Analysis of Residual Stresses on the Vibration of a Circular Sensor Diaphragm with Surface Effects

2016 ◽  
Vol 33 (3) ◽  
pp. 323-329 ◽  
Author(s):  
S.-S. Zhou ◽  
S.-J. Zhou ◽  
A.-Q. Li ◽  
B.-L. Wang
Keyword(s):  
Residual Stresses ◽  
Natural Frequency ◽  
Flexural Rigidity ◽  
Plate Theory ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Transition Range ◽  
Biochemical Sensors ◽  
Tension Parameter ◽  
Wide Range

AbstractResonant micro-biochemical sensors play important roles in a wide range of emerging applications to detect biochemical molecules. As the resonators of micro-biochemical sensors, the vibration characteristics of circular sensor diaphragms are important for the design of diaphragm-based resonant micro-biochemical sensors. In this paper, the influence of residual stresses on the vibration of a circular sensor diaphragm with surface effects is analyzed. Based on the Kirchhoff's plate theory and surface elasticity theory, the governing equation is presented. The material characteristic lengths for different surface effects are obtained. The influences of residual stresses on the effective flexural rigidity and natural frequency of the diaphragm with surface effects are discussed. Results show that the influence of residual stresses on the effective flexural rigidity becomes obvious with the increasing of residual stresses. The first order natural frequency increases rapidly when the tension parameter is larger than 30 for the stiffened surfaces, while for the softened surfaces the value is 10. Moreover, surface effects can influence the transition range of diaphragm from the plate behavior to membrane behavior in terms of the tension parameter. The transition range can be enlarged by the stiffened surface and be shortened by the softened surface. The analysis and results are helpful for the design of sensor diaphragm-based resonant micro-biochemical sensors and some related researches.

scholarly journals Surface Effects on the Vibration and Buckling of Double-Nanobeam-Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
Dong-Hui Wang ◽  
Gang-Feng Wang
Keyword(s):  
Natural Frequency ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Nanoelectromechanical Systems ◽  
Beam Model ◽  
Cross Sectional ◽  
Axial Buckling ◽  
Cross Sectional Size ◽  
Euler Bernoulli Beam ◽  
Deformation Modes

Surface effects on the transverse vibration and axial buckling of double-nanobeam-system (DNBS) are examined based on a refined Euler-Bernoulli beam model. For three typical deformation modes of DNBS, we derive the natural frequency and critical axial load accounting for both surface elasticity and residual surface tension, respectively. It is found that surface effects get quite important when the cross-sectional size of beams shrinks to nanometers. No matter for vibration or axial buckling, surface effects are just the same in three deformation modes and usually enhance the natural frequency and critical load. However, the interaction between beams is clearly distinct in different deformation modes. This study might be helpful for the design of nano-optomechanical systems and nanoelectromechanical systems.

Transient Response of a Circular Nanoplate Subjected to Low Velocity Impact

2017 ◽  
Vol 09 (08) ◽  
pp. 1750114 ◽  
Author(s):  
Jie Liu ◽  
Hua Liu ◽  
Jia-Ling Yang ◽  
Xi-Qiao Feng
Keyword(s):  
Transient Response ◽  
Plate Theory ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Surface Effects ◽  
Dynamic Responses ◽  
Low Velocity Impact ◽  
Low Velocity ◽  
Surface Residual Stress ◽  
Impact Problems

The transient response of a circular nanoplate subjected to the normal impact by a nanosphere (e.g., C[Formula: see text]) is investigated theoretically. The nanoplate is modeled by the Kirchhoff thin plate theory. Gurtin–Murdoch’s theory is employed to account for the surface effects of the nanoplate with surface elasticity and surface residual stress. The van der Waals interaction between the nanosphere and the nanoplate is also taken into account. The governing equations for the vibration of the nanoplate impinged by a rigid nanosphere are established by using the Hamilton’s principle. The displacement field in the circular nanoplate is obtained by using the Fourier–Bessel expansion method. We reveal some physical mechanisms in the nanoimpact problem that are different from those in macroscopic impact problems, and surface effects have pronounced influences on the dynamic responses of a plate when its thickness shrinks to a few nanometers.

scholarly journals Investigating Surface Effects on Thermomechanical Behavior of Embedded Circular Curved Nanosize Beams

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohsen Daman
Keyword(s):  
Natural Frequency ◽  
Surface Properties ◽  
Nonlocal Parameter ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Buckling Load ◽  
Opening Angle ◽  
Governing Equations ◽  
Critical Buckling Load ◽  
Elastic Foundations

To investigate the surface effects on thermomechanical vibration and buckling of embedded circular curved nanosize beams, nonlocal elasticity model is used in combination with surface properties including surface elasticity, surface tension, and surface density for modeling the nanoscale effect. The governing equations are determined via the energy method. Analytically Navier method is utilized to solve the governing equations for simply supported nanobeam at both ends. Solving these equations enables us to estimate the natural frequency and critical buckling load for circular curved nanobeam including Winkler and Pasternak elastic foundations and under the effect of a uniform temperature change. The results determined are verified by comparing the results with available ones in literature. The effects of various parameters such as nonlocal parameter, surface properties, Winkler and Pasternak elastic foundations, temperature, and opening angle of circular curved nanobeam on the natural frequency and critical buckling load are successfully studied. The results reveal that the natural frequency and critical buckling load of circular curved nanobeam are significantly influenced by these effects.

Theoretical study of the prestressing strand's stress by computer modeling methods

2020 ◽  
Vol 76 (11) ◽  
pp. 1139-1148
Author(s):  
A. G. Korchunov ◽  
E. M. Medvedeva ◽  
E. M. Golubchik
Keyword(s):  
Residual Stresses ◽  
High Strength ◽  
Pearlitic Steel ◽  
Internal Stresses ◽  
Steel Microstructure ◽  
Compressive Stresses ◽  
Wide Range ◽  
Prestressing Strands ◽  
Increasing Temperature ◽  
Wire Strand

The modern construction industry widely uses reinforced concrete structures, where high-strength prestressing strands are used. Key parameters determining strength and relaxation resistance are a steel microstructure and internal stresses. The aim of the work was a computer research of a stage-by-stage formation of internal stresses during production of prestressing strands of structure 1х7(1+6), 12.5 mm diameter, 1770 MPa strength grade, made of pearlitic steel, as well as study of various modes of mechanical and thermal treatment (MTT) influence on their distribution. To study the effect of every strand manufacturing operation on internal stresses of its wires, the authors developed three models: stranding and reducing a 7-wire strand; straightening of a laid strand, stranding and MTT of a 7-wire strand. It was shown that absolute values of residual stresses and their distribution in a wire used for strands of a specified structure significantly influence performance properties of strands. The use of MTT makes it possible to control in a wide range a redistribution of residual stresses in steel resulting from drawing and strand laying processes. It was established that during drawing of up to 80% degree, compressive stresses of 1100-1200 MPa degree are generated in the central layers of wire. The residual stresses on the wire surface accounted for 450-500 MPa and were tension in nature. The tension within a range of 70 kN to 82 kN combined with a temperature range of 360-380°С contributes to a two-fold decrease in residual stresses both in the central and surface layers of wire. When increasing temperature up to 400°С and maintaining the tension, it is possible to achieve maximum balance of residual stresses. Stranding stresses, whose high values entail failure of lay length and geometry of the studied strand may be fully eliminated only at tension of 82 kN and temperature of 400°С. Otherwise, stranding stresses result in opening of strands.

scholarly journals Vibrational analysis of nanoplate with surface irregularity via Kirchhoff plate theory

2021 ◽  
Vol 11 ◽  
pp. 184798042110011
Author(s):  
Mahmoud M Selim ◽  
Taher A Nofal
Keyword(s):  
Natural Frequency ◽  
Plate Theory ◽  
Vibrational Analysis ◽  
Equation Of Motion ◽  
Frequency Equation ◽  
Kirchhoff Plate ◽  
Surface Irregularity ◽  
Structural Element ◽  
Kirchhoff Plate Theory ◽  
Parabolic Form

In this work, an attempt is done to apply the Kirchhoff plate theory to find out the vibrational analyses of a nanoplate incorporating surface irregularity effects. The effects of surface irregularity on natural frequency of vibration of nanomaterials, especially for nanoplates, have not been investigated before, and most of the previous research have been carried for regular nanoplates. Therefore, it must be emphasized that the vibrations of irregular nanoplate are novel and applicable for the nanodevices, in which nanoplates act as the main structure of the nanocomposite. The surface irregularity is assumed in the parabolic form at the surface of the nanoplate. A novel equation of motion and frequency equation is derived. The obtained results provide a better representation of the vibration behavior of irregular nanoplates. It has been observed that the presence of surface irregularity affects considerably on the natural frequency of vibrational nanoplates. In addition, it has been seen that the natural frequency of nanoplate decreases with the increase of surface irregularity parameter. Finally, it can be concluded that the present results may serve as useful references for the application and design of nano-oscillators and nanodevices, in which nanoplates act as the most prevalent nanocomposites structural element.

PREDICTION OF PEEK RESIN PROPERTIES FOR PROCESSING MODELING USING MOLECULAR DYNAMICS

2021 ◽  
Author(s):  
KHATEREH KASHMARI ◽  
PRATHAMESH DESHPANDE ◽  
SAGAR PATIL ◽  
SAGAR SHAH ◽  
MARIANNA MAIARU ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Residual Stresses ◽  
Crystallization Kinetics ◽  
Material Properties ◽  
Elevated Temperatures ◽  
Processing Parameters ◽  
Thermomechanical Properties ◽  
Volumetric Shrinkage ◽  
Processing Temperature ◽  
Wide Range

Polymer Matrix Composites (PMCs) have been the subject of many recent studies due to their outstanding characteristics. For the processing of PMCs, a wide range of elevated temperatures is typically applied to the material, leading to the development of internal residual stresses during the final cool-down step. These residual stresses may lead to net shape deformations or internal damage. Also, volumetric shrinkage, and thus additional residual stresses, could be created during crystallization of the semi-crystalline thermoplastic matrix. Furthermore, the thermomechanical properties of semi-crystalline polymers are susceptible to the crystallinity content, which is tightly controlled by the processing parameters (processing temperature, temperature holding time) and material properties (melting and crystallization temperatures). Hence, it is vital to have a precise understanding of crystallization kinetics and its impact on the final component's performance to accurately predict induced residual stresses during the processing of these materials. To enable multi-scale process modeling of thermoplastic composites, molecular-level material properties must be determined for a wide range of crystallinity levels. In this study, the thermomechanical properties and volumetric shrinkage of the thermoplastic Poly Ether Ether Ketone (PEEK) resin are predicted as a function of crystallinity content and temperature using molecular dynamics (MD) modeling. Using crystallization-kinetics models, the thermo-mechanical properties are directly related to processing time and temperature. This research can ultimately predict the residual stress evolution in PEEK composites as a function of processing parameters.

Residual stress and failure analyses of polymer matrix composites considering thermal cycling and temperature effects based on classical laminate plate theory

2018 ◽  
Vol 53 (21) ◽  
pp. 3021-3032 ◽  
Author(s):  
AR Ghasemi ◽  
A Tabatabaeian ◽  
M Moradi
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Thermal Cycling ◽  
Polymer Matrix Composites ◽  
Plate Theory ◽  
Laminate Plate ◽  
Failure Behavior ◽  
Matrix Composites ◽  
Failure Index ◽  
Classical Laminate Plate Theory

The effects of temperature and thermal cycling on the residual stress and failure behavior of different polymer matrix composites have been investigated in this paper. A new algorithm within the framework of the classical laminate plate theory (CLPT) has been presented to calculate the residual stresses. The modified Tsai-Wu failure criterion has been employed to study the failure behavior of different stacking sequences. Numerical results show that the residual stress and failure index of the composites decrease with the increase of the temperature. It has also been established that thermal cycling condition leads to reduction of the residual stresses and increment of the failure index.

Maximizing the Fundamental Natural Frequency of Triangular Composite Plates

1996 ◽  
Vol 118 (2) ◽  
pp. 141-146 ◽  
Author(s):  
S. Abrate
Keyword(s):  
Natural Frequency ◽  
Material Properties ◽  
Composite Structures ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Laminated Composite ◽  
Composite Plates ◽  
Mode Shapes ◽  
Fundamental Natural Frequency ◽  
Wide Range

While many advances were made in the analysis of composite structures, it is generally recognized that the design of composite structures must be studied further in order to take full advantage of the mechanical properties of these materials. This study is concerned with maximizing the fundamental natural frequency of triangular, symmetrically laminated composite plates. The natural frequencies and mode shapes of composite plates of general triangular planform are determined using the Rayleigh-Ritz method. The plate constitutive equations are written in terms of stiffness invariants and nondimensional lamination parameters. Point supports are introduced in the formulation using the method of Lagrange multipliers. This formulation allows studying the free vibration of a wide range of triangular composite plates with any support condition along the edges and point supports. The boundary conditions are enforced at a number of points along the boundary. The effects of geometry, material properties and lamination on the natural frequencies of the plate are investigated. With this stiffness invariant formulation, the effects of lamination are described by a finite number of parameters regardless of the number of plies in the laminate. We then determine the lay-up that will maximize the fundamental natural frequency of the plate. It is shown that the optimum design is relatively insensitive to the material properties for the commonly used material systems. Results are presented for several cases.

Asymmetric Bifurcation of Initially Curved Nanobeam

2015 ◽  
Vol 82 (9) ◽  
Author(s):  
X. Chen ◽  
S. A. Meguid
Keyword(s):  
Symmetry Breaking ◽  
Degrees Of Freedom ◽  
Surface Elasticity ◽  
Beam Theory ◽  
Surface Effects ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Reduced Order ◽  
Euler Bernoulli Beam ◽  
Bifurcation Behavior

In this paper, we investigate the asymmetric bifurcation behavior of an initially curved nanobeam accounting for Lorentz and electrostatic forces. The beam model was developed in the framework of Euler–Bernoulli beam theory, and the surface effects at the nanoscale were taken into account in the model by including the surface elasticity and the residual surface tension. Based on the Galerkin decomposition method, the model was simplified as two degrees of freedom reduced order model, from which the symmetry breaking criterion was derived. The results of our work reveal the significant surface effects on the symmetry breaking criterion for the considered nanobeam.

scholarly journals Parametric structural modelling of fish bone active camber morphing aerofoils

2018 ◽  
Vol 29 (9) ◽  
pp. 2008-2026 ◽  
Author(s):  
Andres E Rivero ◽  
Paul M Weaver ◽  
Jonathan E Cooper ◽  
Benjamin KS Woods
Keyword(s):  
Analytical Model ◽  
Composite Laminates ◽  
Plate Theory ◽  
Ritz Method ◽  
Linear Equations ◽  
Variable Stiffness ◽  
Automated Analysis ◽  
Fish Bone ◽  
Two Dimensional ◽  
Wide Range

Camber morphing aerofoils have the potential to significantly improve the efficiency of fixed and rotary wing aircraft by providing significant lift control authority to a wing, at a lower drag penalty than traditional plain flaps. A rapid, mesh-independent and two-dimensional analytical model of the fish bone active camber concept is presented. Existing structural models of this concept are one-dimensional and isotropic and therefore unable to capture either material anisotropy or spanwise variations in loading/deformation. The proposed model addresses these shortcomings by being able to analyse composite laminates and solve for static two-dimensional displacement fields. Kirchhoff–Love plate theory, along with the Rayleigh–Ritz method, are used to capture the complex and variable stiffness nature of the fish bone active camber concept in a single system of linear equations. Results show errors between 0.5% and 8% for static deflections under representative uniform pressure loadings and applied actuation moments (except when transverse shear exists), compared to finite element method. The robustness, mesh-independence and analytical nature of this model, combined with a modular, parameter-driven geometry definition, facilitate a fast and automated analysis of a wide range of fish bone active camber concept configurations. This analytical model is therefore a powerful tool for use in trade studies, fluid–structure interaction and design optimisation.

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