate.
SOLUTION TO THE THERMOELASTIC PLATE VIBRATION PROBLEM IF THE THREE PLATE EDGES ARE SIMPLY SUPPORTED AND THE FOURTH ONE IS RIGIDLY FIXED
Egorychev Oleg Aleksandrovich (Autor:in) / Egorychev Oleg Olegovich (Autor:in) / Fedosova Anastasia Nikolaeva (Autor:in)
2012
Aufsatz (Zeitschrift)
Elektronische Ressource
Unbekannt
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