## 1 Introduction
All of these above approaches can effectively change some natural frequencies of a structure to targeted values. However, a problem has received less attention: the undesired changes of the other natural frequencies of the original structure as a result of the modifications, which is known as the frequency \"spill-over\" phenomenon. In order to overcome this problem, many scholars have studied this challenging research topic using the partial eigenvalue assignment problem, which aims to assign some natural frequencies to desired locations and keep all the other frequencies unchanged. Partial frequency assignment can be achieved fairly easily by means of active control. Many researchers [21; 22; 23; 24; 25] studied this problem based on the stiffness matrix perturbation, the receptance measurements, or a combination of these two. [PERSON] et al. [26; 27; 28] presented hybrid optimization methods for the robust and minimum norm partial quadratic eigenvalue assignment problems, which are suitable for systems with and without time delays. Based on [28], [PERSON] et al. [29] proposed a modified conjugate gradient method to solve the problem only using receptance. Compared with the hybrid method given by [PERSON] et al. [22] for the single-input systems, [PERSON] [30] solved the multi-input partial quadratic eigenvalue assignment problem using a multi-step hybrid method combining the system matrices and the receptance measurements. [PERSON] and [PERSON] [31] described a new theory that was applicable to both the single-input-multiple-output and multiple-input-multiple-output vibration control of practical engineering structures using the receptance method. [PERSON] et al. [32; 33; 34] presented some algorithms to solve the partial eigenvalue assignment for high-order systems by single-input control or multi-input control. Many researchers [35; 36; 37] also studied this problem based on various feedback signals, such as the sound pressure signal, displacement feedback signal, and acceleration feedback signal. In fact, considering the low cost and maintenance required for system stability, it is expected to achieve a partial eigenvalues (or natural frequencies) assignment, depending on passive control or passive structural modification. However, this is a far more difficult task and challenge; as a result, few research papers have been introduced to solve this problem. In recent years, some researchers have tried to study partial frequency assignments via passive control, which is more challenging but more useful than active control. Passive structural modifications of mass-spring systems for the partial assignment of natural frequencies were addressed by [PERSON] and [PERSON] [38], and two different methods were presented. Compared with the work in [38], [PERSON] et al. [39] proposed a new method to assign a subset of natural frequencies of general structures with low spill-over, and optimal structural modifications were determined through a three-step procedure considering both the prescribed eigenvalues and the feasibility constraints. The method mentioned above in [38] was shown to work for only simple systems and small modifications. In this paper, the main objective is a further theoretical development of the passive partial frequency assignment methods proposed by the research group of one of the authors ([PERSON] and [PERSON] [38]). Its practical application to realistic large systems, which involves more stringent physical constrains, and its feasibility to bigger frequency modifications are investigated. In addition, it is for the first time demonstrated that the assignment of close eigenvalues can be achieved through the theory of structural modification. In this paper, a simplified model of a \"real\" marine diesel engine propulsion system and a complex branched shaft system of a diesel generator set for torsional vibration control are investigated to achieve the partial assignment of natural frequencies. Various operation conditions and practical restrictions are considered.