## 1 Introduction  
Structural vibration under random excitation is a common kind of response in engineering applications. Random vibration is often harmful since the fatigue life and performance of the structure can deteriorate, especially in civil engineering, vehicles and aerospace, so a vibration suppression technique is necessary. There are three main kinds of vibration control: passive, semi-active and active [1]. Active vibration control using smart materials can achieve better performance but it also has many disadvantages: required energy input, need for sensing and feedback segments, complexity of implementation, etc. These shortcomings are more prominent in random vibrations because random responses are often persistent, uncertain and high-frequency. Also, some kinds of active control methods are not guaranteed to be stable. Therefore, semi-active and passive vibration controls are still the main methods for random vibration control of engineering structures. For example, [PERSON] [2] utilized magneto-rheological dampers to control car vibrations due to random road conditions. To suppress vibrations under narrow-band excitations, [PERSON] [3] proposed a mixed \(H_{2}/H_{\infty}\) optimization method for a vibration absorber. A hybrid vibration absorber was proposed in [4] for random vibration control of cantilever beams. However, most kinds of passive and semi-active devices introduce considerable mass to the structure, which limits their applications. Shunt circuit damping is a kind of passive or semi-active vibration control technique raised by [PERSON] and [PERSON] [5]. In this method the mechanical energy of the vibrating structure is first converted into electrical energy and then dissipated by the resistance in the shunt circuit. According to the type of transducer, shunt circuit damping can be divided into piezoelectric shunt circuits and electromagnetic shunt circuits [6], and the types of shunt circuit include resistive shunt circuits [7], resonant shunt circuits [8], negative capacity shunt circuits [9], switch shunt circuits [10], etc. Among various shunt damping methods, the piezoelectric resonant shunt is the most widely used method. This method is a passive dissipation method but is sometimes classified as a semi-active method because energy is usually needed to synthesize inductance to avoid using a large-mass inductance coil. In this article the following classification criterion is used: a shunt inductance is said to be passive if it does not input energy into the structure [11]. For broadband random vibration of lightly damped structures, the response energy is concentrated in resonance peaks, so vibration suppression can be realized by adding damping ratios to the modes in the bandwidth. There are many papers that aim for multimode vibration control using a resonant shunt. [PERSON] [12] employed current blocking branches while [PERSON] [13] used parallel \(RLC\) shunts. [PERSON] [14] utilized distributed piezoelectric transducers and distributed electric networks to suppress broadband vibration. In these kinds of methods, in order to realize frequency selection of different modes, a large number of capacitances and inductances must be employed, which increases the complexity of the shunts. Thus, a kind of independent modal resonant shunt was proposed in [15]. In this method, a single mode is controlled using a single transducer and a single shunt circuit. The piezoelectric transducers and resonant shunt circuit are more independent from each other compared with other kinds of multimode shunt methods. Thus this method possesses advantages like fewer inductances and capacitances; greater reliability; easier to set up; etc. In this study, an independent modal resonant shunt is employed to suppress random vibration of a kind of lightly damped structure. In this method, the number of transducers equals the number of modes to be controlled, so it is uneconomical to control all the modes in the bandwidth of excitation.