scholarly journals Computational Synthesis for Nonlinear Dynamics Based Design of Planar Resonant Structures

2012 ◽  
Author(s):  
Astitva Tripathi ◽  
Anil K. Bajaj
Keyword(s):  
Finite Element ◽  
Internal Resonance ◽  
Optimization Techniques ◽  
Mode Shapes ◽  
Nonlinear Phenomena ◽  
Mems Devices ◽  
Modal Interactions ◽  
Internal Resonances ◽  
Element Analysis ◽  
Resonant Structures

Nonlinear phenomena such as internal resonances have significant potential applications in Micro Electro Mechanical Systems (MEMS) for increasing the sensitivity of biological and chemical sensors and signal processing elements in circuits. While several theoretical systems are known which exhibit 1:2 or 1:3 internal resonances, designing systems that have the desired properties required for internal resonance as well as are physically realizable as MEMS devices is a significant challenge. Traditionally, the design process for obtaining resonant structures exhibiting an internal resonance has relied heavily on the designer’s prior knowledge and experience. However, with advances in computing power and topology optimization techniques, it should be possible to synthesize structures with the required nonlinear properties (such as having modal interactions) computationally. In this work, a preliminary method for computer based synthesis of structures consisting of beams for desired internal resonance is presented. The linear structural design is accompalished by a Finite Element Method (FEM) formulation implemented in Matlab to start with a base structure and iteratively modify it to obtain a structure with the desired properties. Possible design criteria are having the first two natural frequencies of the structure in some required ratio (such as 1:2 or 1:3). Once a topology of the structure is achieved that meets the desired criterion (i.e., the program converges to a definite structure), the linear mode shapes of the structure can be extracted from the finite element analysis, and a more complete Lagrangian formulation of the nonlinear elastic structure can be used to develop a nonlinear two-mode model of the structure. The reduced-order model is expected to capture the appropriate resonant dynamics associated with modal interactions between the two modes. The nonlinear response of the structure can be obtained by application of perturbation methods such as averaging on the two-mode model. Many candidate structures are synthesized that meet the desired modal frequency criterion and their nonlinear responses are compared.

scholarly journals Computational Synthesis for Nonlinear Dynamics Based Design of Planar Resonant Structures

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Astitva Tripathi ◽  
Anil K. Bajaj
Keyword(s):  
Finite Element ◽  
Internal Resonance ◽  
Optimization Techniques ◽  
Mode Shapes ◽  
Nonlinear Phenomena ◽  
Mems Devices ◽  
Modal Interactions ◽  
Internal Resonances ◽  
Element Analysis ◽  
Resonant Structures

Nonlinear phenomena such as internal resonances have significant potential applications in micro electro mechanical systems (MEMS) for increasing the sensitivity of biological and chemical sensors and signal processing elements in circuits. While several theoretical systems are known which exhibit 1:2 or 1:3 internal resonances, designing systems that have the desired properties required for internal resonance and that are physically realizable as MEMS devices is a significant challenge. Traditionally, the design process for obtaining resonant structures exhibiting an internal resonance has relied heavily on the designer's prior knowledge and experience. However, with advances in computing power and topology optimization techniques, it should be possible to synthesize structures with the required nonlinear properties (such as having modal interactions) computationally. In this work, a preliminary work on computer based synthesis of structures consisting of beams for desired internal resonance is presented. The linear structural design is accomplished by a Finite Element Method (FEM) formulation implemented in Matlab to start with a base structure and iteratively modify it to obtain a structure with the desired properties. Possible design criteria are having the first two natural frequencies of the structure in some required ratio (such as 1:2 or 1:3). Once a topology of the structure is achieved that meets the desired criterion, the linear mode shapes of the structure can be extracted from the finite element analysis, and a more complete Lagrangian formulation of the nonlinear elastic structure can be used to develop a nonlinear two-mode model of the structure. The reduced-order model is expected to capture the appropriate resonant dynamics associated with modal interactions between the two modes. The nonlinear response of the structure can be obtained by application of perturbation methods such as averaging on the two-mode model. Many candidate structures are synthesized that meet the desired modal frequency criterion and their nonlinear responses are compared.

Design for Internal Resonances in Nonlinear Transverse Vibrations of Hyperelastic Plates

2013 ◽  
Author(s):  
Astitva Tripathi ◽  
Anil K. Bajaj
Keyword(s):  
Finite Element ◽  
Internal Resonance ◽  
Optimization Techniques ◽  
Mode Shapes ◽  
Nonlinear Phenomenon ◽  
Mems Devices ◽  
Modal Interactions ◽  
Internal Resonances ◽  
Element Analysis ◽  
Nonlinear Properties

Nonlinear phenomenon such as internal resonance have significant potential applications in Micro Electro Mechanical Systems (MEMS) for increasing the sensitivity of biological and chemical sensors and signal processing elements in circuits. While several theoretical systems are known which exhibit 1:2 or 1:3 internal resonances, designing systems that have the desired properties required for internal resonance as well as are physically realizable as MEMS devices is a significant challenge. Traditionally, the design process for obtaining resonant structures exhibiting an internal resonance has relied heavily on the designer’s prior knowledge and experience. However, with advances in computing power and topology optimization techniques, it should be possible to synthesize structures with the required nonlinear properties (such as having modal frequencies in certain ratios) computationally. In this work, plate structures which are candidates for internal resonances are obtained using a Finite Element Method (FEM) formulation implemented in Matlab to iteratively modify a base structure to get its first two natural frequencies close to the desired ratio (1:2 or 1:3). Once a structure with desired topology is achieved, the linear mode shapes of the structure can be extracted from the finite element analysis, and a more complete Lagrangian formulation of the Hyperelastic structure can be used to develop a nonlinear two-mode model of the structure. The reduced-order model is expected to capture the appropriate resonant dynamics associated with modal interactions between the two modes, and the nonlinear response can be obtained by application of perturbation methods such as averaging on the two-mode model.

Design for 1:2 Internal Resonances in In-Plane Vibrations of Plates With Hyperelastic Materials

2013 ◽  
Author(s):  
Astitva Tripathi ◽  
Anil K. Bajaj
Keyword(s):  
Finite Element ◽  
Internal Resonance ◽  
Strain Energy ◽  
Quadratic Function ◽  
The Body ◽  
Energy Potential ◽  
Internal Resonances ◽  
Element Analysis ◽  
Hyperelastic Materials ◽  
Aerial Vehicle

With advances in technology, hyperelastic materials are seeing increased use in varied applications ranging from microfluidic pumps, artificial muscles to deformable robots. They have also been proposed as materials of choice in the construction of components undergoing dynamic excitation such as the wings of a micro-unmanned aerial vehicle or the body of a serpentine robot. Since the strain energy potentials of various hyperelastic materials are more complex than quadratic, exploration of their nonlinear dynamic response lends itself to some interesting consequences. In this work, a structure made of a Mooney-Rivlin hyperelastic material and undergoing planar vibrations is considered. Since the stresses developed in a Mooney-Rivlin material are at least a quadratic function of strain, a possibility of 1:2 internal resonance is explored. A Finite Element Method (FEM) formulation implemented in Matlab is used to iteratively modify a base structure to get its first two natural frequencies close to the ratio 1:2. Once a topology of the structure is achieved, the linear modes of the structure can be extracted from the finite element analysis, and a more complete Lagrangian formulation of the hyperelastic structure can be used to develop a nonlinear two-mode model of the structure. The nonlinear response of the structure can be obtained by application of perturbation methods such as averaging on the two-mode model. It is shown that the strain energy potential for the Mooney-Rivlin material makes it possible for internal resonance to occur in such structures.

Application of Computational Mechanics to Tire Design—Yesterday, Today, and Tomorrow

2011 ◽  
Vol 39 (4) ◽  
pp. 223-244 ◽  
Author(s):  
Y. Nakajima
Keyword(s):  
Finite Element ◽  
New Technologies ◽  
Computational Mechanics ◽  
Design Procedure ◽  
Side Wall ◽  
Rolling Resistance ◽  
Optimization Techniques ◽  
Stress Strain ◽  
Element Analysis ◽  
Crown Shape

Abstract The tire technology related with the computational mechanics is reviewed from the standpoint of yesterday, today, and tomorrow. Yesterday: A finite element method was developed in the 1950s as a tool of computational mechanics. In the tire manufacturers, finite element analysis (FEA) was started applying to a tire analysis in the beginning of 1970s and this was much earlier than the vehicle industry, electric industry, and others. The main reason was that construction and configurations of a tire were so complicated that analytical approach could not solve many problems related with tire mechanics. Since commercial software was not so popular in 1970s, in-house axisymmetric codes were developed for three kinds of application such as stress/strain, heat conduction, and modal analysis. Since FEA could make the stress/strain visible in a tire, the application area was mainly tire durability. Today: combining FEA with optimization techniques, the tire design procedure is drastically changed in side wall shape, tire crown shape, pitch variation, tire pattern, etc. So the computational mechanics becomes an indispensable tool for tire industry. Furthermore, an insight to improve tire performance is obtained from the optimized solution and the new technologies were created from the insight. Then, FEA is applied to various areas such as hydroplaning and snow traction based on the formulation of fluid–tire interaction. Since the computational mechanics enables us to see what we could not see, new tire patterns were developed by seeing the streamline in tire contact area and shear stress in snow in traction.Tomorrow: The computational mechanics will be applied in multidisciplinary areas and nano-scale areas to create new technologies. The environmental subjects will be more important such as rolling resistance, noise and wear.

scholarly journals Tuning nonlinear damping in graphene nanoresonators by parametric–direct internal resonance

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Ata Keşkekler ◽  
Oriel Shoshani ◽  
Martin Lee ◽  
Herre S. J. van der Zant ◽  
Peter G. Steeneken ◽  
...  
Keyword(s):  
Parametric Resonance ◽  
Internal Resonance ◽  
Microscopic Theory ◽  
Fold Increase ◽  
Nonlinear Damping ◽  
Supporting Evidence ◽  
Nonlinear Dissipation ◽  
Modal Interactions ◽  
Solid State Physics ◽  
Internal Resonances

AbstractMechanical sources of nonlinear damping play a central role in modern physics, from solid-state physics to thermodynamics. The microscopic theory of mechanical dissipation suggests that nonlinear damping of a resonant mode can be strongly enhanced when it is coupled to a vibration mode that is close to twice its resonance frequency. To date, no experimental evidence of this enhancement has been realized. In this letter, we experimentally show that nanoresonators driven into parametric-direct internal resonance provide supporting evidence for the microscopic theory of nonlinear dissipation. By regulating the drive level, we tune the parametric resonance of a graphene nanodrum over a range of 40–70 MHz to reach successive two-to-one internal resonances, leading to a nearly two-fold increase of the nonlinear damping. Our study opens up a route towards utilizing modal interactions and parametric resonance to realize resonators with engineered nonlinear dissipation over wide frequency range.

Design and Analysis of Foldable Vehicle using Finite Element Simulation

2021 ◽  
Vol 13 (3) ◽  
Author(s):  
Vikas Radhakrishna Deulgaonkar ◽  
S.N. Belsare ◽  
Naik Shreyas ◽  
Dixit Pratik ◽  
Kulkarni Pranav ◽  
...  
Keyword(s):  
Finite Element ◽  
Dynamic Properties ◽  
Mode Shapes ◽  
Vehicle Speed ◽  
Element Analysis ◽  
Dynamic Stresses ◽  
Element Simulation ◽  
Vehicle Structure ◽  
Similar Materials ◽  
Good Agreement

Present work deals with evaluation of stress, deflection and dynamic properties of the folded vehicle structure. The folded vehicle in present case is a single seat vehicle intended to carry one person. Design constraints are the folded dimensions of the vehicle and the maximum vehicle speed is limited to 15m/s. Using classical calculations dimensions of the vehicle are devised. Different materials are used for seat, telescopic support and chassis of the foldable vehicle. computer aided model is prepared using CATIA software. Finite element analysis of the foldable vehicle has been carried out to evaluate the static and dynamic stresses induced in the vehicle components. Meshing of the foldable vehicle is carried using Ansys Workbench. From modal analysis six mode shapes of the foldable vehicle are formulated, corresponding frequencies and deflections are devised. Mesh generator is used to mesh the foldable vehicle. The deflection and frequency magnitudes of foldable vehicle evaluated are in good agreement with the experimental results available in literature for similar materials.

Design for Desired Mode Shapes: Preliminary Results

1998 ◽  
Author(s):  
Elizabeth K. Lai ◽  
G. K. Ananthasuresh
Keyword(s):  
Finite Element ◽  
Feasibility Study ◽  
Mode Shape ◽  
Longitudinal Axis ◽  
Mode Shapes ◽  
Future Research ◽  
Structural Members ◽  
Element Analysis ◽  
Cross Sectional ◽  
Made In

Abstract This paper is concerned with the shape optimization of structures to attain prescribed normal mode shapes. Optimizing structural members in order to have desired mode shapes, besides the desired natural frequencies, is of interest in some applications at both macro and micro scales. After reviewing the relevant past work on the “inverse mode shape” problem, a feasibility study using the lumped spring-mass models and finite element models of an axially vibrating bar is presented. Based on the observations made in the feasibility study with bars, a meaningful optimization problem is formulated and solved. Using finite element analysis and numerical optimization, a method for designing beam-like structures for prescribed mode shapes is developed. The method is demonstrated with an example of designing the cross-sectional area profile of a beam along its longitudinal axis to get a desired fundamental mode shape. The nonuniqueness of the solution is noted and avenues for future research are identified.

Investigation of stiffness of small wind turbine blade based on vibration analysis technique

2019 ◽  
Vol 44 (1) ◽  
pp. 49-59
Author(s):  
Nilesh Chandgude ◽  
Nitin Gadhave ◽  
Ganesh Taware ◽  
Nitin Patil
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Wind Turbine ◽  
Natural Frequency ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Element Analysis ◽  
Finite Element Software ◽  
Small Wind Turbine

In this article, three small wind turbine blades of different materials were manufactured. Finite element analysis was carried out using finite element software ANSYS 14.5 on modeled blades of National Advisory Committee for Aeronautics 4412 airfoil profile. From finite element analysis, first, two flap-wise natural frequencies and mode shapes of three different blades are obtained. Experimental vibration analysis of manufactured blades was carried out using fast Fourier transform analyzer to find the first two flap-wise natural frequencies. Finally, the results obtained from the finite element analysis and experimental test of three blades are compared. Based on vibration analysis, we found that the natural frequency of glass fiber reinforced plastic blade reinforced with aluminum sheet metal (small) strips increases compared with the remaining blades. An increase in the natural frequency indicates an increase in the stiffness of blade.

Dynamic Characteristics and Finite Element Model Updating of Micromachined Torsion Structures

2013 ◽  
Vol 284-287 ◽  
pp. 1831-1835
Author(s):  
Wei Hsin Gau ◽  
Kun Nan Chen ◽  
Yunn Lin Hwang
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Finite Element Model ◽  
Model Updating ◽  
Speckle Pattern ◽  
Element Model ◽  
Mode Shapes ◽  
Electronic Speckle Pattern Interferometry ◽  
Finite Element Model Updating ◽  
Element Analysis

In this paper, two experimental techniques, Electronic Speckle Pattern Interferometry and Stroboscopic Interferometry, and two different finite element analysis packages are used to measure or to analyze the frequencies and mode shapes of a micromachined, cross-shaped torsion structure. Four sets of modal data are compared and shown having a significant discrepancy in their frequency values, although their mode shapes are quite consistent. Inconsistency in the frequency results due to erroneous inputs of geometrical and material parameters to the finite element analysis can be salvaged by applying the finite element model updating procedure. Two updating cases show that the optimization sequences converge quickly and significant improvements in frequency prediction are achieved. With the inclusion of the thickness parameter, the second case yields a maximum of under 0.4% in frequency difference, and all parameters attain more reliable updated values.

Free Vibration Analysis of PZT Glide Heads

1999 ◽  
Vol 121 (4) ◽  
pp. 984-988 ◽  
Author(s):  
Alex Y. Tsay ◽  
Jin-Hui Ouyang ◽  
C.-P. Roger Ku ◽  
I. Y. Shen ◽  
David Kuo
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Natural Frequencies ◽  
Laser Doppler Vibrometer ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Bonding Length ◽  
Measured Displacement

This paper studies natural frequencies and mode shapes of a glide head with a piezoelectric transducer (PZT) through calibrated experiments and a finite element analysis. In the experiments, the PZT transducer served as an actuator exciting the glide head from 100 kHz to 1.3 MHz, and a laser Doppler vibrometer (LDV) measured displacement of the glide head at the inner or outer rail. The natural frequencies were measured through PZT impedance and frequency response functions from PZT to LDV. In the finite element analysis, the glide head was meshed by brick elements. The finite element results show that there are two types of vibration modes: slider modes and PZT modes. Only the slider modes are important to glide head applications. Moreover, natural frequencies predicted from the finite element analysis agree well with the experimental results within 5% of error. Finally, the finite element analysis identifies four critical slider dimensions whose tolerance will significantly vary the natural frequencies: PZT bonding length, wing thickness, slider thickness, and air bearing recess depth.

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