www.tjprc.org SCOPUS Indexed Journal editor@tjprc.org ANALYSIS OF NUMERICAL SOLUTIONS OF A HEREDITARY DEFORMABLE SYSTEM BOTIR USMONOV, Q. RAKHIMOV & A. AKHMEDOV Department of Information Engineering, Tashkent University of Information Technologies, Tashkent, Uzbekistan, Central Asia ABSTRACT An investigation of a viscoelastic material damping effect is studied on an example of plenum air-cushion craft model. A numerical investigation was conducted to determine the vertical response characteristic of an open plenum air- cushion structure. The pure vertical motion of an air-cushion structure is investigated using a non-linear mathematical model; this incorporates a simple model to account the hereditary deformable characteristic of the material. KEYWORDS: Viscoelasticity, Hereditary Deformable, Air-Cushion & Integro-Differential Equation Received: Apr 20, 2018; Accepted: May 11, 2018; Published: Jul 07, 2018; Paper Id.: IJMPERDAUG201842 1. INTRODUCTION The term “Viscoelastic” material has quite a broad meaning. For example, in the literature [1 to 6] there is a use of this term if an equation of motion includes a viscous damping term; i. e., the equation of motion is written in terms of current instant values of displacement, velocity, and acceleration. In this study, the equation of motion will include the integral term and history of strain is required for its formulation. Materials yielding such a constitutive relation (requiring history) are also called viscoelastic, but the term “hereditary” materials will be used in this study to distinguish them. Hereditary properties are present in any composite material [1, 2 and 3]. The definition of the hereditary medium will give below. At this stage, we just note that the class of viscoelastic materials includes a subclass the hereditary materials; i. e., these two terms are not identical. In this study, numerical integration is applied for solution of the integro-differential equation. According to the correspondence (Volterra) principle, a solution of the viscoelastic problem can be obtained from a solution of the corresponding elastic problem be the replacement of elasticity constants by their hereditary analogs (integral operators). In this study, the use of exponential terms for relaxation kernels is utilized. 2. MODEL OF HEREDITARY DYNAMIC SYSTEM Consider the disturbed motion of system near equilibrium with a view to sustaining only vertical motion. As to the constitutive relations, there are different models in use. Different models of viscoelastic material are discussed in references [4, 5, and 6]. Original Article International Journal of Mechanical and Production Engineering Research and Development (IJMPERD) ISSN (P): 2249-6890; ISSN (E): 2249-8001 Vol. 8, Issue 4, Aug 2018, 403-408 © TJPRC Pvt. Ltd.