332
8 Thermoelastic Vibrations of Timoshenko Microbeams
93. Salajeghe, S., Khadem, S.E., Rasekh, M.: Nonlinear analysis of thermoelastic damping in
axisymmetric vibration of micro circular thin-plate resonators. Appl. Math. Model. 36, 5991–
6000 (2012)
94. Tunvir, K., Ru, C.Q., Mioduchowski, A.: Large-deflection effect on thermoelastic dissipation
of microbeam resonators. J. Therm. Stress 35, 1076–1094 (2012)
95. Rochus, V., Rixen, D.J., Golinval, J.C.: Electrostatic coupling of MEMS structures: transient
simulations and dynamic pull-in. Nonlinear Anal. Theor. Meth. Appl. 63, 1619–1633 (2005)
96. Krysko, A.V., Awrejcewicz, J., Pavlov, S.P., Bodyagina, K.S., Zhigalov, M.V., Krysko, V.A.:
Non-linear dynamics of size-dependent Euler-Bernoulli beams with topologically optimized
microstructure and subjected to temperature field. Int. J. Non-Lin. Mech. 104, 75–86 (2018)
97. Awrejcewicz, J., Pavlov, S.P., Bodyagina, K.S., Zhigalov, M.V., Krysko, V.A.: Design of composite structures with extremal elastic properties in the presence of technological constraints.
Compos. Struct. 174, 19–25 (2017)
98. Timoshenko, S.P., Goodier, J.N.: Theory of Elasticity, 2nd edn. McGraw-Hill, New York
(1951)
99. Feng, J.T., Zhao, Y.P.: Influence of different amount of Au on the wetting behavior of PDMS
membrane. Biomed. Microdev. 10(1), 65–72 (2008)
100. Voyiadjis, G.Z., Abu Al-Rub, R.K.: Gradient plasticity theory with a variable length scale
parameter. Int. J. Sol. Struct. 42(14), 3998–4029 (2005)
101. Han, S.M., Benaroya, H., Wei, T.: Dynamics of transversely vibrating beams using four
engineering theories. J. Sound Vib. 225(5), 935–988 (1999)
102. Gorman, D.J.: Free Vibration Analysis of Beams and Shafts. Wiley, New York (1975)
103. Hao, Z., Erbil, A., Ayazi, F.: An analytical model for support loss in micromachined beam
resonators with in-plane flexural vibrations. Sens. Actuators A 109, 156–164 (2003)
104. Mahi, A., Adda Bedia, E.A., Tounsi, A., Machab, I.: An analytical method for temperaturedependent free vibration analysis of functionally graded beams with general boundary conditions. Comput. Struct. 92, 1877–1887 (2010)
105. Araujo dos Santos, J.V., Reddy, J.N.: Free vibration and buckling analysis of beams with a
modified couple-stress theory. Int. J. Appl. Mech. 4(3), 1250026 (2012)
8 Thermoelastic Vibrations of Timoshenko Microbeams
93. Salajeghe, S., Khadem, S.E., Rasekh, M.: Nonlinear analysis of thermoelastic damping in
axisymmetric vibration of micro circular thin-plate resonators. Appl. Math. Model. 36, 5991–
6000 (2012)
94. Tunvir, K., Ru, C.Q., Mioduchowski, A.: Large-deflection effect on thermoelastic dissipation
of microbeam resonators. J. Therm. Stress 35, 1076–1094 (2012)
95. Rochus, V., Rixen, D.J., Golinval, J.C.: Electrostatic coupling of MEMS structures: transient
simulations and dynamic pull-in. Nonlinear Anal. Theor. Meth. Appl. 63, 1619–1633 (2005)
96. Krysko, A.V., Awrejcewicz, J., Pavlov, S.P., Bodyagina, K.S., Zhigalov, M.V., Krysko, V.A.:
Non-linear dynamics of size-dependent Euler-Bernoulli beams with topologically optimized
microstructure and subjected to temperature field. Int. J. Non-Lin. Mech. 104, 75–86 (2018)
97. Awrejcewicz, J., Pavlov, S.P., Bodyagina, K.S., Zhigalov, M.V., Krysko, V.A.: Design of composite structures with extremal elastic properties in the presence of technological constraints.
Compos. Struct. 174, 19–25 (2017)
98. Timoshenko, S.P., Goodier, J.N.: Theory of Elasticity, 2nd edn. McGraw-Hill, New York
(1951)
99. Feng, J.T., Zhao, Y.P.: Influence of different amount of Au on the wetting behavior of PDMS
membrane. Biomed. Microdev. 10(1), 65–72 (2008)
100. Voyiadjis, G.Z., Abu Al-Rub, R.K.: Gradient plasticity theory with a variable length scale
parameter. Int. J. Sol. Struct. 42(14), 3998–4029 (2005)
101. Han, S.M., Benaroya, H., Wei, T.: Dynamics of transversely vibrating beams using four
engineering theories. J. Sound Vib. 225(5), 935–988 (1999)
102. Gorman, D.J.: Free Vibration Analysis of Beams and Shafts. Wiley, New York (1975)
103. Hao, Z., Erbil, A., Ayazi, F.: An analytical model for support loss in micromachined beam
resonators with in-plane flexural vibrations. Sens. Actuators A 109, 156–164 (2003)
104. Mahi, A., Adda Bedia, E.A., Tounsi, A., Machab, I.: An analytical method for temperaturedependent free vibration analysis of functionally graded beams with general boundary conditions. Comput. Struct. 92, 1877–1887 (2010)
105. Araujo dos Santos, J.V., Reddy, J.N.: Free vibration and buckling analysis of beams with a
modified couple-stress theory. Int. J. Appl. Mech. 4(3), 1250026 (2012)