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Vibration Analysis of viscoelastic Sandwich Plates Under the Effects of Nonlinearities and Random Excitations

Mahmoudkhani, Saeed |

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 44235 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Haddadpour, Hassan
  7. Abstract:
  8. Different aspects of oscillatory behaviors of sandwich structures with viscoelastic cores are investigated in the present study in four parts. In the first part, an analytical study is conducted to determine the variation of linear frequencies and damping ratio of different families of modes with system parameters. The participation of different families of modes such as the so-called pumping or thickness-shear modes along with the overall bending modes in the transverse response of the structure to transverse wide-band excitation is also investigated in this part. The formulation of the problem is established by assuming quadratic variation of displacement components of the core through the thickness and the solution is provided by using the normal mode method. In the second part, the theoretical formulation is derived by special attention on the fact that a weak core constrained between stiffer layers may experience higher values of transverse shear strains and rotations in bending deformations. In this regard, the method of assuming different order of magnitudes for linear strains and rotations is used to derive approximate kinetic and constitutive equations of nonlinear incompressible viscoelastic core. The equations of motion consist of seven nonlinear partial differential equations obtained by the Hamilton’s principle and two equations corresponding to incompressibility of the core, which are solved by direct application of the 5th-order multiple scale method. The linear partial differential equations, obtained during the perturbation solution, are solved by the method of eigenfunction expansion and the nonhomogeneous boundary conditions are dealt with, by transforming to homogeneous boundaries, or using the extended Green’s formula. In the third part, the nonlinear vibration is investigated under the narrow-band excitation by using the finite difference method to solve the Fokker-Plank equation corresponding to the phase-amplitude equation. The bi-modality of the response probability density is explored for different system parameters. In the fourth part, the vibration of near-square sandwich plate is investigated under the wide-band excitation, using the non-Gaussian closure method, and the appearance of the multi-mode response due to the internal resonance is explored
  9. Keywords:
  10. Nonlinear Vibration ; Moderate Transvers Shear Strain ; Viscoelastic Sandwich Plate ; Random Excitation ; Multiple Scales Method (MMS)

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