The results of linearization of the basic equations describing a compressible viscous fluid in which low-amplitude oscillations occur or solids move or that interacts with elastic bodies in which small perturbations propagate are discussed. The general solutions of the linearized equations are presented. The results of studying wave processes in hydroelastic systems using the three-dimensional linearized theory of finite deformations and theory of compressible viscous fluid are discussed. The results of studying the propagation of acoustic waves of various types in waveguides with plane and circular cylindrical interfaces between elastic and liquid media and the influence of large (finite) initial deformations, viscosity and compressibility of the fluid on acoustic waves are presented. Studies of the motion of objects in compressible ideal and viscous fluids under the action of radiation forces due to the acoustic field are reviewed. The emphasis is placed on the studies that use a method involving the solution of hydrodynamic problems for a compressible fluid with solid particles and the evaluation of the forces acting on these particles. The radiation force is determined as the constant component of the hydrodynamic force. The numerical results are presented in the form of plots, which are then analyzed

Analogies between linearized and linear elasticity theory problems for homogeneous initial states

Dynamics of Elastic Bodies, Solid Particles, and Fluid Parcels in a Compressible Viscous Fluid (Review)

Three-dimensional theory of elastic stability under finite subcritical deformations

Finite deformations of an elastic anisotropic body

Analogies between linearized and linear problems for compressible elastic bodies

Using tensor notations a general theory is developed for small elastic deformations, of either a compressible or incompressible isotropic elastic body, superposed on a known finite deformation, without assuming special forms for the strain-energy function. The theory is specialized to the case when the finite deformation is pure homogeneous. When two of the principal extension ratios are equal the changes in displacement and stress due to the small superposed deformation are expressed in terms of two potential functions in a manner which is analogous to that used in the infinitesimal deformation of hexagonally aeolotropic materials. The potential functions are used to solve the problem of the infinitesimally small indentation, by a spherical punch, of the plane surface of a semi-infinite body of incompressible isotropic elastic material which is first subjected to a finite pure homogeneous deformation symmetrical about the normal to the force-free plane surface.

Analogies between linearized and linear elasticity theory problems for homogeneous initial states

Citations

Dynamics of Elastic Bodies, Solid Particles, and Fluid Parcels in a Compressible Viscous Fluid (Review)

Three-dimensional theory of elastic stability under finite subcritical deformations

Finite deformations of an elastic anisotropic body

Analogies between linearized and linear problems for compressible elastic bodies

References

General theory of small elastic deformations superposed on finite elastic deformations

On linearized problems of elasticity theory

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