Modern Trends in Structural and Solid Mechanics 2

4 Chapter 4Figure 4.1. Coordinate system of a micro-beam Figure 4.2. Sign convention for the positive axial force f, the shear force s an...Figure 4.3. Boundary conditions for the axial displacement and the axial force Figure 4.4. Boundary conditions for the bending displacement, the bending rotati...Figure 4.5. Amplitudes of displacements and forces at the ends of the micro-beam Figure 4.6. Alignment of the local (OXY) and global ( ) coordinate systems Figure 4.7. Natural frequencies and mode shapes of a micro-beam with the simply ...Figure 4.8. Natural frequencies and mode shapes of a micro-beam with the cantile...Figure 4.9. Natural frequencies and mode shapes of a micro-beam with the clamped...Figure 4.10. Effect of the material length scale parameter l/h on the fundamenta...Figure 4.11. An L-shaped micro-frame ( L =20h , b =2h , h =17.6 μm) Figure 4.12. Mode shapes of an L-shaped micro-frame for l/h = 1 Figure 4.13. A micro portal frame (L=20h, b=2h, h=17.6 μm) Figure 4.14. Mode shapes of a micro portal frame for l/h = 1

5 Chapter 5Figure 5.1. The nonlinear terms in the axial direction. a) Constant terms; b) te...Figure 5.2. The nonlinear terms in the transversal direction. a) Terms proportio...Figure 5.3. The nonlinear terms in the rotational direction. a) Terms proportion...Figure 5.4. a) ω0 and b) ω2 for varying l. n = 1, κh = 0Figure 5.5. The L2 norm percentage of the various nonlinear terms in the constan...Figure 5.6. The L2 norm percentage of the various nonlinear terms in the part pr...Figure 5.7. The L2 norm percentage of the various nonlinear terms in the part pr...Figure 5.8. The L2 norm percentage of the various nonlinear terms in the part pr...Figure 5.9. The L2 norm percentage of the various nonlinear terms in the part pr...Figure 5.10. The L2 norm percentage of the various nonlinear terms in the part p...Figure 5.11. The L2 norm percentage of the various nonlinear terms in a) the con...Figure 5.12. The L2 norm percentage of the various nonlinear terms in a) the par...Figure 5.13. The L2 norm percentage of the various nonlinear terms in a) the par...Figure 5.14. The L2 norm percentage of the various nonlinear terms in a) the con...Figure 5.15. The L2 norm percentage of the various nonlinear terms in a) the con...Figure 5.16. The L2 norm percentage of the various nonlinear terms in a) the par...Figure 5.17. The L2 norm percentage of the various nonlinear terms in a) the par...Figure 5.18. The L 2norm percentage of the various nonlinear terms in a) the par...Figure 5.19. The L 2norm percentage of the various nonlinear terms in a) the par...

6 Chapter 6Figure 6.1. Grid beam. For a color version of this figure, see www.iste.co.uk/ch...Figure 6.2. Single cell of the grid beam and its deformation modes for two diffe...Figure 6.3. Static response of a grid beam to lateral forces: (a) rigid transver...Figure 6.4. Buckling of a uniformly compressed grid beam (Ferretti (2018)): (a) ...Figure 6.5. Lateral displacements for the first three modes (n = 25), continuo...Figure 6.6. Base-isolated tower building under wind flow: (a) cellular beam, (b)...Figure 6.7. Critical wind velocity of the base-isolated beam: (a) versus the sti...

7 Chapter 7Figure 7.1. Comparison between the conventional approach and the innovative appr...Figure 7.2. Critical response, derived by the innovative approach, positioned in...Figure 7.3. SDOF elastic–plastic system with negative post-yield stiffness. For ...Figure 7.4. Elastic–plastic collapse response of the SDOF system subjected to cr...Figure 7.5. Energy balance law for the elastic–plastic collapse response of the ...Figure 7.6. Collapse limit input velocity for various post-yield stiffness ratio...Figure 7.7. Modeling of the main part of a near-fault ground motion into one-cyc...Figure 7.8. Displacement and restoring-force responses under Rinaldi Sta. FN wit...Figure 7.9. Trajectories in restoring-force characteristics for CASEs-A, B, C (H...Figure 7.10. Three cases (A, B, C) for three input velocity levels and four case...Figure 7.11. Restoring-force characteristics for Collapse Patterns 1’–4’. For a ...Figure 7.12. Collapse Pattern 1’ (CASE-A): (a) Restoring-force characteristic an...Figure 7.13. Collapse limit input velocity for various intervals of two impulses...Figure 7.14. Response analysis simulation for various combinations of input velo...

8 Chapter 8Figure 8.1. (a) SDOF Bouc–Wen oscillator; (b) first loading branch; and (c) rest...Figure 8.2. SDOF oscillator: frequency response curves for varying forcing ampli...Figure 8.3. Response amplitude versus resonance frequency: (a) and (b) . For ...Figure 8.4. 2DOF system: (a) top-hysteresis and (b) base-hysteresis configuratio...Figure 8.5. 2DOF top configuration close to a (1:1) internal resonance (ω2A/ω1A ...Figure 8.6. 2DOF top-hysteresis oscillator close to a (3:1) internal resonance ω...Figure 8.7. 2DOF base-hysteresis configuration close to a (3:1) resonance: (a) F...Figure 8.8. 2DOF base-hysteresis configuration close to (3:1) resonance for IA1 ...Figure 8.9. 2DOF base-hysteresis oscillator close to (2:1) internal resonance (ω...

9 Chapter 9Figure 9.1. Schematic of an infinite elastic membrane with periodically inserted...Figure 9.2. Comparisons of the distributed delta function δh(x) for different va...Figure 9.3. Ratio of the amplitude of the overall transmission to the initial wa...Figure 9.4. Ratio of the amplitude of the overall transmission to the initial wa...Figure 9.5. Ratios of the amplitudes of successive reflections [9.37] and transm...Figure 9.6. Ratios of the amplitudes of the overall reflection [9.41] and transm...Figure 9.7. Schematic of an infinite elastic membrane with a square lattice of s...

10 Chapter 10Figure 10.1. A horizontal soil layer under three-dimensional point loads. For a ...Figure 10.2. Layered half-space under three-dimensional forces. For a color vers...Figure 10.3. Foundation-site model and discretization of foundation. For a color...Figure 10.4. Flexible foundation nodes and discretization of foundation. For a c...Figure 10.5. Foundation-site models and discretization of foundations. For a col...Figure 10.6. Dynamic soil stiffness of the square foundation on a layer and half...Figure 10.7. Dynamic soil stiffness of the circular foundation on a layer and ha...Figure 10.8. Dynamic soil stiffness of the circular foundation on half-space. Fo...Figure 10.9. Dynamic soil stiffness of circular foundation on a layer and half-s...Figure 10.10. Primary and secondary systems in a nuclear power plant. For a colo...Figure 10.11. Dynamic soil stiffness of a reactor building. For a color version ...Figure 10.12. Horizontal transfer matrix of a reactor building Figure 10.13. FLIRS of a reactor building Figure 10.14. Comparison of FRS at node 4 at the reactor building. For a color v...

1 Chapter 1 Table 1.1. Comparison of frequencies obtained using various approximation method...

2 Chapter 4Table 4.1. Natural frequencies of a simply supported (S–S) micro-beam Table 4.2. Natural frequencies of a cantilever (C–F) micro-beam Table 4.3. Natural frequencies of a clamped–clamped (C–C) micro-beam Table 4.4. Natural frequencies of an L-shaped micro-frame Table 4.5. Natural frequencies of a micro portal frame

3 Chapter 5Table 5.1. The L2 norm percentage of the various nonlinear terms in the axial eq...Table 5.2. The L 2norm percentage of the various nonlinear terms in the transver...Table 5.3. The L2 norm percentage of the various nonlinear terms in the rotation...