Dynamic equations of motion for inextensible beams and plates

• Published in: Archive of applied mechanics (1991) Vol. 92; no. 6; pp. 1929 - 1952
• Main Authors: Deliyianni, Maria, McHugh, Kevin, Webster, Justin T., Dowell, Earl
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2022; Springer Nature B.V
• Subjects: Cantilever beams; Cantilever plates; Classical Mechanics; Engineering; Equations of motion; Lagrange multiplier; Mathematical models; Nonlinear differential equations; One dimensional models; Original; Partial differential equations; Rectangular plates; Stiffness; Theoretical and Applied Mechanics; 74K20; Inextensibility; Cantilever; Nonlinear elasticity; Energy harvesting; 74B20; 35L77; quasilinear PDE; 93A30

The large deflections of cantilevered beams and rectangular plates are modeled and discussed. Traditional nonlinear elastic models (e.g., von Karman’s) employ elastic restoring forces based on the effect of stretching on bending, and these are less applicable to cantilevers. Recent experimental work...