Topology optimization [
6] is currently regarded as a powerful design tool for improving structural performance. In the past 30 years, topology optimization methods, such as density-based method [
7,
8], evolutionary structural optimization method [
9,
10], level-set method [
11,
12], and phase-field method [
13], have been successfully applied to structural dynamic design problems. Existing studies have focused on single or multiple eigenfrequency indexes, such as maximizing natural frequency [
14–
17] or obtaining the desired eigenfrequencies of certain orders [
18,
19], minimizing dynamic compliance [
17,
19–
22], and maximizing frequency bandgap [
23–
25]. Suppressing or utilizing structural resonance caused by external excitation is typically a major concern, and it has been comprehensively studied in eigenfrequency optimization problems. Meanwhile, specified eigenmode designs with topology optimization methods have also been investigated further. For example, setting the maximization of the vibration amplitude of a planar mechanism as the objective function, Tcherniak [
26] derived the modal sensitivity involved in the modal superposition method. Nishiwaki et al. [
27] and Maeda et al. [
28] proposed a topological design method for vibrating structures with specified eigenfrequencies and portions of specified eigenmode shapes by adopting a multi-objective function that comprehensively balances eigenfrequencies, eigenmode shapes, and stiffness. Tsai and Cheng [
29] introduced a modal assurance criterion into structural topology optimization for maximizing the fundamental frequency and obtaining user-defined vibration modes. Xue et al. [
30] studied an improved bidirectional evolutionary structural optimization method to achieve modal control and vibration suppression by minimizing amplitudes at specific points. With the superior dynamic properties obtained using topological optimization tools, new conceptual configurations have been proposed for the design of piezoelectric transducers [
31–
33], actuators, and microplate resonators [
34,
35]. For most existing methods, local or global approximation to the desired mode shapes can be achieved by controlling eigenmode amplitudes at certain points in the structures. However, strict control of the nodal lines is not guaranteed.