A linear static problem of bending of a multilayer plate with homogeneous isotropic layers is considered. The deflection is assumed to have harmonic shape in the tangential directions. For calculation of the bending stiffness we introduce two dimensionless parameters: a small thickness parameter equal to the ratio of the thickness to the deformation wavelength in the tangential directions, and a large inhomogeneity parameter equal to the ratio of the maximum and minimum Young’s moduli of the layers. The plane of these parameters is split into four regions, in which different models are available for calculating the bending stiffness. The first of these is the Kirchhoff - Love model based on the hypothesis of straight non-deformable normal. In the second region, the Timoshenko - Reissner model with a shear parameter is used, calculated by an asymptotic formula of the second order of accuracy. The third region is based on assumptions on inextensible normal fiber and large heterogeneity. Finally, in the fourth region, compression of the normal is taken into account, and an approximate formula for bending stiffness is proposed for a three-layer plate. Error estimation of the models is carried out on test examples by comparison with the exact numerical solution of the three-dimensional problem of the elasticity theory. The possibility of suitability of the bending stiffness for calculating the plate eigenfrequencies is discussed.

考虑具有均质各向同性层的多层板弯曲的线性静态问题。假定挠曲在切线方向上具有谐波形状。为了计算抗弯刚度，我们引入了两个无量纲参数：一个小的厚度参数，等于切向方向上的厚度与变形波长的比值；一个大的非均匀性参数，等于该切点方向的最大和最小杨氏模量的比值。层。这些参数的平面分为四个区域，在其中可以使用不同的模型来计算弯曲刚度。第一个是基于直线不可变形法线的假设的Kirchhoff-Love模型。在第二个区域中，使用带有剪切参数的Timoshenko-Reissner模型，由二阶精度的渐近公式计算得出。第三个区域基于不可扩展的普通纤维和较大异质性的假设。最后，在第四区域中，考虑法线的压缩，并为三层板提出了抗弯刚度的近似公式。通过与弹性理论的三维问题的精确数值解进行比较，在测试示例上进行模型的误差估计。讨论了弯曲刚度是否适合计算板本征频率的可能性。提出了三层板抗弯刚度的近似公式。通过与弹性理论的三维问题的精确数值解进行比较，在测试示例上进行模型的误差估计。讨论了弯曲刚度是否适合计算板本征频率的可能性。提出了三层板抗弯刚度的近似公式。通过与弹性理论的三维问题的精确数值解进行比较，在测试示例上进行模型的误差估计。讨论了弯曲刚度是否适合计算板本征频率的可能性。