Free vibration analysis of delaminated beams - Liu, Yang (2015)
In this thesis, new non-dimensional parameters are introduced, and analytical solutions are developed to study the vibration of delaminated beams in civil and structural engineering, including beams with step axial force and cross-section, beams subjected to static end moments and beams fully or partially supported by elastic foundation; as well as the vibration of delaminated beams in aerospace engineering, including beams with edge cracks, rotating Timoshenko beams and functionally graded beams. Euler-Bernoulli beam theory is adopted for the study of beams with step axial force and cross-section, beams subjected to axial force static end moments, beams supported by elastic foundation and beams with edge cracks; while Timoshenko beam theory is adopted to study the vibration of delaminated rotating beams and Kirchhoff-Love hypothesis is adopted for the study of functionally graded beams with single delamination. Both ‘Free mode’ and ‘constrained mode’ assumptions in delamination vibration are studied in this thesis. This thesis focuses on how the effects of delamination (its size, thickness-wise location and length-wise location) on natural frequencies, mode shapes, buckling loads and critical moments for lateral instability are affected by the stepped axial force (its amplitude and location), the stepped cross-section (the stepped cross-section ratio and location), the static end moments, the elastic foundation (its stiffness, length and location), the crack (its depth and location), the rotating speed and Timoshenko effect (shear deformation and rotary inertia), as well as the material gradient for functionally graded beams. The use of these analytical solutions allows inexpensive simulations of slight variations in the system, such as changes in the physical parameters (delamination lengths and locations) and boundary conditions. This thesis provides analytical and exact solutions that can also serve as the benchmark for FEM and other numerical solutions.