Özet

Plane and anti-plane dynamic problems for an elastic rectangle loaded along its sides are considered. Low-frequency perturbations to rigid body translations are calculated. The derivation involves the solutions of non-homogeneous boundary value problems for harmonic and bi-harmonic equations. The explicit solution for the harmonic problem for transverse anti-plane translation is expressed through Fourier series. The bi-harmonic problem corresponding to the longitudinal in-plane translation is studied in greater detail for an elongated rectangle, which also may be treated using the elementary theory for plate extension. The derived perturbations incorporate the variations of displacements and stresses over the interior of the rectangle, including the case of self-equilibrated loading. The latter is obviously outside the range of validity of the classical rigid body framework.

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Perturbed rigid body motions of an elastic rectangle

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