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.

Assessment of Hybrid Method on Investigation of Dynamic Behaviour of Isotropic Rectangular Plates Resting on Two-Parameters Foundation

Dynamic behaviour of isotropic rectangular plate resting on two-parameter foundation is investigated. The governing partial differential equation is transformed to ordinary differential equation due to Galerkin method of separation. The hybrid method of Laplace transform and variation parameters method is used to analyze the ordinary differential equation. Introduction of exact method helps in fast convergence of the results. Obtained analytical solutions are compared with existing literature and confirmed as accurate. They are used to examine the effect of controlling parameters on the plate natural frequencies. Due to obtained results it is obvious that, the increase of both elastic foundation parameter and aspect ratio results in increasing the natural frequency. The solution is found immediately by means of a few iterations

Buckling and Free Vibration of a Single Pile Considering the Effect of Soil–Structure Interaction

The buckling response and free vibration characteristics of a single pile in the elastic foundation are investigated. Considering the effect of soil–structure interaction and geometric nonlinearity, the nonlinear equation of motion for a single pile is derived by Hamilton’s principle. Then, closed-form solutions of the critical load and buckled configuration of the pile are obtained analytically, and the natural frequencies of the pre- and post-buckling pile are examined. Finally, the effect of elastic foundation parameter on the critical load of the pile is discussed, and the effect of axial load on the natural frequencies of the pile is also explored. Numerical results show that the effect of elastic foundation parameter plays a dominant role on the critical load and buckled configuration of the pile, and the shear parameter affects the critical load directly. The axial load effect on the dynamic characteristics of the pre-buckling pile is significant, meanwhile, it may contribute very small to the post-buckling pile when the axial load exceeds some specific values.

Vibration Analysis of Bilayered Graphene Sheets for Building Materials in Thermal Environments Based on the Element-Free Method

Graphene sheets are widely applied due to their unique and highly valuable properties, such as energy conservation materials in buildings. In this paper, we investigate the vibration behavior of double layer graphene sheets (DLGSs) in thermal environments which helps probe into the mechanism of energy conservation of graphene sheets in building materials. The nonlocal elastic theory and classical plate theory (CLPT) are used to derive the governing equations. The element-free method is employed to analyze the vibration behaviors of DLGSs embedded in an elastic medium. The accuracy of the solutions in this study is demonstrated by comparison with published results in the literature. Furthermore, a number of numerical results are presented to investigate the effects of various parameters (boundary conditions, nonlocal parameter, aspect ratio, side length, elastic foundation parameter, and temperature) on the frequency of DLGSs.

Forced Response of Polar Orthotropic Tapered Circular Plates Resting on Elastic Foundation

Forced axisymmetric response of polar orthotropic circular plates of linearly varying thickness resting on Winkler type of elastic foundation has been studied on the basis of classical plate theory. An approximate solution of problem has been obtained by Rayleigh Ritz method, which employs functions based upon the static deflection of polar orthotropic circular plates. The effect of transverse loadings has been studied for orthotropic circular plate resting on elastic foundation. The transverse deflections and bending moments are presented for various values of taper parameter, rigidity ratio, foundation parameter, and flexibility parameter under different types of loadings. A comparison of results with those available in literature shows an excellent agreement.

Dynamics of a beam-column element on an elastic foundation

An exact analytical solution of a harmonically vibrating beam-column element resting on an elastic Winkler foundation is derived. The solution covers four cases comprised of constant compressive or tensile axial force with the restrictions ks – mω2 < 0 and ks – mω2 > 0. The proposed solution is not restricted to a particular range of magnitudes of the foundation parameter. Closed form solutions of dynamic shape functions are explicitly derived for each sub-case to obtain frequency-dependent dynamic stiffness terms that constitute the exact dynamic stiffness matrices. Four numerical examples are provided to demonstrate the merits of the present study.

Vibrations And Stability Of Bernoulli-Euler And Timoshenko Beams On Two-Parameter Elastic Foundation

The vibration and stability analysis of uniform beams supported on two-parameter elastic foundation are performed. The second foundation parameter is a function of the total rotation of the beam. The effects of axial force, foundation stiffness parameters, transverse shear deformation and rotatory inertia are incorporated into the accurate vibration analysis. The work shows very important question of relationships between the parameters describing the beam vibration, the compressive force and the foundation parameters. For the free supported beam, the exact formulas for the natural vibration frequencies, the critical forces and the formula defining the relationship between the vibration frequency and the compressive forces are derived. For other conditions of the beam support conditional equations were received. These equations determine the dependence of the frequency of vibration of the compressive force for the assumed parameters of elastic foundation and the slenderness of the beam.