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Original Articles

Transient analysis of a three-layer microbeam subjected to electric potential

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Pages 20-40 | Received 22 Nov 2016, Accepted 05 Feb 2017, Published online: 28 Feb 2017

Figures & data

Figure 1. The schematic of a simply-supported three-layer Euler–Bernoulli microbeam.

Figure 1. The schematic of a simply-supported three-layer Euler–Bernoulli microbeam.

Figure 2. Dimensionless deflection of a nanoplate in terms of non-homogeneity index for .

Figure 2. Dimensionless deflection of a nanoplate in terms of non-homogeneity index for .

Figure 3. Dimensionless deflection of a nanoplate in terms of non-homogeneity index for .

Figure 3. Dimensionless deflection of a nanoplate in terms of non-homogeneity index for .

Figure 4. Two-dimensional distribution of phase velocities in terms of two parameters of Pasternak’s foundation for .

Figure 4. Two-dimensional distribution of phase velocities in terms of two parameters of Pasternak’s foundation for .

Figure 5. The phase velocities of three-layer nano/microbeam in terms of wave number and non-homogeneity index.

Figure 5. The phase velocities of three-layer nano/microbeam in terms of wave number and non-homogeneity index.

Figure 6. The phase velocities of microbeam in terms of two parameters of foundation and for .

Figure 6. The phase velocities of microbeam in terms of two parameters of foundation and for .

Figure 7. The natural frequencies of microbeam in terms of dimensionless microscale parameters and .

Figure 7. The natural frequencies of microbeam in terms of dimensionless microscale parameters and .

Figure 8. Two-dimensional distribution of the natural frequencies of microbeam in terms of dimensionless microscale parameters and for .

Figure 8. Two-dimensional distribution of the natural frequencies of microbeam in terms of dimensionless microscale parameters and for .

Figure 9. Two-dimensional distribution of the natural frequencies of microbeam in terms of two parameters of Pasternak’s foundation for .

Figure 9. Two-dimensional distribution of the natural frequencies of microbeam in terms of two parameters of Pasternak’s foundation for .

Figure 10. Dimensionless transverse displacement of microbeam in terms of two parameters of foundation and for .

Figure 10. Dimensionless transverse displacement of microbeam in terms of two parameters of foundation and for .

Figure 11. Dimensionless transverse displacement of microbeam in terms of applied voltage and shear parameter of foundation for .

Figure 11. Dimensionless transverse displacement of microbeam in terms of applied voltage and shear parameter of foundation for .

Figure 12. Two-dimensional dimensionless deflection of microbeam in terms of two parameters of foundation and for .

Figure 12. Two-dimensional dimensionless deflection of microbeam in terms of two parameters of foundation and for .

Figure 13. Dimensionless transverse displacement of microbeam in terms of non-homogeneity index and Winkler’s parameter of foundation .

Figure 13. Dimensionless transverse displacement of microbeam in terms of non-homogeneity index and Winkler’s parameter of foundation .

Figure 14. Distribution of electric potential in terms of two parameters of foundation and for .

Figure 14. Distribution of electric potential in terms of two parameters of foundation and for .

Figure 15. Two-dimensional distribution of electric potential in terms of two parameters of foundation and for .

Figure 15. Two-dimensional distribution of electric potential in terms of two parameters of foundation and for .

Figure 16. Distribution of electric potential of microbeam in terms of non-homogeneity index and Winkler’s parameter of foundation .

Figure 16. Distribution of electric potential of microbeam in terms of non-homogeneity index and Winkler’s parameter of foundation .