## 1 Introduction  
Synchrotron radiation refers to electromagnetic waves emitted by free electrons moving at speeds close to the speed of light, under the influence of a magnetic field, and emitted along the tangential direction of their trajectory, as show in Figure 1. Its spectral range covers from infrared to hard X-rays. Synchrotron light exhibits characteristics such as continuous spectrum, short pulse duration, broad-spectrum, high collimation, high polarization, high purity, and high brightness. Therefore, synchrotron light sources are crucial research tools in fields such as biology, materials science, and medicine. Synchrotron light is a continuous spectrum polychromatic light, and most experiments require wavelength selection or continuous scanning within a specific range. Therefore, in practical applications, monochromators are commonly used for wavelength selection. For beams ranging from below 2 nm to the hard X-ray region, crystal monochromators are widely used as spectrometers. Their operating principle is based on the Bragg diffraction equation, adjusting the Bragg angle to select specific wavelengths [1; 2]. Angular stability is one of the key performance indexes of the double-crystal monochromator, and its precision directly affects the energy of the outgoing light, the stability of the luminous flux, and the stability of the spot location [3]. In beamlines, the distance from the DCM to the sample under test is typically from 10 to 20 m. Minute angular rotations of the crystals in the Pitch direction, on the order of arcseconds, can cause micron-level displacements of the light spot on the sample, and affect the accuracy of the Bragg angle [4; 5; 6]. With the continuous development of synchrotron applications and the construction of fourth-generation synchrotron light sources, existing DCMs in third-generation synchrotron light sources are no longer able to meet the stability requirements of these advanced sources. To enhance the stability of the monochromator crystals, vibration is a critical factor to address. Sources of vibration include turbulence, vaporization, and pump-induced oscillations within the cooling system of the first crystal. When multiple sources of excitation overlap, the vibrations of the cooling system become highly complex, making it challenging to suppress these vibrations effectively. Additionally, operational activities surrounding the monochromator can introduce vibrations [7; 8; 9]. To tackle the stability issues of the monochromator, it is essential to develop a vibration isolation system capable of simultaneously attenuating vibrations from both the cooling system of the crystals and external facility operations. The DCM requires isolation from vibrations ranging from several hertz to several hundred hertz. For this requirement, a quasi-zero stiffness (QZS) isolation system can be chosen. A QZS isolation system is a low-frequency isolation system composed of parallel positive stiffness and negative stiffness components. When the system is at rest, the positive stiffness component provides support to maintain stability. During dynamic operation, the negative stiffness component counteracts the stiffness of the positive stiffness component. The connection stiffness of the system is close to zero, so as to reduce the transmission of force in the vibration process and achieve the purpose of vibration isolation [10; 11; 12]. QZS vibration isolation technology was born in the late 1990s to early 2000s, and its design ideas are generally categorized as follows, for example, using tilting springs [13; 14], scissors [15; 16; 17], or cam [18; 19; 20] structures to achieve QZS effect. Another method is to use the restoring force of a compression flexure beam to provide negative stiffness, which is combined with positive stiffness elements to form a QZS system [21; 22; 23]. Still another more specialized  
Figure 1: Synchrotron radiation principle. form is the use of magnetic fields to generate negative stiffness, which is highly nonlinear in this type of structure [24; 25; 26].