Research On Vibration Characteristics Of System With Dry Friction Boundary

A kind of mechanical model of mechanical components with clearances in thermal environmentis extracted from engineering practice. Depending on different contact boundary conditions, threedifferent lateral vibration differential equations are established. Temperature stress of beam andcritical temperature causing instability are analyzed owning to variable temperature. Consideringmotions of beam under influence of dry friction and temperature stress, analytical solutions for naturalfrequency equation and modes which are orthogonal are derived. According to analytical solutionsand finite element program solutions by Matlab, non-linear influence of variable temperature onnatural frequency is discussed. Dimensionless modal coordinate equation is established. Influence ofvariable temperature on transformation relationship between actual and dimensionless modalcoordinate is discussed. Using method of harmonic balance and half cycle steady state solution,stick-free steady state vibration along with existence condition is analyzed. Temperature range can bedetermined within which system can produce stick-free motions under certain actual harmonicexcitation including amplitude and frequency. An analysis for two-stop stick-slip motions isconcerned. The exact solution under one-third sub-harmonic excitation along with existence conditionis presented. Temperature range can be determined within which system can produce2-stop stick-slipmotions under given one-third sub-harmonic excitation. Exact solutions for stick-free and two-stopstick-slip motions are confirmed by the numeric simulations using central difference method.