An artificial small perturbation parameter and nonlinear plate vibrations

• Published in: Journal of sound and vibration Vol. 283; no. 3; pp. 561 - 571
• Main Authors: Andrianov, I.V., Danishevs’kyy, V.V., Awrejcewicz, J.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 20.05.2005; Elsevier
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Amplitude frequency characteristic; Mode coupling; Free vibration; Algebraic equation; Coupled modes; Rectangular plate; Resonance; Asymptotic approximation; Non linear effect; Vibrational mode; Modeling; Small parameter method
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2004.04.041

Nonlinear natural in-plane vibrations of a rectangular plate are studied using three small parameters. Firstly, the nonlinearity is assumed to be small. Then, a solution to a problem of the zeroth order (linear) is sought in the form of an asymptotic series with respect to the ratio of stiffness characteristics. For internal resonance, vibration modes are coupled via an infinite system of nonlinear algebraic equations, and the artificial small parameter approach is proposed to solve the obtained system. Analytical formulas for the amplitude–frequency characteristics are derived and the solutions are compared with numerical results.