title: The Green's matrix and the boundary integral equations for analysis of time-harmonic dynamics of elastic helical springs.
abstract: Helical springs serve as vibration isolators in virtually any suspension system. Various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions. The method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time-harmonic dynamics of elastic springs in the framework of Bernoulli-Euler beam theory. In this paper, the derivations of the Green's matrix, of the Somigliana's identities, and of the boundary integral equations are presented. The vibrational power transmission in an infinitely long spring is analyzed by means of the Green's matrix. The eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations. In the course of analysis, the essential features and advantages of the method of boundary integral equations are highlighted. The reported analytical results may be used to study the time-harmonic motion in any wave guide governed by a system of linear differential equations in a single spatial coordinate along its axis.
authors.affiliation: Department of Mechanical and Manufacturing Engineering, Aalborg University, Pontoppidanstraede 101, DK9220, Aalborg, Denmark. svs@m-tech.aau.dk
authors.forename: Sergey V
authors.initials: SV
authors.lastname: Sorokin
mesh_terms: D000162:Acoustics / Q000295:instrumentation*; D003198:Computer Simulation; D004548:Elasticity; D004738:Engineering / Q000295:instrumentation*; D004867:Equipment Design; D018499:Linear Energy Transfer; D016014:Linear Models; D009038:Motion; D009716:Numerical Analysis, Computer-Assisted; D013997:Time Factors; D014732:Vibration