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.

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.

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.

A Domain Decomposition Method for Vibration Analysis of Conical Shells With Uniform and Stepped Thickness

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
Yegao Qu ◽  
Yong Chen ◽  
Yifan Chen ◽  
Xinhua Long ◽  
Hongxing Hua ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Forced Vibrations ◽  
Uniform Thickness ◽  
Weighted Residual Method ◽  
Conical Shells ◽  
Free And Forced Vibrations ◽  
Special Cases

An efficient domain decomposition method is proposed to study the free and forced vibrations of stepped conical shells (SCSs) with arbitrary number of step variations. Conical shells with uniform thickness are treated as special cases of the SCSs. Multilevel partition hierarchy, viz., SCS, shell segment and shell domain, is adopted to accommodate the computing requirement of high-order vibration modes and responses. The interface continuity constraints on common boundaries and geometrical boundaries are incorporated into the system potential functional by means of a modified variational principle and least-squares weighted residual method. Double mixed series, i.e., the Fourier series and Chebyshev orthogonal polynomials, are adopted as admissible displacement functions for each shell domain. To test the convergence, efficiency and accuracy of the present method, free and forced vibrations of uniform thickness conical shells and SCSs are examined under various combinations of classical and nonclassical boundary conditions. The numerical results obtained from the proposed method show good agreement with previously published results and those from the finite element program ANSYS. The computational advantage of the approach can be exploited to gather useful and rapid information about the effects of geometry and boundary conditions on the vibrations of the uniform and stepped conical shells.

Response of an Axially-Loaded Terfenol-D Rod to a Harmonic Base Excitation

2013 ◽  
Author(s):  
Meghashyam Panyam ◽  
Mohammed F. Daqaq
Keyword(s):  
Energy Harvesting ◽  
Frequency Response ◽  
Linear Models ◽  
Multiple Scales ◽  
Dynamic Performance ◽  
Response Amplitude ◽  
Elastic Behavior ◽  
Nonlinear Frequency ◽  
Base Excitation ◽  
Fundamental Vibration

Performance characteristics of the giant magnetostrictive alloy, Terfenol-D, have been studied by many researchers for actuation, sensing and energy harvesting applications. Mathematical models characterizing the magneto-elastic behavior and describing the effects of bias conditions — compressive prestress and magnetic bias — on the material performance, have been developed. For the most part, the models used to describe the material are linear models that can hide essential features of the dynamic performance. While nonlinear constitutive models of Terfenol-D exist, such models have not been utilized to study the dynamic frequency response characteristics that are essential towards a comprehensive understanding of its performance in actuation, sensing or energy harvesting. To address this problem, this effort investigates the role of empirically determined material nonlinearities in the dynamic performance of Terfenol-D. Towards that objective, a polynomial type stress-strain relation is used to construct a nonlinear distributed-parameters model for a Terfenol-D rod fixed at one end and mass loaded at the other while being subjected to a sinusoidal base excitation. Additionally, the model accounts for the rod being subjected to an axial prestress prior to excitation. Using the method of multiple scales, the nonlinear frequency response of the rod is investigated by obtaining analytical expressions for the steady-state response amplitude. It is demonstrated that the axial prestress results in a shift in the fundamental vibration frequencies of the rod and a change in the effective nonlinearity of the system. A qualitative analysis of the solution reveals that, the magnitude of axial load can be used to maximize the response amplitude over a larger bandwidth of frequencies.

scholarly journals A nonlinear viscoelastic model for NSGT nanotubes conveying fluid incorporating slip boundary conditions

2019 ◽  
Vol 25 (12) ◽  
pp. 1883-1894 ◽  
Author(s):  
Ali Farajpour ◽  
Hamed Farokhi ◽  
Mergen H. Ghayesh
Keyword(s):  
Boundary Conditions ◽  
Frequency Response ◽  
Viscoelastic Model ◽  
Strain Gradient Theory ◽  
Nonlinear Frequency ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Nonlinear Viscoelastic ◽  
Nonlinear Viscoelastic Model ◽  
Conveying Fluid

A nonlinear viscoelastic model is developed for the dynamics of nanotubes conveying fluid. The influences of strain gradients and stress nonlocality are incorporated via a nonlocal strain gradient theory (NSGT). Since at nanoscales, the assumptions of no-slip boundary conditions are not valid, the Beskok–Karniadakis theory is used to overcome this problem. The coupled nonlinear differential equations are derived via performing an energy/work balance. The derived equations along the transverse and axial axes are simultaneously solved to obtain the nonlinear frequency response. For this purpose, Galerkin's technique together with a continuation method are utilized. The frequency response is investigated in both subcritical and supercritical flow regimes.

Nonlinear Free and Forced Vibrations of In-Plane Bi-Directional Functionally Graded Rectangular Plate with Temperature-Dependent Properties

2020 ◽  
Vol 20 (08) ◽  
pp. 2050097
Author(s):  
Soheil Hashemi ◽  
Ali Asghar Jafari
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Rectangular Plate ◽  
Forced Vibrations ◽  
Functionally Graded ◽  
Nonlinear Frequency ◽  
Temperature Dependent ◽  
Partial Differential ◽  
Free And Forced Vibrations ◽  
Temperature Dependent Properties

In this paper, the nonlinear free and forced vibrations analysis of in-plane bi-directional functionally graded (IBFG) rectangular plate with temperature-dependent properties is studied for the first time. For this purpose, with the aid of von Karman nonlinearity strain–displacement relations, the partial differential equations of motion are developed based on the first-order shear deformation theory (FSDT). Then, the nonlinear partial differential equations are transformed into the time-dependent nonlinear ordinary differential equations by applying the Galerkin method. The primary and super harmonic resonances are analyzed by the method of multiple scales (MMS). The material properties are assumed to be temperature-dependent and graded in the thickness direction according to the power-law distribution. The effects of some system parameters, such as vibration amplitude, volume fraction indexes, length-to-thickness ratio, temperature and aspect ratio on the nonlinear frequency and also frequency responses curve, are discussed in detail. To validate the analysis, the results of this paper are compared with the published data and good agreements are found.

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