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Mysel’s Formula for Small Vibrations Superimposed Upon Large Static Deformations of Piezoelastic Bodies
Abstract Maysel’s formula was originally developed for the linear static theory of thermoelasticity, [I]. It renders the thermoelastic displacement by a convenient volume integration, using isothermal influence functions as the kernels of the integrals. Maysel’s formula was brought to the knowledge of a wider audience through the book on thermoelasticity by W. Nowacki [2]. Later, Nowacki presented an important extension of this formula to the dynamic problem of piezo-thermoelasticity, [3]. Nowacki’s extension makes use of Green’s functions of the coupled piezo-thermoelastic problem. The proof of Maysel’s original formula presented by Parkus [4] demonstrates that the simple form of Maysel’s original formulation can be retained also in the case of coupling between temperature and elastic deformation, because the latter coupling needs not to be addressed in the proof The value of Maysel’s original formula thus lies in the fact that known solutions of an auxiliary isothermal force problem can be utilized for presenting a formal solution of the linear coupled thermoelastic problem. The coupling to the thermal field can be often neglected in practical applications, particularly in the case of quasi-static motions.
Mysel’s Formula for Small Vibrations Superimposed Upon Large Static Deformations of Piezoelastic Bodies
Abstract Maysel’s formula was originally developed for the linear static theory of thermoelasticity, [I]. It renders the thermoelastic displacement by a convenient volume integration, using isothermal influence functions as the kernels of the integrals. Maysel’s formula was brought to the knowledge of a wider audience through the book on thermoelasticity by W. Nowacki [2]. Later, Nowacki presented an important extension of this formula to the dynamic problem of piezo-thermoelasticity, [3]. Nowacki’s extension makes use of Green’s functions of the coupled piezo-thermoelastic problem. The proof of Maysel’s original formula presented by Parkus [4] demonstrates that the simple form of Maysel’s original formulation can be retained also in the case of coupling between temperature and elastic deformation, because the latter coupling needs not to be addressed in the proof The value of Maysel’s original formula thus lies in the fact that known solutions of an auxiliary isothermal force problem can be utilized for presenting a formal solution of the linear coupled thermoelastic problem. The coupling to the thermal field can be often neglected in practical applications, particularly in the case of quasi-static motions.
Mysel’s Formula for Small Vibrations Superimposed Upon Large Static Deformations of Piezoelastic Bodies
Irschik, Hans (author) / Pichler, Uwe (author)
2003-01-01
12 pages
Article/Chapter (Book)
Electronic Resource
English
Intermediate State , Reference Configuration , Reciprocity Relation , Elastic Coefficient , Ponderomotive Force Engineering , Mechanical Engineering , Materials Science, general , Artificial Intelligence (incl. Robotics) , Civil Engineering , Appl.Mathematics/Computational Methods of Engineering , Mechanics
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