The use of maximum rate of dissipation criterion to model beams with internal dissipation



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Texas A&M University


This thesis deals with a systematic procedure for the derivation of exact expression for the frequency equation of composite beams undergoing forced vibration with damping. The governing differential equations of motion of the composite beam are derived analytically for bending and shear deformation. The basic equations of Timoshenko beam theory and assumption of maximum rate of dissipation are employed. The principle involved is that of vibration energy dissipation due to damping as a result of deformation of materials in sandwich beam. The boundary conditions for displacements and forces for the cantilever beam are imposed and the frequency equation is obtained. The expressions for the amplitude of displacements are also derived in explicit analytical form. Numerical results of the displacement amplitude in cantilever sandwich beam varying with damping coefficient are evaluated.