• PhD Thesis_Vatankhah_final2 (1)
• 1 (251)
  • Boundary stabilization of non-classical micro-scale beams (251)
    • 1 Introduction (251)
    • 2 A review of strain gradient theory for elasticity and problem formulation (252)
    • 3 Boundary stabilization of a vibrating non-classical micro-scale cantilever beam (253)
      • 3.1 The advantages of boundary control of PDE models (253)
      • 3.2 Boundary stabilization of a vibrating non-classical micro-cantilever beam (254)
      • 3.3 Stabilization of the system via incomplete boundary control inputs (257)
    • 4 Numerical implementations (260)
      • 4.1 Derivation of strain gradient beam element stiffness and mass matrices (260)
      • 4.2 Simulation results (261)
      • 4.3 Verification of the newly established beam elements (265)
    • 5 Conclusion (265)
    • References (266)
• 2 (267)
  • Nonlinear forced vibration of strain gradient microbeams (267)
    • 1 Introduction (267)
    • 2 Preliminaries (268)
    • 3 Nonlinear analysis (271)
      • 3.1 Hardening nonlinearity caused by mid-plane stretching (271)
        • 3.1.1 Primary resonance (273)
        • 3.1.2 Super-harmonic resonance (276)
        • 3.1.3 Sub-harmonic resonance (278)
        • 3.1.4 Verification (280)
      • 3.2 Softening nonlinearity caused by van-der-Waals force (280)
    • 4 Conclusion (285)
    • References (286)
• 3 (287)
• 4 (295)
• Abstract (303)
• In the name of God (304)