请用science杂志的语言风格帮我润色以下段落：Foundation beam structures are widely used in various engineering applications including highways railways pipelines and airport runways Accurate modeling of foundations is cr

Foundation beam structures are commonly used in various engineering applications, such as highways, railways, pipelines, and airport runways. Accurate modeling of foundations is crucial for characterizing the rheological properties of foundation materials and their dynamic behavior during dynamic analysis. This is essential for developing reliable and robust engineering designs. Therefore, the dynamic issues of beam structures under moving loads have been a topic of great interest to many researchers. Accurate foundation modeling is critical in characterizing the rheological properties of foundation materials and their dynamic behavior during dynamic analysis, which is essential for developing reliable and robust engineering designs.

Previous studies have focused on the dynamic response of pavements under moving loads, with the majority of studies assuming an elastic foundation, such as the Winkle and Pasternak foundations. Other researchers have investigated the response of various beam structures, such as the Euler-Bernoulli beam, Rayleigh beam-columns, and Timoshenko beams, under different moving loads and foundation conditions.

In practical engineering, foundations often exhibit viscoelastic behavior, and using viscoelastic models to simulate the foundation can more accurately describe its mechanical behavior. Researchers have utilized various methods, such as Fourier transform, Laplace transform, and Green's function, to investigate the dynamic response of beams on viscoelastic foundations under different moving loads.

However, most studies have utilized the classical integer order viscoelastic model, neglecting the higher-order differential term or limiting the model's scope of use. To address this, some researchers have begun to use the fractional viscoelastic model to study the dynamic response of foundation beams. This model can describe the properties of materials more accurately with fewer parameters and has better memory performance.

Few studies have investigated the response of beams on fractional derivative foundations, with most studies focusing on finite beams and very limited studies addressing the response of infinite beams. Additionally, most studies do not take into account the effect of lateral forces between soils. Therefore, this paper utilizes a fractional viscoelastic Pasternak model to simulate the foundation and investigates the dynamic response of an Euler beam under a moving load, as well as the influence of the order of fractional derivatives and various foundation beam parameters on the vibration response.