Flexural edge waves in a Kirchhoff plate, carrying periodically spaced spring–mass​ resonators at its edge and laid on a Winkler foundation, are considered. A spectral element method is applied on a representative unit cell to develop the dynamic stiffness matrix of the structure. In light of structural periodicity, Bloch wave theorem is used to derive a quadratic eigenvalue problem of the wave propagation constants, which are numerically solved for. Frequency bands are analyzed using the attenuation and phase constants. Two types of bandgaps are identified: one is attributed to the existence of attached resonators and the other is due to the fact that these resonators are arranged periodically. It is found that these bandgaps are influenced by the value of the resonator’s natural frequency and the stiffness of the elastic foundation. The analytically realized bandgap structures agree very well with the finite-element obtained dispersion curves by COMSOL.

考虑了基尔霍夫板中的弯曲边缘波，该弯曲边缘波在边缘处带有周期性间隔的弹簧-质量谐振器，并放置在Winkler基础上。将光谱元素方法应用于代表性的晶胞上，以开发结构的动态刚度矩阵。根据结构的周期性，使用布洛赫波定理来推导波传播常数的二次特征值问题，并对其进行数值求解。使用衰减和相位常数分析频段。确定了两种类型的带隙：一种归因于所连接的谐振器的存在，另一种归因于这些谐振器是周期性排列的事实。发现这些带隙受谐振器固有频率的值和弹性基础的刚度的影响。