The general approach to estimate the displacement of rounded objects (specifically, gas bubbles and solid spheres) in elastic incompressible media in response to applied acoustic radiation force is presented. In this study, both static displacement and transient motion are analyzed using the linear approximation. To evaluate the static displacement of the spherical inclusion, equations coupling the applied force, displacement, and shear modulus of the elastic medium are derived. Analytical expressions to estimate the static displacement of solid spheres and gas bubbles are presented. Under a continuously applied static force, both the solid sphere and the initially spherical gas bubble are displaced, and the bubble is deformed. The transient responses of the inclusions are described using motion equations. The displacements of the inclusion in elastic incompressible lossless media are analyzed using both frequency-domain and time-domain formalism, and the equations of motion are derived for both a solid sphere and a gas bubble. For a short pulsed force, an analytical solution for the equations of motion is presented. Finally, transient displacement of the gas bubble in viscoelastic media is considered.
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