Dynamic higher order equations

• The subject of this thesis is to derive and evaluate governing equations and correspondingboundary conditions for solid cylinders and rectangular plates, where the materialconstituting the cylinder or plate are governed by classical elasticity, micropolar elasticityor a functionally graded case of the previously mentioned models. This is achieved by asystematic power series expansion approach, by either adopting a generalized Hamilton'sprinciple or a direct approach.For the solid cylinders a power series expansion in the radial coordinate for the sought fields are adopted. Equations of motion together with consistent sets of end boundaryconditions are derived in a systematic fashion up to arbitrary order using a generalizedHamilton's principle. Governing equations are obtained for longitudinal, torsional, andexural modes. In the case of the rectangular plate, a power series expansion of thesought fields are adopted in the thickness coordinate. Governing equations of motion, forextensional and exural case, together with consistent sets of edge boundary conditionsare derived in a systematic fashion up to arbitrary order with use of the direct approach.Both the governing equations for the solid cylinder and the rectangular plate areasymptotically correct to all studied orders. Numerical examples are presented fordifferent sorts of problems, using exact theory, the present series expansion theories ofdifferent order, various classical theories and other newly developed approximate theories.These results cover dispersion curves, eigenfrequencies, various curves of cross sectionalquantities such as displacements, stresses and micro-rotations, as well as fixed frequencymotion due to prescribed end displacement or lateral distributed forces. The resultsillustrate that the present approach may render benchmark solutions provided higher ordertruncations are used, and act as engineering equations when using low order truncations.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering (hsv//eng)

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Teknisk mekanik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Applied Mechanics (hsv//eng)

Nyckelord

Torsion

Series expansion

Elasticity

Micropolar

Functionally graded material

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