Hamlehdar M, Kasaeian A, Safaei MR (2019) Energy harvesting from fluid flow using piezoelectrics: a critical review. Renew Energy 143:1826–1838
Liu H, Zhong J, Lee C et al (2018) A comprehensive review on piezoelectric energy harvesting technology: materials, mechanisms, and applications. Appl Phys Rev 5(4):041306
Baz A (2019) Active acoustic metamaterial with tunable effective density using a disturbance rejection controller. J Appl Phys 125(7):074503
Afzal MS, Shim H, Roh Y (2018) Design of a piezoelectric multilayered structure for ultrasound sensors using the equivalent circuit method. Sensors 18:12
Nguyen VT, Kumar P, Leong JYC (2018) Finite element modellingand simulations of piezoelectric actuators responses with uncertainty quantification. Computation 6(4):60
Prasad SAN, Gallas Q, Horowitz S et al (2006) Analytical electroacoustic model of a piezoelectric composite circular plate. AIAA J 44(10):2311–2318
Bakhtiari-Shahri M, Moeenfard H (2019) Optimal design of a stable fuzzy controller for beyond pull-in stabilization of electrostatically actuated circular microplates. J Vib Acoust 141(1):011019.1-011019.9
Wang T, He J, Wang J, et al (2018) Numerical and Experimental Study of Valve-Less Micropump Using Dynamic Multiphysics Model. In: 2018 IEEE 13th annual international conference on nano/micro engineered and molecular systems (NEMS). IEEE, pp 300–303
Shahri MB, Moeenfard H (2019) Energy harvesting from unimorph piezoelectric circular plates under random acoustic and base acceleration excitations. Mech Syst Signal Process 130:502–523
Chen S, Xie X, Kan J et al (2019) A hydraulic-driven piezoelectric pump with separable channel for drug delivery. Sens Actuat A 295:210–216
Hu Y, Liang X, Wang W (2017) Deflection of circular diaphragm-type piezoactuators coupling with gas compression in micropumps. Microsyst Technol 23(12):5329–5341
Yuan TC, Yang J, Chen LQ (2019) Nonlinear vibration analysis of a circular composite plate harvester via harmonic balance. Acta Mech Sin 35(4):912–925
Sahoo SR, Ray MC (2019) Active damping of geometrically nonlinear vibrations of smart composite plates using elliptical SCLD treatment with fractional derivative viscoelastic layer. Eur J Mech A/Solids 78:103823
Sun W, Jo S, Seok J (2019) Development of the optimal bluff body for wind energy harvesting using the synergetic effect of coupled vortex induced vibration and galloping phenomena. Int J Mech Sci 156:435–445
Chong SV, Williams GVM (2019) Magnetoelectric effect in magnetostrictive-piezoelectric composites containing magnetite nanoparticles. Sens Actuat A 288:101–106
Lam DCC, Yang F, Chong ACM et al (2003) Experiments and theory in strain gradient elasticity. J Mech Phys Solids 51(8):1477–1508
Li Z, He Y, Zhang B et al (2019) Experimental investigation and theoretical modelling on nonlinear dynamics of cantilevered microbeams. Eur J Mech A/Solids 78:103834
Akgöz B, Civalek Ö (2013) Buckling analysis of functionally graded microbeams based on the strain gradient theory. Acta Mech 224(9):2185–2201
Toupin R (1962) Elastic materials with couple-stresses. Arch Ration Mech Anal 11(1):385–414
Mindlin RD, Tiersten HF (1962) Effects of couple-stresses in linear elasticity. Arch Ration Mech Anal 11(1):415–448
Yang F, Chong ACM, Lam DCC et al (2002) Couple stress based strain gradient theory for elasticity. Int J Solids Struct 39(10):2731–2743
Hadjesfandiari AR, Dargush GF (2011) Couple stress theory for solids. Int J Solids Struct 48(18):2496–2510
Neff P, Jeong J (2009) A new paradigm: the linear isotropic Cosserat model with conformally invariant curvature energy. ZAMM J Appl Math Mech 89(2):107
Mindlin RD (1964) Micro-structure in linear elasticity. Arch Ration Mech Anal 16(1):51–78
Münch I, Neff P, Madeo A et al (2017) The modified indeterminate couple stress model: why Yang et al.’s arguments motivating a symmetric couple stress tensor contain a gap and why the couple stress tensor may be chosen symmetric nevertheless. ZAMM-J Appl Math Mech 97(12):1524–1554
Neff P, Münch I, Ghiba ID et al (2016) On some fundamental misunderstandings in the indeterminate couple stress model. A comment on recent papers of AR Hadjesfandiari and GF Dargush. Int J Solids Struct 81:233–243
Mindlin RD, Eshel NN (1968) On first strain-gradient theories in linear elasticity. Int J Solids Struct 4(1):109–124
Aifantis EC (1992) On the role of gradients in the localization of deformation and fracture. Int J Eng Sci 30(10):1279–1299
Zhou S, Li A, Wang B (2016) A reformulation of constitutive relations in the strain gradient elasticity theory for isotropic materials. Int J Solids Struct 80:28–37
Polizzotto C (2013) A second strain gradient elasticity theory with second velocity gradient inertia-part I: constitutive equations and quasi-static behavior. Int J Solids Struct 50(24):3749–3765
Zhao B, Liu T, Chen J et al (2019) A new Bernoulli-Euler beam model based on modified gradient elasticity. Arch Appl Mech 89(2):277–289
Fu G, Zhang Z, Fu J et al (2022) On the strain gradient effects on buckling of the partially covered laminated microbeam. Appl Math Model 102:472–491
Yue YM, Xu KY, Tan ZQ et al (2019) The influence of surface stress and surface-induced internal residual stresses on the size-dependent behaviors of Kirchhoff microplate. Arch Appl Mech 89(7):1301–1315
Barretta R, Faghidian SA, De Sciarra FM (2019) Stress-driven nonlocal integral elasticity for axisymmetric nano-plates. Int J Eng Sci 136:38–52
Mohammadi M, Mohseni E, Moeinfar M (2019) Bending, buckling and free vibration analysis of incompressible functionally graded plates using higher order shear and normal deformable plate theory. Appl Math Model 69:47–62
Thai CH, Ferreira AJM, Rabczuk T et al (2018) Size-dependent analysis of FG-CNTRC microplates based on modified strain gradient elasticity theory. Eur J Mech A/Solids 72:521–538
Akgöz B, Civalek Ö (2015) A novel microstructure-dependent shear deformable beam model. Int J Mech Sci 99:10–20
Akgöz B, Civalek Ö (2014) Longitudinal vibration analysis for microbars based on strain gradient elasticity theory. J Vib Control 20(4):606–616
Ebrahimi F, Barati MR, Civalek Ö (2020) Application of Chebyshev-Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures. Eng Comput 36(3):953–964
Farzam A, Hassani B (2019) Size-dependent analysis of FG microplates with temperature-dependent material properties using modified strain gradient theory and isogeometric approach. Compos B Eng 161:150–168
Shahrbabaki EA (2018) On three-dimensional nonlocal elasticity: free vibration of rectangular nanoplate. Eur J Mech A/Solids 71:122–133
Alizadeh M, Fattahi AM (2019) Non-classical plate model for FGMs. Eng Comput 35(1):215–228
Li M, Soares CG, Yan R (2021) Free vibration analysis of FGM plates on Winkler/Pasternak/Kerr foundation by using a simple quasi-3D HSDT. Compos Struct 264:113643
Nguyen HX, Atroshchenko E, Ngo T et al (2019) Vibration of cracked functionally graded microplates by the strain gradient theory and extended isogeometric analysis. Eng Struct 187:251–266
Quintana MV, Raffo JL (2019) A variational approach to vibrations of laminated composite plates with a line hinge. Eur J Mech A/Solids 73:11–21
Thanh CL, Tran LV, Vu-Huu T et al (2019) Size-dependent nonlinear analysis and damping responses of FG-CNTRC micro-plates. Comput Methods Appl Mech Eng 353:253–276
Li A, Ji X, Zhou S et al (2021) Nonlinear axisymmetric bending analysis of strain gradient thin circular plate. Appl Math Model 89:363–380
Zhou YF, Wang ZM (2019) Dynamic instability of axially moving viscoelastic plate. Eur J Mech A/Solids 73:1–10
Akgöz B, Civalek Ö (2015) A microstructure-dependent sinusoidal plate model based on the strain gradient elasticity theory. Acta Mech 226(7):2277–2294
Ullah S, Zhong Y, Zhang J (2019) Analytical buckling solutions of rectangular thin plates by straightforward generalized integral transform method. Int J Mech Sci 152:535–544
Ansari R, FaghihShojaei M, Mohammadi V et al (2014) Size-dependent vibrations of post-buckled functionally graded Mindlin rectangular microplates. Latin Am J Solids Struct 11(13):2351–2378
Zenkour AM, Aljadani MH (2019) Porosity effect on thermal buckling behavior of actuated functionally graded piezoelectric nanoplates. Eur J Mech A/Solids 78:103835
Tenenbaum J, Deutsch A, Eisenberger M (2019) Analytical buckling loads for corner supported rectangular orthotropic and symmetrically laminated plates. ZAMM-J Appl Math Mech 99(11):e201900142
Arefi M, Kiani M, Rabczuk T (2019) Application of nonlocal strain gradient theory to size dependent bending analysis of a sandwich porous nanoplate integrated with piezomagnetic face-sheets. Compos B Eng 168:320–333
Chen W, Wang Y (2016) A model of composite laminated Reddy plate of the global-local theory based on new modified couple-stress theory. Mech Adv Mater Struct 23(6):636–651
Ghorbanpour Arani A, Zamani MH (2019) Investigation of electric field effect on size-dependent bending analysis of functionally graded porous shear and normal deformable sandwich nanoplate on silica Aerogel foundation. J Sandwich Struct Mater 21(8):2700–2734
Gao F, Sun W (2019) Nonlinear finite element modeling and vibration analysis of the blisk deposited strain-dependent hard coating. Mech Syst Signal Process 121:124–143
Mohammadimehr M, Emdadi M, Afshari H et al (2018) Bending, buckling and vibration analyses of MSGT microcomposite circular-annular sandwich plate under hydro-thermo-magneto-mechanical loadings using DQM. Int J Smart Nano Mater 9(4):233–260
Basak S, Raman A, Garimella SV (2005) Dynamic response optimization of piezoelectrically excited thin resonant beams. J Vib Acoust 127(1):18–27
Morris CJ, Forster FK (2000) Optimization of a circular piezoelectric bimorph for a micropump driver. J Micromech Microeng 10(3):459
Zhang J, Zhao Q, Ullah S et al (2021) A new analytical solution of vibration response of orthotropic composite plates with two adjacent edges rotationally-restrained and the others free. Compos Struct 2021:113882
Nguyen NV, Lee J, Nguyen-Xuan H (2019) Active vibration control of GPLs-reinforced FG metal foam plates with piezoelectric sensor and actuator layers. Compos B Eng 172:769–784
Roque CMC, Grasa J (2021) Geometrically nonlinear analysis of laminated composite plates using RBF-PS meshless method. Compos Struct 2021:113830
Zuo W, Li P, Du J et al (2019) Thermoelastic damping in trilayered microplate resonators. Int J Mech Sci 151:595–608
Nematollahi MS, Mohammadi H (2019) Geometrically nonlinear vibration analysis of sandwich nanoplates based on higher-order nonlocal strain gradient theory. Int J Mech Sci 156:31–45
Shiva K, Raghu P, Rajagopal A et al (2019) Nonlocal buckling analysis of laminated composite plates considering surface stress effects. Compos Struct 226:111216
Mondal S, Ramachandra LS (2019) Stability and failure analyses of delaminated composite plates subjected to localized heating. Compos Struct 209:258–267
Magnucki K, Witkowski D, Magnucka-Blandzi E (2019) Buckling and free vibrations of rectangular plates with symmetrically varying mechanical properties-Analytical and FEM studies. Compos Struct 220:355–361
Arefi M, Bidgoli EMR, Rabczuk T (2019) Effect of various characteristics of graphene nanoplatelets on thermal buckling behavior of FGRC micro plate based on MCST. Eur J Mech A/Solids 77:103802
Fu G, Zhou S, Qi L (2019) The size-dependent static bending of a partially covered laminated microbeam. Int J Mech Sci 152:411–419
Ji X, Li A, Zhou S (2017) A comparison of strain gradient theories with applications to the functionally graded circular micro-plate. Appl Math Model 49:124–143
Yang Y, Li XF (2019) Bending and free vibration of a circular magnetoelectroelastic plate with surface effects. Int J Mech Sci 157:858–871
Ansari R, Gholami R, Shojaei MF et al (2015) Bending, buckling and free vibration analysis of size-dependent functionally graded circular/annular microplates based on the modified strain gradient elasticity theory. Eur J Mech A/Solids 49:251–267
Wang S, Kan J, Wang B et al (2013) Modeling and simulation of a piezodisc generator under central load. Int J Appl Electromagnet Mech 41(4):349–360