TECHNICAL PAPER Response of thermoelastic microbeams to a periodic external transverse excitation based on MCS theory A. E. Abouelregal 1,2 Received: 25 May 2017 / Accepted: 10 October 2017 Ó Springer-Verlag GmbH Germany 2017 Abstract In this paper, we investigated the dynamics vibration of clamped–clamped microbeams exposed to associate exterior cross excitation. The theory of modified couple stress (MCS) and thermoelasticity model based on replacing Fourier’s law (LS) are applied to the constructed model. In sight of on Laplace transform technique, an analytical method is utilized to get the deflection and therefore the temperature fields. The inverse of Laplace transforms are calculated numerically utilizing Fourier development methods. The effects of angular frequency of the external force and couple stress term on temperature, deflection, displacement and bending moment are taken into consideration. Numerical results we obtained are dis- played in graphs and discussed. 1 Introduction Small-scale electromechanical systems (MEMS) are gad- gets, advancements and technologies that have been improved from the microelectronics engineering. Researchers have considered diverse approaches to make MEMS gadgets utilizing microelectronic creation strategy. MEMS gadgets have interesting features, for example, the littler size, the capacity to work in strict condition, and power productivity. MEMS systems are extensively being utilized in today’s technology. So studying the problems alluding to MEMS, possesses an extraordinary signifi- cance. One of the important fields of study is the strength examination of the excited systems. Parametrically excited micro-electromechanical gadgets are ever progressively being utilized as a part of radio, computer and laser designing (Belovodsky et al. 2002; Ghayesh et al. 2013). Some researchers, for example, Koiter (1964), Mindlin and Tiersten (1962) and Toupin (1962) introduced the model of couple stress of elasticity as a non-classical the- ory capable to calculate the size influences when two material constants of higher-order appearance in the cor- responding essential equations. Applying the couple stress theory, some researchers studied the size effects in some problems (Anthoine 2000; Yang et al. 2002; Ma et al. 2008; Asghari et al. 2010; Kumar 2016; Zenkour and Abouelregal 2014; Carrera et al. 2015; Abouelregal and Zenkour 2014, 2015). This paper explains the effect of MCS theory on deflection and temperature of an isotropic thermoelastic microbeam based on Euler–Bernoulli. The vibration of the microbeam subjected to exterior transverse excitation has been researched with regards to theory of thermoelasticity. The effect length scale parameter of the material and the excitation force magnitude and angular frequency of the external excitation have been treated numerically for a nickel micro-beam. 2 The governing equations The basic equations in the MSC theory for a linear ther- moelastic isotropic material in infinitesimal deformation is given by (Yang et al. 2002; Hadjesfandiari and Dargush 2011): & A. E. Abouelregal ahabogal@gmail.com 1 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt 2 Department of Mathematics, College of Science and Arts, Aljouf University, Al-Qurayyat, Saudi Arabia 123 Microsyst Technol DOI 10.1007/s00542-017-3589-0