Combination resonances and anti-resonances in systems parametrically excited by harmonic variation of linear damping coefficients

Systems with harmonically varying components of linear damping coefficients are investigated. The possibility of initiating a combination resonances is considered for the case of a linear positive damping. Contrary to thesystems excited parametrically by varying the stiffness of springs, the combination resonances can occur at the parametric frequencies which are close to the sum and difference of two natural frequencies of the abbreviated system. As an example, a system with two degrees of freedom is analysed to show the necessary conditions for suppressing self-excited vibration through parametric anti-resonance.