A Quasi-3D Higher-Order Theory for Bending of FG Nanoplates Embedded in an Elastic Medium in a Thermal Environment

This paper presents the effects of temperature and the nonlocal coefficient on the bending response of functionally graded (FG) nanoplates embedded in an elastic foundation in a thermal environment. The effects of transverse normal strain, as well as transverse shear strains, are considered where the variation of the material properties of the FG nanoplate are considered only in thickness direction. Unlike other shear and deformations theories in which the number of unknown functions is five and more, the present work uses shear and deformations theory with only four unknown functions. The four-unknown normal and shear deformations model, associated with Eringen nonlocal elasticity theory, is used to derive the equations of equilibrium utilizing the principle of virtual displacements. The effects due to nonlocal coefficient, side-to-thickness ratio, aspect ratio, normal and shear deformations, thermal load and elastic foundation parameters, as well as the gradation in FG nanoplate bending, are investigated. In addition, for validation, the results obtained from the present work are compared to ones available in the literature.

Active control of a sandwich plate with reinforced magnetostrictive faces and viscoelastic core, resting on elastic foundation

The current study presents a vibration investigation of a laminated plate considering a viscoelastic core with embedded magnetostrictive layers. The simply-supported plate is supported via Pasternak’s substrate medium. Based on different plate theories and employing Hamilton’s principle, the system of governing differential equations is derived. The mechanical properties of the viscoelastic core are described depend on the time varies based on Kelvin–Voigt model. Actuating magnetostrictive layers are utilized to control the vibration damping process of the system with the assistance of feedback and constant gain distributed control. The analytical solution is obtained to investigate the influence of half wave numbers, thickness ratios, core thickness, aspect ratios, lamination schemes, elastic foundation parameters, damping coefficient, feedback coefficient magnitude, magnetostrictive layers location, on the vibrational behavior of laminated plate. Some observations about the vibration damping process of the present plate are displayed. The results refer to that the vibration suppression rate depends on the thickness of the plate, the feedback control value, the foundation constants, and the viscoelastic structural damping significantly. Moreover, the study can be providing benchmark tests to validate future contributions on the viscoelastic smart structural issues and developing the design of smart viscoelastic structures and control of their vibrations.

STABILITAS PELAT ORTHOTROPIK AKIBAT BEBAN LEDAKAN FRIEDLANDER DAN BEBAN IN-PLANE

Slab behavior due to static and dynamic load needs to be considered when designing a slab. Friedlander is one of the examples of dynamic loads. This dynamic load can give different responses on slab. This research discusses about orthotropic plate on Pasternak foundation with fixed boundary condition and in-plane and Friedlander load. Three phases on Friedlander load are positive phase, negative phase, and free vibration phase. This research is conducted to find out critical buckling load due to variation of Pasternak foundation parameters which is spring coefficient and shear coefficient. The system responses are deflection and bending moment due to variation of Pasternak foundation parameter, critical loading, position of loads, depth of soil, and duration of positive phase. Analysis is carried out using Modified Bolotin Method to obtain natural frequencies and mode shape of the system. Result of this research are displayed in graphics and tables. Based on the results, the maximum limit of the critical compressive load is 77% of the critical load used. The increasing of soil coefficient, the greater the deflection that occurs. The position of the load that is close to the center of the span will make the deflection even greater. The deflection that occurs is greater when the depth of the soil increases and the duration of the blast load is getting longer. The greater the thickness of the plate, the smaller the deflection. Keywords : Modified Bolotin Method, Friedlander blast load, plate deflection, critical load, Pasternak FoundationAbstrakPerilaku pelat akibat adanya beban statik dan beban dinamik perlu menjadi pertimbangan pada saat mendesain pelat. Salah satu contoh beban dinamik adalah beban ledakan setempat (Friedlander). Beban dinamik dapat memberikan respon yang beragam pada pelat. Penelitian ini membahas mengenai pelat orthotropik di atas pondasi Pasternak dengan kondisi jepit dengan beban in-plane dan beban ledakan setempat (Friedlander). Beban ledakan setempat (Friedlander) dianalisis dalam tiga fase yaitu fase positif, fase negatif, dan fase getaran bebas. Penelitian dilakukan untuk mengetahui beban tekuk kritis akibat variasi koefisien pondasi Pasternak yaitu koefisien pegas dan koefisien geser. Respons sistem yang diamati adalah lendutan dan momen yang dihasilkan akibat adanya variasi terhadap parameter pondasi Pasternak, besaran beban kritis, posisi beban, kedalaman tanah, dan durasi fase positif beban. Analisis dilakukan dengan Modified Bolotin Method untuk mendapatkan frekuensi alami dan ragam getar yang terjadi. Hasil analisis akan dibandingkan dalam bentuk grafik dan tabel. Berdasarkan hasil penelitian, batas maksimum beban tekan kritis adalah 77% dari beban kritis yang digunakan. Koefisien tanah yang semakin besar akan membuat lendutan yang terjadi semakin besar. Posisi beban yang mendekati tengah bentang akan membuat lendutan semakin besar. Lendutan yang terjadi semakin besar apabila kedalaman tanah semakin meningkat dan durasi beban ledakan yang semakin lama. Apabila semakin besar tebal pelat maka lendutan yang terjadi semakin kecil.

Photothermoelastic Interactions in Silicon Microbeams Resting on Linear Pasternak Foundation Based on DPL Model

In this work, the photothermal interactions in semiconductor microbeams during the photo-thermo-elastic process have been investigated using the generalized photothermal theory. The proposed mathematical model is constructed based on the Euler–Bernoulli model, the heat equation with two-phase lag and coupled plasma wave equation that indicates the prediction of thermal, elastic and photovoltaic effects in the microbeam resonators. Based on the introduced model, the dynamic influence of thermoelastic photovoltaic microbeam resting on an elastic foundation medium with two parameters has been studied. The Winkler foundation parameter is one of these parameters while the second is the shear foundation parameter. In the field of Laplace transform, the governing equations have been solved while the inverse transforms are found numerically using a tried-and-true approximation technique based on Fourier transform series. The numerical calculations of thermophysical field variables have been discussed and graphically presented. The effects of the magnetic field, Winkler and shear foundation parameters, and lifetime of photogenerated electron have been investigated and studied in detail. Comparisons have been made between the proposed model and previous models that have been derived as special cases from the presented results.

Perturbation Method for Thermal Post-buckling Analysis of Shear Deformable FG-CNTRC Beams with Different Boundary Conditions

This research aims to analyze the thermal buckling and post-buckling of carbon nanotube (CNT) reinforced composite beams. It is assumed that the beam is rested on a nonlinear elastic foundation which contains the Winkler spring, shear layer, and nonlinear spring. Distribution of CNTs across the thickness may be non-uniform which results in a functionally graded media. The elastic properties of the beam are evaluated using the refined rule of mixtures which contains efficiency parameters. Temperature dependency of the constituents is also taken into account. Using three different beam models, namely, first-order, third-order, and sinusoidal theories, the governing equations for the composite beam are established. Three different types of edge supports are considered which are pinned–pinned, clamped–clamped, and clamped–roller. With the aid of the two-step perturbation technique, closed-form expressions are extracted to obtain the elevated temperature as a function of the post-buckling deflection in the beam. Results of this study are compared with the available data in the literature. After that, new results are given to discuss the effects of important factors such as foundation parameters, geometrical characteristics, boundary conditions, the CNT volume fraction, and CNT pattern. It is shown that the critical buckling temperature of pinned–pinned and clamped–roller beams is the same while their post-buckling responses are totally different.

Fundamental frequencies of bidirectional functionally graded sandwich beams partially supported by foundation using different beam theories

Investigation on the influence of beam theory and partial foundation support on natural frequencies play an important role in design of structures. In this paper, fundamental frequencies of a bidirectional functionally graded sandwich (BFGSW) beam partially supported by an elastic foundation are evaluated using various beam theories. The core of the sandwich beam is homogeneous while its two face sheets are made from three distinct materials with material properties varying in both the length and thickness directions by power gradation laws. The finite element method is employed to derive equation of motion and to compute the frequencies of the beam. The effects of the material gradation, the foundation parameters and the span to height ratio on the frequencies are studied in detail and highlighted. The difference of the frequencies obtained by different beam theories is also examined and discussed. The numerical results of the paper are useful in designing BFGSW beams with desired fundamantal frequencies.

A New Sinusoidal Shear Deformation Theory for Static Bending Analysis of Functionally Graded Plates Resting on Winkler–Pasternak Foundations

In this article, a new sinusoidal shear deformation theory was developed for static bending analysis of functionally graded plates resting on elastic foundations. The proposed theory used an undefined integral term to reduce the number of the unknown to four without any shear correction factors. The high accuracy and efficiency of the proposed theory were proved thanks to the comparisons of the present results with other available solutions. And then, the proposed theory was successfully applied to investigate the bending behavior of the functionally graded plates resting on Winkler–Pasternak foundations. The governing equations of motion were established by using Hamilton’s principle, and the Navier’s solution technique was employed to solve these equations. The effects of some factors of the geometrics, the materials properties, and the elastic foundation parameters on the bending behaviors of the FGM plates were investigated intensely. Also, some novel results and special phenomenon were carried out.

Vibration Analysis of Piezoelectric Composite Plate Resting on Nonlinear Elastic Foundations Using Sinc and Discrete Singular Convolution Differential Quadrature Techniques

In this work, free vibration of the piezoelectric composite plate resting on nonlinear elastic foundations is examined. The three-dimensionality of elasticity theory and piezoelectricity is used to derive the governing equation of motion. By implementing two differential quadrature schemes and applying different boundary conditions, the problem is converted to a nonlinear eigenvalue problem. The perturbation method and iterative quadrature formula are used to solve the obtained equation. Numerical analysis of the proposed schemes is introduced to demonstrate the accuracy and efficiency of the obtained results. The obtained results are compared with available results in the literature, showing excellent agreement. Additionally, the proposed schemes have higher efficiency than previous schemes. Furthermore, a parametric study is introduced to investigate the effect of elastic foundation parameters, different materials of sensors and actuators, and elastic and geometric characteristics of the composite plate on the natural frequencies and mode shapes.