Analytical Solution for Vibrations of a Modified Timoshenko Beam on Visco-Pasternak Foundation Under Arbitrary Excitations

An analytical solution is derived for dynamic response of a modified Timoshenko beam with an infinite length resting on visco-Pasternak foundation subjected to arbitrary excitations. The modified Timoshenko beam model is employed to further consider the rotary inertia caused by the shear deformation of a beam, which is usually neglected by the traditional Timoshenko beam model. By using Fourier and Laplace transforms, the governing equations of motion are transformed from partial differential forms into algebraic forms in the Laplace domain. The analytical solution is then converted into the time domain by applying inverse transforms and convolution theorem. Some widely used loading cases, including moving line loads for nondestructive testing, travelling loads for seismic wave passage, and impulsive load for impact vibration, are also discussed in this paper. The proposed generic solutions are verified by comparing their degraded results to the known solutions in other literature. Several examples are performed to further investigate the differences of the beam responses obtained from the modified and the traditional Timoshenko beam models. Results show that the modified Timoshenko beam simulates the beam responses more accurately than the traditional model, especially under the dynamic loads with a high frequency. The analytical solutions proposed in this paper can be conveniently used for design and applied as an effective tool for practitioners.

Design and Analysis of Road Load Detection Machine Based on Computer Technology

In this paper, an experimental device is designed for measuring vehicle dynamic load, the structure and stress of the equipment are analyzed by computer technology. The device design mainly includes vehicle, road surface, vehicle transmission, and control [1]. The vehicle is designed based on a 2-DOF vehicle model, the road is designed based on the Pasternak foundation model, and the control mainly uses a single-chip microcomputer. The dynamic response of vehicles to the road at different speeds is analyzed through the experiment [2].

Wrinkle Formation and Initial Defect Sensitivity of Steered Tow in Automated Fiber Placement

This paper aims to study the wrinkle formation of a prepreg with initial defect during steering in automated fiber placement (AFP). Wrinkle formation has a detrimental effect on the mechanical properties of the final product, limiting the AFP applications. A theoretical model for wrinkle formation has been developed in which a Pasternak foundation and a Koiter imperfection model are adapted to model viscoelastic characteristics of the prepreg tack and initial defect of the prepreg, respectively. The initial defect is defined as a slight deviation of the tow’s mid-plane from a horizontal shape. The initial defect is generated in the tow by moving the tow through the guidance system, pressure of the roller, and resin tackiness. Galerkin method, along with the finite difference method (FDM), are employed to solve the wrinkle problem equation. The proposed method is able to satisfy the different boundary conditions for the wrinkle problem completely. The numerical results show that increasing the initial defect leads to a decrease in critical load and an increase in critical steering radius. To validate the theoretical model, experimental results are presented and compared with model-predicted results. It is shown that the model is well able to capture the trends and values of wrinkle formation wavelengths obtained from the experiment.

Free vibration analysis on axially graded beam resting on variable Pasternak foundation

Free vibration analysis is conducted on axially functionally graded Euler-Bernoulli beam resting on variable Pasternak foundation. The material properties of the beam and the stiffness of the foundation are considered to be varying linearly along the axial direction. Two types of boundary conditions namely; clamped and simply supported are used in the analysis. The problem is formulated using Rayleigh-Ritz method and governing equations are derived with the help of Hamilton’s principle. The numerical results are generated for different material gradation parameter, foundation parameter and boundary conditions and the effect of these parameters on the free vibration behaviour of the beam is discussed.

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.