Dynamics of longitudinal impact in uniform and composite rods with effects of various support conditions

In this work, we consider two coupled initial-boundary value problems, which, based on the Saint-Venant theory, model the longitudinal impact phenomena in a semi-infinite rod. The mathematical formulation of the problem is two mixed problems for the one-dimensional wave equation with conjugation conditions. The Cauchy conditions are specified on the spatial half-line. The initial condition for the partial derivative with respect to the time variable has a discontinuity of the first kind at one point. The boundary condition, which includes the unknown function and its first- and second-order partial derivatives, is specified on the time half-line. The solution is constructed by the method of characteristics in an explicit analytical form. The uniqueness of the solution is proved, and the conditions under which a piecewise-smooth solution exists are established. The classical solution to a mixed problem with matching conditions is considered.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Dynamics of longitudinal impact in uniform and composite rods with effects of various support conditions

Cited by 2 publications

References 36 publications

Semi-analytical solution to elastic–plastic contact-impact between a 316 stainless steel rod with truncated cone nose and rigid flat

Semi-analytical solution to elastic–plastic contact-impact between a 316 stainless steel rod with truncated cone nose and rigid flat

Classical solution to mixed problems from the theory of longitudinal impact on an elastic semi-infinite rod in the case of separation of the impacting body after the collision

Contact Info

Product

Resources

About