Quantitative quadratic physical observables pertaining to the longitudinal and transverse scattering asymmetry parameters are described in the context of the acoustic scattering theory, and their generalized mathematical expressions are derived for a cylinder material submerged in a non-viscous fluid and located arbitrarily in the field of an acoustical sheet of arbitrary shape (or beam in 2D). The derived partial-series expansions in cylindrical coordinates depend on the beam-shape coefficients of the acoustical sheet and the scattering coefficients of the cylinder. Depending on its sign, the longitudinal scattering asymmetry parameter is used to quantify the amount of energy scattered in either the forward ($\theta =0$) or backward ($\theta =\pi$) directions, while the sign of its transverse counterpart identifies the energy scattered in either the positive ($\theta =\pi$/2) or negative ($\theta$ = –$\pi$/2) lateral directions, respectively. For symmetric scattering with respect to $\theta =\pm$ $\pi$/2, the longitudinal and transverse scattering asymmetry parameters vanish. Moreover, for a symmetric acoustical sheet centered on the cylinder, the transverse scattering asymmetry parameter is zero, while its longitudinal counterpart can alternate between negative, positive or neutral values depending on particle size and acoustical-sheet parameters. The analysis is extended to derive the expressions for the resonance scattering asymmetry parameters by removing a nonresonant smooth “background” coefficient corresponding to the totally rigid- or soft-body scattering. Numerical results for the longitudinal and transverse scattering asymmetry parameters and their resonance counterparts considering an elastic cylinder placed arbitrarily in nonparaxial symmetric Gaussian and asymmetric Airy acoustical sheets chosen as examples illustrate the analysis, with particular emphasis on the cylinder size and acoustical-sheet parameters. The results are of particular importance in scattering applications, imaging, particle characterization, negative (pulling) radiation force in tractor beams and acoustical tweezers, acoustic radiative transfer and remote sensing, and other related fields.

在声学散射理论的背景下描述了与纵向和横向散射不对称参数有关的定量二次物理可观测量，并且它们的广义数学表达式是针对浸没在非粘性流体中并任意位于非粘性流体场中的圆柱材料推导出来的。任意形状的声学片（或 2D 中的梁）。圆柱坐标中导出的部分级数展开取决于声学片的波束形状系数和圆柱的散射系数。根据其符号，纵向散射不对称参数用于量化前向散射的能量（$\theta =0$) 或向后 ($\theta =\pi$) 方向，而其横向对应物的符号标识在任一正 ($\theta =\pi$/2) 或负 ($\theta$ = –$\pi$/2) 横向，分别。对于对称散射$\theta =\pm$ $\pi$/2，纵向和横向散射不对称参数消失。此外，对于以圆柱为中心的对称声学板，横向散射不对称参数为零，而其纵向对应项可以根据颗粒大小和声学板参数在负值、正值或中性值之间交替。扩展分析以推导出共振的表达式通过去除与完全刚体或软体散射相对应的非共振平滑“背景”系数来计算散射不对称参数。纵向和横向散射不对称参数及其共振对应物的数值结果考虑任意放置在非旁轴对称高斯和非对称艾里声学片中的弹性圆柱体作为示例说明了分析，特别强调了圆柱体尺寸和声学片材参数。结果在散射应用、成像、粒子表征、牵引光束和声学镊子中的负（拉）辐射力、声学辐射传输和遥感以及其他相关领域中具有特别重要的意义。