scholarly journals Vibrations of a Slightly Curved Microbeam Resting on an Elastic Foundation with Nonideal Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Gözde Sarı ◽  
Mehmet Pakdemirli
Keyword(s):  
Boundary Conditions ◽  
Frequency Response ◽  
Elastic Foundation ◽  
Axial Load ◽  
Multiple Scales ◽  
Mode Shapes ◽  
Nonlinear Frequency ◽  
Nonlinear Elastic Foundation ◽  
Curved Microbeam ◽  
Nonlinear Elastic

An investigation into the dynamic behavior of a slightly curved resonant microbeam having nonideal boundary conditions is presented. The model accounts for midplane stretching, an applied axial load, and a small AC harmonic force. The ends of the curved microbeam are on immovable simple supports and the microbeam is resting on a nonlinear elastic foundation. The forced vibration response of curved microbeam due to the small AC load is obtained analytically by means of direct application of the method of multiple scales (a perturbation method). The effects of the nonlinear elastic foundation as well as the effect of curvature on the vibrations of the microbeam are examined. It is found that the effect of curvature is of softening type. For sufficiently high values of the coefficients, the elastic foundation and the axial load may suppress the softening behavior resulting in hardening behavior of the nonlinearity. The frequencies and mode shapes obtained are compared with the ideal boundary conditions case and the differences between them are contrasted on frequency-response curves. The frequency response and nonlinear frequency curves obtained may provide a reference for the choice of reasonable resonant conditions, design, and industrial applications of such systems. Results may be beneficial for future experimental and theoretical works on MEMS.

Effects of Tuned Mass Damper on Fixed-Fixed 3D Nonlinear String Resting on Nonlinear Elastic Foundation

2017 ◽  
Vol 17 (04) ◽  
pp. 1750047 ◽  
Author(s):  
Yi-Ren Wang ◽  
Li-Ping Wu
Keyword(s):  
Elastic Foundation ◽  
Internal Resonance ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Maximum Amplitude ◽  
Tuned Mass Damper ◽  
Mode Shapes ◽  
Nonlinear Elastic Foundation ◽  
Mass Damper ◽  
Nonlinear Elastic

This paper studies the vibration of a nonlinear 3D-string fixed at both ends and supported by a nonlinear elastic foundation. Newton’s second law is adopted to derive the equations of motion for the string resting on an elastic foundation. Then, the method of multiple scales (MOMS) is employed for the analysis of the nonlinear system. It was found that 1:3 internal resonance exists in the first and fourth modes of the string when the wave speed in the transverse direction is [Formula: see text] and the elasticity coefficient of the foundation is [Formula: see text]. Fixed point plots are used to obtain the frequency responses of the various modes and to identify internal resonance through observation of the amplitudes and mode shapes. To prevent internal resonance and reduce vibration, a tuned mass damper (TMD) is applied to the string. The effects of various TMD masses, locations, damper coefficients ([Formula: see text]), and spring constants ([Formula: see text]) on overall damping were analyzed. The 3D plots of the maximum amplitude (3D POMAs) and 3D maximum amplitude contour plots (3D MACPs) are generated for the various modes to illustrate the amplitudes of the string, while identifying the optimal TMD parameters for vibration reduction. The results were verified numerically. It was concluded that better damping effects can be achieved using a TMD mass ratio [Formula: see text]–0.5 located near the middle of the string. Furthermore, for damper coefficient [Formula: see text], the use of spring constant [Formula: see text]–13 can improve the overall damping.

scholarly journals Vibration Analysis of Magneto-Electro-Thermo NanoBeam Resting on Nonlinear Elastic Foundation Using Sinc and Discrete Singular Convolution Differential Quadrature Method

2019 ◽  
Vol 13 (7) ◽  
pp. 49 ◽  
Author(s):  
Ola Ragb ◽  
Mokhtar Mohamed ◽  
M.S. Matbuly
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Differential Quadrature Method ◽  
Nonlocal Parameter ◽  
Differential Quadrature ◽  
Mode Shapes ◽  
Electric Voltage ◽  
Nonlinear Elastic Foundation ◽  
Axial Forces ◽  
Nonlinear Elastic

Magneto-Electro-Thermo nanobeam resting on a nonlinear elastic foundation is presented. This beam is subjected to the external electric voltage and magnetic potential, mechanical potential and temperature change. Also, we added the new material PTZ-5H-COFe2O4. The governing equations and boundary conditions are derived using Hamilton principle. These equations are discretized by using three differential quadrature methods and iterative quadrature technique to determine the natural frequencies and mode shapes. Numerical analysis is introduced to explain the influence of computational characteristics of the proposed schemes on convergence, accuracy and efficiency of the obtained results. The obtained results agreed with the previous analytical and numerical ones. A detailed parametric study is conducted to investigate the influences of different boundary conditions, various composite materials, nonlinear elastic foundation, nonlocal parameter, the length-to-thickness ratio, external electric and magnetic potentials, axial forces, temperature and their effects on the vibration characteristics of Magneto-Electro-Thermo-Elastic nanobeam.

scholarly journals Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect

Nanomaterials ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 3066
Author(s):  
Amin Alibakhshi ◽  
Shahriar Dastjerdi ◽  
Mohammad Malikan ◽  
Victor A. Eremeyev
Keyword(s):  
Size Effect ◽  
Boundary Conditions ◽  
Frequency Response ◽  
Multiple Scales ◽  
Forced Vibrations ◽  
Response Force ◽  
Nonlinear Frequency ◽  
Large Rotation ◽  
Free And Forced Vibrations ◽  
Stiffening Effect

In recent years, the static and dynamic response of micro/nanobeams made of hyperelasticity materials received great attention. In the majority of studies in this area, the strain-stiffing effect that plays a major role in many hyperelastic materials has not been investigated deeply. Moreover, the influence of the size effect and large rotation for such a beam that is important for the large deformation was not addressed. This paper attempts to explore the free and forced vibrations of a micro/nanobeam made of a hyperelastic material incorporating strain-stiffening, size effect, and moderate rotation. The beam is modelled based on the Euler–Bernoulli beam theory, and strains are obtained via an extended von Kármán theory. Boundary conditions and governing equations are derived by way of Hamilton’s principle. The multiple scales method is applied to obtain the frequency response equation, and Hamilton’s technique is utilized to obtain the free undamped nonlinear frequency. The influence of important system parameters such as the stiffening parameter, damping coefficient, length of the beam, length-scale parameter, and forcing amplitude on the frequency response, force response, and nonlinear frequency is analyzed. Results show that the hyperelastic microbeam shows a nonlinear hardening behavior, which this type of nonlinearity gets stronger by increasing the strain-stiffening effect. Conversely, as the strain-stiffening effect is decreased, the nonlinear frequency is decreased accordingly. The evidence from this study suggests that incorporating strain-stiffening in hyperelastic beams could improve their vibrational performance. The model proposed in this paper is mathematically simple and can be utilized for other kinds of micro/nanobeams with different boundary conditions.

Nonlinear Vibrations of Rectangular Mooney-Rivlin Membrane Resting on a Nonlinear Elastic Foundation

2014 ◽  
Author(s):  
Renata M. Soares ◽  
Paulo B. Gonçalves
Keyword(s):  
Elastic Foundation ◽  
Nonlinear Oscillations ◽  
Equations Of Motion ◽  
Incompressible Material ◽  
Mode Shapes ◽  
Element Formulation ◽  
Nonlinear Elastic Foundation ◽  
The Galerkin Method ◽  
Nonlinear Elastic ◽  
Foundation Parameters

The aim of the present work is to investigate the nonlinear vibration response of a pre-stretched rectangular hyperelastic membrane resting on a nonlinear elastic foundation. The membrane is composed of an isotropic, homogeneous and hyperelastic material, which is modeled as a Mooney-Rivlin incompressible material. The elastic foundation is described by a Winkler type nonlinear model with cubic nonlinearity. First the exact solution of the membrane under a biaxial stretch is obtained. Then the equations of motion of the pre-stretched membrane resting on the nonlinear foundation are derived. From the linearized equations, the natural frequencies and mode shapes of the membrane are obtained analytically. Then the natural modes are used to approximate the nonlinear deformation field using the Galerkin method. The results compare well with the results evaluated for the same membrane using a nonlinear finite element formulation. The results show the strong influence of the initial stretching ratio and foundation parameters on the linear and nonlinear oscillations and stability of the membrane.

Extremely large oscillation and nonlinear frequency of a multi-scale hybrid disk resting on nonlinear elastic foundation

2020 ◽  
Vol 154 ◽  
pp. 106840 ◽  
Author(s):  
Ali Shariati ◽  
Aria Ghabussi ◽  
Mostafa Habibi ◽  
Hamed Safarpour ◽  
Mehran Safarpour ◽  
...  
Keyword(s):  
Elastic Foundation ◽  
Nonlinear Frequency ◽  
Multi Scale ◽  
Large Oscillation ◽  
Nonlinear Elastic Foundation ◽  
Nonlinear Elastic

Study of plate vibrating in fluids having part-through crack at random angles and locations

2021 ◽  
pp. 095440622110127
Author(s):  
Ruqia Ikram ◽  
Asif Israr
Keyword(s):  
Frequency Response ◽  
Multiple Scales ◽  
Peak Amplitude ◽  
Nonlinear Frequency ◽  
Response Curves ◽  
Crack Location ◽  
Cracked Plate ◽  
Nonlinear Frequency Response ◽  
Angle Crack ◽  
Crack Angle

This study presents the vibration characteristics of plate with part-through crack at random angles and locations in fluid. An experimental setup was designed and a series of tests were performed for plates submerged in fluid having cracks at selected angles and locations. However, it was not possible to study these characteristics for all possible crack angles and crack locations throughout the plate dimensions at any fluid level. Therefore, an analytical study is also carried out for plate having horizontal cracks submerged in fluid by adding the influence of crack angle and crack location. The effect of crack angle is incorporated into plate equation by adding bending and twisting moments, and in-plane forces that are applied due to antisymmetric loading, while the influence of crack location is also added in terms of compliance coefficients. Galerkin’s method is applied to get time dependent modal coordinate system. The method of multiple scales is used to find the frequency response and peak amplitude of submerged cracked plate. The analytical model is validated from literature for the horizontally cracked plate submerged in fluid as according to the best of the authors’ knowledge, literature lacks in results for plate with crack at random angle and location in the presence of fluid following validation with experimental results. The combined effect of crack angle, crack location and fluid on the natural frequencies and peak amplitude are investigated in detail. Phenomenon of bending hardening or softening is also observed for different boundary conditions using nonlinear frequency response curves.

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