The size effect on the free vibration and bending of a curved FG micro/nanobeam is studied in this paper. Using the Hamilton principle the differential equations and boundary conditions is derived for a nonlocal Euler-Bernoulli curved micro/nanobeam.  The material properties vary through radius direction. Using the Navier approach an analytical solution for simply supported boundary conditions is obtained where the power index law of FGM, the curved micro/nanobeam opening angle, the effect of aspect ratio and nonlocal parameter on natural frequencies and the radial and tangential displacements were analyzed. It is concluded that increasing the curved micro/nanobeam opening angle results in decreasing and increasing the frequencies and displacements, respectively. To validate the natural frequencies of curved nanobeam, when the radius of it approaches to infinity, is compared with a straight FG nanobeam and showed a good agreement.

Analyzing ecosystem service values (ESV) is crucial for achieving sustainable development. The main objective of this study was to assess the ecosystem services of the Cisadane watershed in Indonesia, with specific goals: (i) examining the spatiotemporal dynamics of ESV using multi-year land use and land cover (LULC) data from 2000 to 2021, (ii) exploring trade-offs and synergies among various ecosystem services, and (iii) investigating the sensitivity of ESV to changes in LULC. The results unveiled a significant decrease in forested areas (21.2%) and rice fields (10.2%), leading to a decline in ESV of $196.37 billion (33.17%) from 2010 to 2021. Throughout the period from 2000 to 2021, interactions between ESV were mainly synergistic. Projected from the baseline year (2021), the decline in ESV is expected to persist, ranging from $24.78 billion to $124.28 million by 2030 and from $45.78 billion to $124.28 million by 2050. The total estimated ecosystem values exhibited an inelastic response in terms of ecosystem value coefficients. The study also emphasizes an inelastic response in total estimated ESV coefficient concerning ecosystem value coefficients. These findings underscore the urgent need for targeted conservation efforts and sustainable land management practices to mitigate the further decline in ecosystem services and safeguard the long-term well-being of the Cisadane watershed and its inhabitants.

The present research is on the propagation of Rayleigh waves in a homogenous thermoelastic solid half-space by considering the compact form of six different theories of thermoelasticity. The medium is subjected to an insulated boundary surface that is free from normal stress, tangential stress, and a temperature gradient normal to the surface. After developing a mathematical model, a dispersion equation is obtained with irrational terms. To apply the algebraic method, this equation must be converted into a rational polynomial equation. From this, only those roots are filtered out, which has satisfied both of the above equations for the propagation of waves decaying with depth. With the help of these roots, different characteristics are computed numerically, like phase velocity, attenuation coefficient, and path of particles. Various particular cases are compared graphically by using phase velocity and attenuation coefficient. The elliptic path of surface particles in Rayleigh wave propagation is also presented for the different theories using physical constants of copper material for different depths and thermal conductivity.

The study examines the impact of various theories on the reflection and transmission phenomena caused by obliquely incident longitudinal and transverse waves at the interface between a continuously elastic solid half-space and a thermoelastic half-space, using multiple thermoelastic models. Numerical calculations reveal that the thermoelastic medium supports one transmitted transverse wave and two transmitted longitudinal waves. The modulus of amplitude proportions is analyzed as a function of the angle of incidence, showing distinct variations across the studied models. Energy ratios, derived from wave amplitudes under consistent surface boundary conditions for copper, are computed and compared across angles of incidence. The results demonstrate that the total energy ratio consistently sums to one, validating energy conservation principles. Graphical comparisons of amplitude proportions and energy ratios for SV and P waves across different models illustrate significant differences in wave behavior, emphasizing the influence of thermoelastic properties on wave transmission and reflection.