Nonlinear Flexural Waves in Large-Deflection Beams
The equation of motion for a large-deflection beam in the Lagrangian description are derived using the coupling of flexural deformation and midplane stretching as a key source of nonlinearity and taking into account the transverse, axial and rotary inertia effects. Assuming a traveling wave solution, the nonlinear partial differential equations are then transformed into ordinary differential equations. Qualitative analysis indicates that the system can have either a homoclinic orbit or a heteroclinic orbit, depending on whether the rotary inertia effect is taken into account. Furthermore, exact periodic solutions of the nonlinear wave equations are obtained by means of the Jacobi elliptic function expansion. When the modulus of the Jacobi elliptic function m → 1 in the degenerate case, either a solitary wave solution or a shock wave solution can be obtained.
Key wordslarge-deflection beam nonlinear flexural wave Jacobi elliptic function expansion
Unable to display preview. Download preview PDF.
- Bhatnager, P.L., Nonlinear Waves in One-dimensional Dispersive System. Oxford: Clarendon Press, 1979.Google Scholar
- Liu, Z.F., Wang Tiefeng and Zhang, S.Y., Study on propagation properties of nonlinear flexural waves in the beams. Chinese Journal of Theoretical and Applied Mechanics, 2007, 39(2): 238–244 (in Chinese).Google Scholar
- Li, Z.B., The Traveling Wave Solutions of Nonlinear Mathematical Physical Equations. Beijing: Science Press, 2007 (in Chinese).Google Scholar