Executive Summary : | Small-scale structures are utilized increasingly as electrochemical devices, field emission devices, sensors, and probes. These high-precision applications take advantage of the exceptional characteristics of microstructures, such as their high fundamental frequency, ultralow power consumption, great force and displacement sensitivity, and huge quality factors. Parametric excitations are used by parametric bandwidth filters to filter frequencies. A parametric oscillator uses parametric resonance for mass sensing and parametric amplification. The cantilevers of the Atomic Force Microscope are designed in such a way that, stress-concentrated regions are developed, to increase the sensitivity of the piezo resistors. Organic solar cells operate in complicated environments withstanding temperature loads. The MEMS/NEMS devices are subjected to electrical, magnetic, thermal, and mechanical loadings based on their application in real-life situations. Thus, precise knowledge of these structures' resonance frequency, nonlinear stability, and responses under various loading conditions become crucial. However, these structures cannot be studied with classical continuum mechanics since their behavior deviates from that of macro-/nano structures as a result of the amplification of small-scale effects. It is possible to do analysis using experimentation and molecular dynamics (MD), although doing so is time-consuming and costly. In this context, the non-classical continuum theories can be used to capture the small-scale effects. In this project, the sem-analytical methodology will be developed utilizing non-classical continuum theories for the studying of non-linear static, and dynamic behaviour of small-scale (micro/nano) structures (plates and shell panels) under localized thermal and mechanical loadings. The small-scale effects of the small-scale structures will be incorporated by using the nonlocal strain gradient theory. In this theory, both the material length scale and nonlocal parameters are calibrated using MD simulations by comparing natural frequencies of small-scale structures. Due to the localized loadings, the analytical expressions of in-plane stresses within the small-scale structures will be derived by solving the elasticity problems. Using both analytical expressions of in-plane stresses and a developed semi-analytical methodology, the non-linear stability, vibration, and responses of the small-scale structure will be investigated. |