The effect of two-parameter of Pasternak foundations on the dynamics and stability of multi-span pipe conveying fluids

Abstract

In this paper, the dynamics and stability of multi-span pipe conveying fluid embedded in Pasternak foundation is studied. Based on Euler-Bernoulli beam theory, the dynamics of multi-span pipe conveying fluid embedded in two parameters Pasternak foundation is analyzed. The dynamic stiffness method (DSM) is used to solve the control equation. A seven span pipe is calculated. The affection of two parameters of Pasternak foundation is mainly studied. Along with increasing the elastic stiffness K and shear stiffness G, the frequency is also increasing.

Dispersion of an inhomogeneous sandwich plate having imperfect interfaces and supported by the Pasternak foundation

“…Vibrational analysis of elastic structures supported on foundations requires knowledge of both structural and foundation parameters, and further investigations of structures interacting with elastic foundations are frequently carried out by modeling foundation. Various innovative foundation models like Winkler foundation [28][29][30][31][32][33][34], Visco-elastic foundation [31,35], two-parameter Winkler-Pasternak foundation [36][37][38][39][40][41][42] and Visco-Pasternak foundation [43][44][45] have been used to analyze the dynamic and static excitation of beams, plates, and multilayered structures. Younesian et al [44] and Wang et al [45] offered a comprehensive overview of elastic structures on different foundation models, which included everything from the most basic foundation models to the most complex, as well as the most recent theories on the subject.…”

“…The realistic foundation-structural behavior is highly complicated, and many foundation models have been developed to handle this complexity. According to Wu et al [36], in the elastic foundation approximation model, there are two types of extended models: the Winkler model and the Pasternak model. The Winkler foundation model is a conventional one that consists of a number of separate linear spring systems.…”

“…Numerous multilayered structures are built utilizing various material combinations based on industrial use or demand and are then interacted with innovative and hybrid foundations to examine the foundationstructure interaction. A detailed discussion of the interaction of structures with the Pasternak foundation may be found in [36][37][38][39][40][41][42][43] and references therein. Exclusively, the dispersion response of three-layered plates with different material properties and layers configuration, interacting with the Pasternak foundation, subject to porosity in the core layer and hygrothermal effects have been discussed in [37,38], respectively.…”