Steady state forced response of a mechanical oscillator with combined parametric excitation and clearance type non-linearity

• Published in: Journal of sound and vibration Vol. 185; no. 5; pp. 743 - 765
• Main Authors: Blankenship, G.W., Kahraman, A.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 07.09.1995; Elsevier
• Subjects: Applied sciences; Drives; Engineering Sciences; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Mechanical engineering. Machine design; Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Vibrations and mechanical waves; Parametric excitation; Numerical methods; Instrumentation; Frequency domain method; Mechanical clearance; Experimental study; Harmonic balance; Newton Raphson method; Oscillators; Rotating machinery; Algebraic equation; Non linear effect; Mechanical transmissions
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1006/jsvi.1995.0416

A mechanical system exhibiting combined parametric excitation and clearance type non-linearity is examined analytically and experimentally in an effort to explain complex behavior that is commonly observed in the steady state forced response of rotating machines. The specific case of a preloaded mechanical oscillator having a periodically time-varying stiffness function and subject to a symmetric backlash condition is considered. A generalized solution methodology is proposed based on the harmonic balance method. The resulting non-linear algebraic equations are solved by using a direct Newton-Raphson technique, in which a closed form Jacobian matrix is computed using frequency domain methods. Analytical solutions are validated by comparison with numerical integration results and experimental measurements obtained from a gear dynamics test rig.