194
6 Mathematical Models of Micro- and Nano-cylindrical Panels in Temperature Field
28. Park, S.K., Gao, X.L.: Bernoulli-Euler beam model based on a modified couple stress theory.
Micromech. Microeng. 16(11), 2355–2359 (2006)
29. Rajabi, F., Ramezani, S.: A nonlinear microbeam model based on strain gradient elasticity
theory with surface energy. Arch. Appl. Mech. 82, 363–376 (2012)
30. Ma, H.M., Gao, X.-L., Reddy, J.N.: A microstructure-dependent Timoshenko beam model
based on a modified couple stress theory. J. Mech. Phys. Sol. 56, 3379–3396 (2008)
31. Asghari, M., Kahrobaiyan, M.H., Nikfar, M., Ahmadian, M.T.: A size-dependent nonlinear
Timoshenko microbeam model based on the strain gradient theory. Acta Mech. 223, 1233–
1249 (2012)
32. Ansari, R., Gholami, R., Darabi, M.A.: A nonlinear Timoshenko beam formulation based on
strain gradient theory. J. Mech. Mater. Struct. 7(2), 1749–1761 (2012)
33. Awrejcewicz, J., Krysko, V.A., Papkova, I.V., Krysko, A.V.: Deterministic Chaos in OneDimentional Continuous Systems. World Scientific, Singapore (2016)
34. Awrejcewicz, J.A., Krysko, V.A., Zhigalov, M.V., Saltykova, O.A., Krysko, A.V.: Chaotic
vibrations in flexible multilayered Bernoulli-Euler and Timoshenko type beams. Lat. Am. J.
Sol. Struct. 5(4), 319–363 (2008)
35. Krysko, A.V., Awrejcewicz, J., Saltykova, O.A., Zhigalov, M.V., Krysko, V.A.: Investigations
of chaotic dynamics of multi-layer beams using taking into account rotational inertial effects.
Comm. Nonlin. Sci. Num. Simul. 19(8), 2568–2589 (2014)
36. Krysko, V.A., Awrejcewicz, J.: Nonclassical Thermoelastic Problems in Nonlinear Dynamics
of Shells. Springer, Berlin (2003)
37. Krysko, V.A., Awrejcewicz, J.: Chaos in Structural Mechanics. Springer, Berlin (2008)
38. Krysko, V.A., Awrejcewicz, J., Krysko, A.V.: Thermo-Dynamics of Plates and Shells. Springer,
Berlin (2007)
39. Krysko, V.A., Awrejcewicz, J., Vakakis, A.: Nonlinear Dynamics of Continuous Elastic Systems. Springer, Berlin (2004)
40. Simsek, M., Reddy, J.N.: Bending and vibration of functionally graded microbeams using a
new higher order beam theory and the modified couple stress theory. Int. J. Eng. Sci. 64, 37–53
(2013)
41. Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents from a
time series. Phys. D 16, 285–317 (1985)
42. Nowacki, W.: Theory of Elasticity. Mir, Moscow (1975)
43. Krysko, A.V., Awrejcewicz, J., Zhigalov, M.V., Pavlov, S.P., Krysko, V.A.: Nonlinear behaviour
of different flexible size-dependent beams models based on the modified couple stress theory.
Part 1. Governing equations and static analysis of flexible beams. Int. J. Non-Lin. Mech. 93,
96–105 (2017)
44. Ansari, R., Gholami, R.: Size-dependent vibration of functionally graded curved microbeams
based on the modified strain gradient elasticity theory. Arch. Appl. Mech. 83, 1439–1449
(2013)
45. Novozhilov, V.V.: Introduction to Nonlinear Theory of Elasticity. Gostechizdat, Moscow
46. Franklin, J.N.: On Tikhonov’s method for ill-posed problems. Math. Comput. 28(128), 889–907
(1974)
47. Muschtari, H.M.: Some generalizations of the theory of thin shells. Proc. Phys. Math. Soc.
Kazan Univ. XI(8) (1938)
48. Muschtari, H.M.: On the stability of a round thin cylindrical shell under torsion. Proc. Kazan
Aviat. Instit. 2 (1934)
49. Timoshenko, S.P.: On the correction for shear of differential equation for transverse vibration
of prismatic bar. Philosoph. Mag. 41, 744–746 (1921)
50. Bernoulli, J.: Essait theoretique sur les vibrations de plaques elastiques rectangulaires et libres.
Nova Acta Acad. Petropolit. 5, 197–219 (1789)
51. Euler, L.: Sur la force des colones. Memories de L’Academie de Berlin 13, 252–282 (1757)
52. Love, A.: A Tretise on the Mathematical Theory of Eelasticity (1927)
53. Awrejcewicz, J., Krysko, A., Saltykova, O.A., Zhigalov, M.V., Soldatov, V.V.: Investigations
of complex vibrations of beams within the framework of the Sheremet’ev-Pelekh kinematic
model using the wavelet transform. J. Mach. Manufact. Reliab. 39(4), 313–317 (2010)
6 Mathematical Models of Micro- and Nano-cylindrical Panels in Temperature Field
28. Park, S.K., Gao, X.L.: Bernoulli-Euler beam model based on a modified couple stress theory.
Micromech. Microeng. 16(11), 2355–2359 (2006)
29. Rajabi, F., Ramezani, S.: A nonlinear microbeam model based on strain gradient elasticity
theory with surface energy. Arch. Appl. Mech. 82, 363–376 (2012)
30. Ma, H.M., Gao, X.-L., Reddy, J.N.: A microstructure-dependent Timoshenko beam model
based on a modified couple stress theory. J. Mech. Phys. Sol. 56, 3379–3396 (2008)
31. Asghari, M., Kahrobaiyan, M.H., Nikfar, M., Ahmadian, M.T.: A size-dependent nonlinear
Timoshenko microbeam model based on the strain gradient theory. Acta Mech. 223, 1233–
1249 (2012)
32. Ansari, R., Gholami, R., Darabi, M.A.: A nonlinear Timoshenko beam formulation based on
strain gradient theory. J. Mech. Mater. Struct. 7(2), 1749–1761 (2012)
33. Awrejcewicz, J., Krysko, V.A., Papkova, I.V., Krysko, A.V.: Deterministic Chaos in OneDimentional Continuous Systems. World Scientific, Singapore (2016)
34. Awrejcewicz, J.A., Krysko, V.A., Zhigalov, M.V., Saltykova, O.A., Krysko, A.V.: Chaotic
vibrations in flexible multilayered Bernoulli-Euler and Timoshenko type beams. Lat. Am. J.
Sol. Struct. 5(4), 319–363 (2008)
35. Krysko, A.V., Awrejcewicz, J., Saltykova, O.A., Zhigalov, M.V., Krysko, V.A.: Investigations
of chaotic dynamics of multi-layer beams using taking into account rotational inertial effects.
Comm. Nonlin. Sci. Num. Simul. 19(8), 2568–2589 (2014)
36. Krysko, V.A., Awrejcewicz, J.: Nonclassical Thermoelastic Problems in Nonlinear Dynamics
of Shells. Springer, Berlin (2003)
37. Krysko, V.A., Awrejcewicz, J.: Chaos in Structural Mechanics. Springer, Berlin (2008)
38. Krysko, V.A., Awrejcewicz, J., Krysko, A.V.: Thermo-Dynamics of Plates and Shells. Springer,
Berlin (2007)
39. Krysko, V.A., Awrejcewicz, J., Vakakis, A.: Nonlinear Dynamics of Continuous Elastic Systems. Springer, Berlin (2004)
40. Simsek, M., Reddy, J.N.: Bending and vibration of functionally graded microbeams using a
new higher order beam theory and the modified couple stress theory. Int. J. Eng. Sci. 64, 37–53
(2013)
41. Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents from a
time series. Phys. D 16, 285–317 (1985)
42. Nowacki, W.: Theory of Elasticity. Mir, Moscow (1975)
43. Krysko, A.V., Awrejcewicz, J., Zhigalov, M.V., Pavlov, S.P., Krysko, V.A.: Nonlinear behaviour
of different flexible size-dependent beams models based on the modified couple stress theory.
Part 1. Governing equations and static analysis of flexible beams. Int. J. Non-Lin. Mech. 93,
96–105 (2017)
44. Ansari, R., Gholami, R.: Size-dependent vibration of functionally graded curved microbeams
based on the modified strain gradient elasticity theory. Arch. Appl. Mech. 83, 1439–1449
(2013)
45. Novozhilov, V.V.: Introduction to Nonlinear Theory of Elasticity. Gostechizdat, Moscow
46. Franklin, J.N.: On Tikhonov’s method for ill-posed problems. Math. Comput. 28(128), 889–907
(1974)
47. Muschtari, H.M.: Some generalizations of the theory of thin shells. Proc. Phys. Math. Soc.
Kazan Univ. XI(8) (1938)
48. Muschtari, H.M.: On the stability of a round thin cylindrical shell under torsion. Proc. Kazan
Aviat. Instit. 2 (1934)
49. Timoshenko, S.P.: On the correction for shear of differential equation for transverse vibration
of prismatic bar. Philosoph. Mag. 41, 744–746 (1921)
50. Bernoulli, J.: Essait theoretique sur les vibrations de plaques elastiques rectangulaires et libres.
Nova Acta Acad. Petropolit. 5, 197–219 (1789)
51. Euler, L.: Sur la force des colones. Memories de L’Academie de Berlin 13, 252–282 (1757)
52. Love, A.: A Tretise on the Mathematical Theory of Eelasticity (1927)
53. Awrejcewicz, J., Krysko, A., Saltykova, O.A., Zhigalov, M.V., Soldatov, V.V.: Investigations
of complex vibrations of beams within the framework of the Sheremet’ev-Pelekh kinematic
model using the wavelet transform. J. Mach. Manufact. Reliab. 39(4), 313–317 (2010)