###### Abstract
The subsequent delineation encapsulates pivotal stages in the progressive development of vibration isolation techniques. Passive isolation techniques constituted the initial methodologies employed to attenuate vibrations. Passive methodologies for dampening vibrations encompass the utilization of vibration isolators, pads, and mounts affording cushioning. These methodologies are efficacious in mitigating the deleterious effects of vibrations on the system [19]. Active vibration control techniques employ sensors for vibration detection and actuators to generate real-time counteractive forces [20]. These systems continuously monitor vibrations and adjust counteractive forces to minimize the transmitted vibrations. Active techniques are especially effective for reducing vibrations in sensitive equipment and precision machinery. [PERSON] [21] systematically investigated the application of active vibration isolation to reduce the vibrations transmitted from a vibrating base to sensitive equipment and from machinery to the foundation. The controller, configured as static output feedback, was contemplated for designing the components of the active isolation system. Active control was facilitated through the utilization of Hoo control criteria for designing this controller. This criterion was formulated as a cost function and subsequently optimized using the Particle Swarm Optimization (PSO) algorithm. Mass-spring systems were developed to isolate vibrations by introducing an additional mass and a set of springs between the source of vibration and the structure [22; 23]. The mass-spring system functions as a low-pass filter, effectively attenuating vibrations at specific frequencies. Tuned mass dampers (TMDs) are devices comprising a mass connected to a structure via a series of springs and dampers [24; 25] TMDs are designed to resonate at a specific frequency, counteracting and reducing vibrations at that frequency. They are commonly used in tall buildings, bridges, and other structures to mitigate vibrations induced by wind [26]. Hybrid systems: Recently, hybrid techniques combining passive and active elements have gained popularity [27; 28; 29]. These systems utilize a combination of passive damping materials, mechanical systems, and active control mechanisms to achieve optimal vibration isolation. Hybrid systems provide enhanced performance, adaptability, and versatility across various applications. A brief introduction to the negative stiffness phenomenon would be beneficial for understanding the operation of hybrid systems. Negative stiffness occurs when the restoring force of a system decreases with increasing displacement, which can lead to enhanced vibration isolation capabilities. This phenomenon can be realized through specific configurations of mechanical or magnetic components, allowing for improved performance in various vibration isolation applications. A novel three-dimensional hybrid isolation platform was proposed by [PERSON] [30]. To isolate the horizontal and vertical vibrations simultaneously, the platform was designed as a combination of a rolling isolation system and four three-parameter isolators with active damping. Magnetorheological elastomer (MRE), a field-dependent smart material, has found wide application in base isolation for reducing vibrations. However, the MRE isolation system frequently encounters significant drift during strong earthquakes, potentially leading to mechanical failure. Moreover, its performance in the low-frequency range remains constrained. To address these issues, [PERSON] [31] proposed a hybrid vibration isolation system comprising four stiffness-softening MRE isolators and a passive ball-screw inerter. Throughout the development of vibration isolation techniques, the emphasis has been on enhancing performance, adaptability, and efficiency while addressing the specific requirements of diverse applications. As technology continues to advance, further innovations in this field can be expected, leading to more effective and versatile vibration isolation solutions.