Acoustic radiation forces (ARFs) induced by a single Bessel beam with arbitrary order and location on a nonspherical shape are studied using the $T$-matrix method (TMM) in three dimensions. Based on the radiation stress tensor approach and the multipole expansion method for the arbitrary Bessel beam, the ARF expressions are derived in terms of the incident and scattered beam shape coefficients independently with the corresponding homemade code packages. Several numerical experiments are conducted to verify the versatility of the TMM. The axial ARFs of several typical shapes are considered in the analysis, with the emphasis on the axial ARF reversal and the corresponding physical mechanism. This study may guide the experimental setup to find negative axial ARFs quickly and effectively based on the predicted parameters with TMM. Relatively elongated shapes may be helpful for pulling forces in Bessel beams. Furthermore, the lateral ARFs for both convex and concave nonspherical shapes are also investigated with different topological charges, cone angles, and offsets of the particle centroid to the beam axis in a broadband frequency regime. A brief theoretical derivation of the incident beam shape coefficients for the standing Bessel beams is also given. The present work could help to design the acoustic tweezers numerical toolbox, which provides an acoustical alternative to the optical tweezers toolbox.

In this paper, a novel enriched three-node triangular element with the augmented interpolation cover functions is proposed based on the original linear triangular element for two-dimensional solids. In this enriched triangular element, the augmented interpolation cover functions are employed to enrich the original standard linear shape functions over element patches. As a result, the original linear approximation space can be effectively enriched without adding extra nodes. To eliminate the linear dependence issue of the present method, an effective scheme is used to make the system matrices of the numerical model completely positive-definite. Through several typical numerical examples, the abilities of the present enriched three node triangular element in forced and free vibration analysis of two-dimensional solids are studied. The results show that, compared with the original linear triangular element, the present element can not only provide more accurate numerical results, but also have higher computational efficiency and convergence rate.

Acoustic radiation torque (ART) plays an important role in the subject of acoustophoresis, which could induce the spinning rotation of particles on their own axes. The partial wave series method (PWSM) and T matrix method (TMM) are employed to investigate the three-dimensional radiation torques of both spherical and nonspherical objects in a single Bessel beam over broader frequencies (from Rayleigh scattering to geometric-optics regimes), with emphasis on the parametric conditions for torque reversal and the corresponding physical mechanisms. For elastic objects, the dipole, quadrupole, and even several higher-scattering modes are dominant to induce the axial ARTs beyond the Rayleigh limit with a relatively large offset from the particle centroid to the beam axis in Bessel beams. The reversals appear with parametric conditions (including wave number, cone angle, and offset) for the extrema or null values of the corresponding cylindrical Bessel functions. The reversal of transverse ART from a rigid nonspherical particle is also investigated in an ordinary Bessel beam and the geometrical surface roughness is briefly studied for the effect on the radiation torques. This suggests the possibility of acoustic tweezers controlling the spinning motion of particles within and beyond the Rayleigh limit.

An exact solution of expansion coefficients for a T-matrix method interacting with acoustic scattering of arbitrary order Bessel beams from an obstacle of arbitrary location is derived analytically. Because of the failure of the addition theorem for spherical harmonics for expansion coefficients of helicoidal Bessel beams, an addition theorem for cylindrical Bessel functions is introduced. Meanwhile, an analytical expression for the integral of products including Bessel and associated Legendre functions is applied to eliminate the integration over the polar angle. Note that this multipole expansion may also benefit other scattering methods and expansions of incident waves, for instance, partial-wave series solutions.