tailieunhanh - Normal impact of a rigid cone-shaped against a viscoelastic plate on viscoelastic foundation

This paper considers the problem of a low-velocity normal impact of a rigid cone-shaped upon a viscoelastic plate. The contact force is defined by the modified Hertz's contact law. Approximate solutions of the system of nonlinear integro-differential equations for the contact force and local indentation have been obtained. | VNU Journal of Science Mathematics Physics Vol. 37 No. 4 2021 95-101 Original Article Normal Impact of A Rigid Cone-shaped against A Viscoelastic Plate on Viscoelastic Foundation Duong Tuan Manh VNU University of Engineering and Technology 144 Xuan Thuy Cau Giay Hanoi Vietnam Received 10 July 2021 Revised 18 July 2021 Accepted 18 July 2021 Abstract This paper considers the problem of a low-velocity normal impact of a rigid cone-shaped upon a viscoelastic plate. The contact force is defined by the modified Hertz s contact law. Approximate solutions of the system of nonlinear integro-differential equations for the contact force and local indentation have been obtained. Keywords Normal impact viscoelastic plate Kelvin-Voigt model. 1. Introduction The problems with the analysis of the impact of two bodies have a widespread application in various fields of science and technology. Because these problems belong to dynamic contact interaction their solutions are connected with severe mathematical and calculation difficulties. Some approaches and methods have been suggested in articles by Abrate 1 Rossikhin and Shitikova 2 . Rossikhin et al. 3 investigated the collision of two viscoelastic shells viscoelastic features of which are described by the standard linear solid model. During the impact process the local bearing of the materials of the colliding viscoelastic shells is taken into account the solution in the contact domain is found via the modified Hertz contact theory involving the operator representation of viscoelastic analogs of Young s modulus and Poisson s ratio. In the paper we will consider a special but very important for engineering practice case when a rigid cone-shaped impacts a viscoelastic plate. _ Corresponding author. E-mail address https 2588-1124 95 96 D. T. Manh VNU Journal of Science Mathematics Physics Vol. 37 No. 4 2021 95-101 2. Problem Formulation Let us consider the problem on a transverse .