290
F. Lin et al.
the time–domain DQM. It is observed from results of two examples, the accuracy and
efficiency of time–domain DQ method is excellent under certain number of nodes. It
is simple and easy for the mathematical principle of space–time DQM to implement
in program, so it has a bright application prospect in the dynamic analysis field and
is worthy of a further study.
References
1. Bellman, R., Casti, J.: Differential quadrature and long-term integration. J. Math. Anal. Appl.
34(2), 235–238 (1971)
2. Kitipornchai, S., Ke, L.L., Yang, J., Xiang, Y.: Nonlinear vibration of edge cracked functionally
graded Timoshenko beams. J. Sound Vib. 324(3–5), 962–982 (2009)
3. Ke, L.L., Xiang, Y., Yang, J., Kitipornchai, S.: Nonlinear free vibration of embedded doublewalled carbon nanotubes based on nonlocal Timoshenko beam theory. Comput. Mater. Sci.
47(2), 409–417 (2009)
4. Fung, T.C.: Solving initial value problems by differential quadrature method - Part 1: first-order
equations. Int. J. Numer. Meth. Eng. 50(6), 1411–1427 (2001)
5. Peng, J.S., Xie, G., Yang, L., Yuan, Y.Q.: A time-domain dq approach for vibration analysis of
beams. Adv. Mater. Res. 631–632, 957–961 (2013)
6. Wang, X.W.: Chapter 6-Static analysis of thin plate. Differential quadrature and differential
quadrature based element methods, pp. 120–133 (2015)
7. Arani, A.G., Jafari, G.S.: Nonlinear vibration analysis of laminated composite Mindlin
micro/nano-plates resting on orthotropic Pasternak medium using DQM. Appl. Math. Mech.English Ed. 36(8), 1033–1044 (2015)
8. Safarpour, M., Rahimi, A.R., Alibeigloo, A.: Static and free vibration analysis of graphene
platelets reinforced composite truncated conical shell, cylindrical shell, and annular plate using
theory of elasticity and DQM. Mech. Based Des. Struct. Mach. 48(4), 496–524 (2020)
9. Xu, Z.L.: Theory of elasticity (the 2nd half). Higher Education Press, Beijing (2006)
10. Kuang, J.H., Chen, C.J.: Dynamic characteristics of shaped micro-actuators solved using the
differential quadrature method. J. Micromech. Microeng. 14(4), 647–655 (2004)
11. Saglam, S., Ozdemir, E., Ozkan, U. Y., Demirel, T. and Makineci, E.: Biomass estimation
of aboveground tree components for Turkey oak (Quercus cerris L.) in south-eastern Turkey.
Environ. Monitor. Assess. 192 (7), 418 (2020)
F. Lin et al.
the time–domain DQM. It is observed from results of two examples, the accuracy and
efficiency of time–domain DQ method is excellent under certain number of nodes. It
is simple and easy for the mathematical principle of space–time DQM to implement
in program, so it has a bright application prospect in the dynamic analysis field and
is worthy of a further study.
References
1. Bellman, R., Casti, J.: Differential quadrature and long-term integration. J. Math. Anal. Appl.
34(2), 235–238 (1971)
2. Kitipornchai, S., Ke, L.L., Yang, J., Xiang, Y.: Nonlinear vibration of edge cracked functionally
graded Timoshenko beams. J. Sound Vib. 324(3–5), 962–982 (2009)
3. Ke, L.L., Xiang, Y., Yang, J., Kitipornchai, S.: Nonlinear free vibration of embedded doublewalled carbon nanotubes based on nonlocal Timoshenko beam theory. Comput. Mater. Sci.
47(2), 409–417 (2009)
4. Fung, T.C.: Solving initial value problems by differential quadrature method - Part 1: first-order
equations. Int. J. Numer. Meth. Eng. 50(6), 1411–1427 (2001)
5. Peng, J.S., Xie, G., Yang, L., Yuan, Y.Q.: A time-domain dq approach for vibration analysis of
beams. Adv. Mater. Res. 631–632, 957–961 (2013)
6. Wang, X.W.: Chapter 6-Static analysis of thin plate. Differential quadrature and differential
quadrature based element methods, pp. 120–133 (2015)
7. Arani, A.G., Jafari, G.S.: Nonlinear vibration analysis of laminated composite Mindlin
micro/nano-plates resting on orthotropic Pasternak medium using DQM. Appl. Math. Mech.English Ed. 36(8), 1033–1044 (2015)
8. Safarpour, M., Rahimi, A.R., Alibeigloo, A.: Static and free vibration analysis of graphene
platelets reinforced composite truncated conical shell, cylindrical shell, and annular plate using
theory of elasticity and DQM. Mech. Based Des. Struct. Mach. 48(4), 496–524 (2020)
9. Xu, Z.L.: Theory of elasticity (the 2nd half). Higher Education Press, Beijing (2006)
10. Kuang, J.H., Chen, C.J.: Dynamic characteristics of shaped micro-actuators solved using the
differential quadrature method. J. Micromech. Microeng. 14(4), 647–655 (2004)
11. Saglam, S., Ozdemir, E., Ozkan, U. Y., Demirel, T. and Makineci, E.: Biomass estimation
of aboveground tree components for Turkey oak (Quercus cerris L.) in south-eastern Turkey.
Environ. Monitor. Assess. 192 (7), 418 (2020)
Précédent