290
7 Mathematical Models of Functionally Graded Beams in Temperature Field
102. Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J., Tong, P.: Experiments and theory in strain
gradient elasticity. J. Mech. Phys. Solids 51, 1477–1508 (2003)
103. Eringen, A.C.: Nonlocal polar elastic continua. Int. J. Eng. Sci. 10, 1–16 (1972)
104. Aifantis, E.C.: Strain gradient interpretation of size effects. Int. J. Fract. 95, 299–314 (1999)
105. Gurtin, M.E., Weissmuller, J., Larche, F.: The general theory of curved deformable inter-faces
in solids at equilibrium. Philos. Mag. A 78, 1093–1109 (1998)
106. 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. Solids 56, 3379–3396 (2008)
107. Begley, M.R., Hutchinson, J.W.: The mechanics of size-dependent indentation. J. Mech. Phys.
Solids 46, 2049–2068 (1998)
108. Nix, W.D., Gao, H.: Indentation size effects in crystalline materials: a law for strain gradient
plasticity. J. Mech. Phys. Solids 46, 411–425 (1998)
109. Reddy, J.N.: Theory and Analysis of Elastic Plates and Shells. Taylor & Francis, Philadelphia
(2007)
110. Awrejcewicz, J., Krysko, V.A., Papkova, I.V., Krysko, A.V.: Routes to chaos in continuous
mechanical systems. Part 1: mathematical models and solution methods. Chaos Solitons Fractals 45, 687–708 (2012)
111. Krysko, A.V., Awrejcewicz, J., Pavlov, S.P., Zhigalov, M.V., Krysko, V.A.: On the iterative
methods of linearization, decrease of order and dimension of the Kármán-type PDEs. Sci.
World J. 2014 (2014), 15 pp
112. Kirichenko, V.F., Awrejcewicz, J., Kirichenko, A.F., Krysko, A.V., Krysko, V.A.: On the
non-classical mathematical models of coupled problems of thermo-elasticity for multi-layer
shallow shells with initial imperfections. Int. J. Non-linear Mech. 74, 51–72 (2015)
113. Awrejcewicz, J., Krysko, A.V., Soldatov, V.: On the wavelet transform application to a study
of chaotic vibrations of the infinite length flexible panels driven longitudinally. Int. J. Bifurc.
Chaos 19(10), 3347–3371 (2009)
114. Awrejcewicz, J., Krysko, A.V., Kutepov, I., Zagniboroda, N., Zhigalov, M., Krysko, V.A.:
Analysis of chaotic vibrations of flexible plates using fast Fourier transforms and wavelets.
Int. J. Struct. Stab. Dyn. 13(7), 1340005-1–1340004-12 (2013)
115. Awrejcewicz, J., Saltykova, O.A., Zhigalov, M.V., Hagedorn, P., Krysko, V.A.: Analysis of
non-linear vibrations of single-layered Euler-Bernoulli beams using wavelets. Int. J. Aerosp.
Lightweight Struct. 1(2), 203–219 (2011)
116. Krysko, A.V., Awrejcewicz, J., Zhigalov, M.V., Krysko, V.A.: On the contact interaction
between two rectangular plates. Nonlinear Dyn. 85(4), 2729–2748 (2016)
117. 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.
Commun. Nonlinear Sci. Numer. Simul. 19(8), 2568–2589 (2014)
118. Krysko, V.A., Awrejcewicz, J., Kutepov, I.E., Zagniboroda, N.A., Serebryakov, A.V., Krysko,
A.V., Papkova, I.V.: Chaotic dynamics of flexible beams with piezoelectric and temperature
phenomena. Phys. Lett. A 377, 2058–2061 (2013)
119. Awrejcewicz, J., Krysko, V.A., Kutepov, I.E., Zagniboroda, N.A., Dobriyan, V., Papkova, I.V.,
Krysko, A.V.: Chaotic vibrations of flexible curvilinear beams in temperature and electric
fields. Int. J. Non-linear Mech. 76, 29–41 (2015)
120. Awrejcewicz, J., Krysko, A.V., Papkova, I.V., Zakharov, V.M., Erofeev, N.P., Krylova, E.Yu.,
Mrozowski, J., Krysko, V.A.: Chaotic dynamics of flexible beams driven by external white
noise. Mech. Syst. Signal Process. 79, 225–253 (2016)
121. Awrejcewicz, J., Krysko, V.A., Papkova, I.V., Krysko, A.V.: Deterministic Chaos in OneDimensional Continuous Systems. World Scientific, Singapore (2016)
122. Timoshenko, S.P.: On the correction for shear of differential equation for transverse vibration
of prismatic bar. Philos. Mag. 41, 744–746 (1921)
123. Krysko, A.V., Awrejcewicz, J., Kutepov, I.E., Zagniboroda, N.A., Dobriyan, V., Krysko,
V.A.: Chaotic dynamics of flexible Euler-Bernoulli beams. Chaos 23(4), 043130-1–04313025 (2013)
7 Mathematical Models of Functionally Graded Beams in Temperature Field
102. Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J., Tong, P.: Experiments and theory in strain
gradient elasticity. J. Mech. Phys. Solids 51, 1477–1508 (2003)
103. Eringen, A.C.: Nonlocal polar elastic continua. Int. J. Eng. Sci. 10, 1–16 (1972)
104. Aifantis, E.C.: Strain gradient interpretation of size effects. Int. J. Fract. 95, 299–314 (1999)
105. Gurtin, M.E., Weissmuller, J., Larche, F.: The general theory of curved deformable inter-faces
in solids at equilibrium. Philos. Mag. A 78, 1093–1109 (1998)
106. 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. Solids 56, 3379–3396 (2008)
107. Begley, M.R., Hutchinson, J.W.: The mechanics of size-dependent indentation. J. Mech. Phys.
Solids 46, 2049–2068 (1998)
108. Nix, W.D., Gao, H.: Indentation size effects in crystalline materials: a law for strain gradient
plasticity. J. Mech. Phys. Solids 46, 411–425 (1998)
109. Reddy, J.N.: Theory and Analysis of Elastic Plates and Shells. Taylor & Francis, Philadelphia
(2007)
110. Awrejcewicz, J., Krysko, V.A., Papkova, I.V., Krysko, A.V.: Routes to chaos in continuous
mechanical systems. Part 1: mathematical models and solution methods. Chaos Solitons Fractals 45, 687–708 (2012)
111. Krysko, A.V., Awrejcewicz, J., Pavlov, S.P., Zhigalov, M.V., Krysko, V.A.: On the iterative
methods of linearization, decrease of order and dimension of the Kármán-type PDEs. Sci.
World J. 2014 (2014), 15 pp
112. Kirichenko, V.F., Awrejcewicz, J., Kirichenko, A.F., Krysko, A.V., Krysko, V.A.: On the
non-classical mathematical models of coupled problems of thermo-elasticity for multi-layer
shallow shells with initial imperfections. Int. J. Non-linear Mech. 74, 51–72 (2015)
113. Awrejcewicz, J., Krysko, A.V., Soldatov, V.: On the wavelet transform application to a study
of chaotic vibrations of the infinite length flexible panels driven longitudinally. Int. J. Bifurc.
Chaos 19(10), 3347–3371 (2009)
114. Awrejcewicz, J., Krysko, A.V., Kutepov, I., Zagniboroda, N., Zhigalov, M., Krysko, V.A.:
Analysis of chaotic vibrations of flexible plates using fast Fourier transforms and wavelets.
Int. J. Struct. Stab. Dyn. 13(7), 1340005-1–1340004-12 (2013)
115. Awrejcewicz, J., Saltykova, O.A., Zhigalov, M.V., Hagedorn, P., Krysko, V.A.: Analysis of
non-linear vibrations of single-layered Euler-Bernoulli beams using wavelets. Int. J. Aerosp.
Lightweight Struct. 1(2), 203–219 (2011)
116. Krysko, A.V., Awrejcewicz, J., Zhigalov, M.V., Krysko, V.A.: On the contact interaction
between two rectangular plates. Nonlinear Dyn. 85(4), 2729–2748 (2016)
117. 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.
Commun. Nonlinear Sci. Numer. Simul. 19(8), 2568–2589 (2014)
118. Krysko, V.A., Awrejcewicz, J., Kutepov, I.E., Zagniboroda, N.A., Serebryakov, A.V., Krysko,
A.V., Papkova, I.V.: Chaotic dynamics of flexible beams with piezoelectric and temperature
phenomena. Phys. Lett. A 377, 2058–2061 (2013)
119. Awrejcewicz, J., Krysko, V.A., Kutepov, I.E., Zagniboroda, N.A., Dobriyan, V., Papkova, I.V.,
Krysko, A.V.: Chaotic vibrations of flexible curvilinear beams in temperature and electric
fields. Int. J. Non-linear Mech. 76, 29–41 (2015)
120. Awrejcewicz, J., Krysko, A.V., Papkova, I.V., Zakharov, V.M., Erofeev, N.P., Krylova, E.Yu.,
Mrozowski, J., Krysko, V.A.: Chaotic dynamics of flexible beams driven by external white
noise. Mech. Syst. Signal Process. 79, 225–253 (2016)
121. Awrejcewicz, J., Krysko, V.A., Papkova, I.V., Krysko, A.V.: Deterministic Chaos in OneDimensional Continuous Systems. World Scientific, Singapore (2016)
122. Timoshenko, S.P.: On the correction for shear of differential equation for transverse vibration
of prismatic bar. Philos. Mag. 41, 744–746 (1921)
123. Krysko, A.V., Awrejcewicz, J., Kutepov, I.E., Zagniboroda, N.A., Dobriyan, V., Krysko,
V.A.: Chaotic dynamics of flexible Euler-Bernoulli beams. Chaos 23(4), 043130-1–04313025 (2013)