STRUCTURAL DYNAMICS PDF
Fundamentals of Structural Dynamics. 1 Course description. Aim of the course is that students develop a “feeling for dynamic problems” and. Faculté des Sciences Appliquées. Twelve Lectures on Structural Dynamics. André PREUMONT. Active Structures Laboratory. Department of Mechanical. (i) Idealisation of material such as homogeneity, isotropy and idealisation of structural behaviour such as linearly elastic, elastic and nonlinear. (ii) Idealisation of.
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1. Structural Dynamics, Dynamic Force and Dynamic System. Structural Dynamics. Conventional structural analysis is based on the concept of statics, which can. STRUCTURAL DYNAMICS BASICS: Real-life structures are subjected to loads which vary with time. Except self weight of the structure, all other loads vary. References: R.W. Clough and J. Penzien 'Dynamics of Structures' A.K.. Chopra 'Dynamics of Structures: Theory and Applications to Earthquake.
By flexible docking of the Bennett linkage model into this map, a second conformation of a Bennett linkage was obtained Fig. These density maps, with resolutions ranging from 5. Although each DNA helix within the Bennett linkages could not be identified under the current resolution, the spatial location and orientation of each arm of Bennett linkages can be defined based on the 3D density maps.
As a result, more conformations were revealed Fig. Scale bars are 20 nm Full size image Statistical analyses of the conformations Aligning all the conformations of DNA origami Bennett linkages shows a variety of conformations Fig. To quantitatively analyze the conformational dynamics and fluctuations, two sets of bending angles formed within the quadrilateral-shape Bennett linkages were measured, i.
Both sets of angles determined the overall conformation of Bennett linkages.
The pink curve was predicted by using kinematic analysis. In contrast, the percentages from kinematic analysis were not like each other or the experimental curves, suggesting the freedom or energies of the conformations were more unevenly distributed than predicted.
Discussion Scaffolded DNA origami has proven to be a powerful and efficient technique to fabricate nanostructures. Recently cryo-electron tomography was used to study the structural diversity of supercoiled DNA The limited tilt angle range was responsible for missing wedge of information in Fourier space.
As a result, the final 3D reconstruction often contains certain artifacts, such as elongation, blurring, and distracting caustics To reduce the effects of the missing wedge, the missing wedge data was estimated via computational algorithms reported by numerous groups 23 , 24 , 25 , For example, a computational approach to fill the missing data in 2D electron crystallography was first reported by Agard and Stroud in the s Recently, a simple Fourier angular filter to effectively suppress the ray artifacts in the single-axis tilting projection acquisition scheme was reported by Kovacik et al.
A statistical reconstruction method, sequential maximum a posteriori expectation maximization was used to compensate the missing-wedge effects by Ruotsalainen et al. An iterative compressed-sensing optimized non-uniform fast Fourier transform reconstruction ICON for missing-wedge restoration was proposed by Sun et al.
Moreover, a generalized Fourier iterative reconstruction algorithm GENFIRE proposed by Miao and colleagues 26 showed a certain capability in reducing the missing wedge artifact to achieve a 3D structure with more isotropic resolution. All those approaches benefited the 3D reconstruction by reducing the missing wedge effects and providing a relatively isotropic resolution 3D density map. In our IPET, a similar missing wedge filling algorithm was also included for 3D reconstruction correction.
In the theoretical model, the conformation of Bennett linkages was characterized by the geometrical constraint from joints that connect adjacent arms of the linkage Fig.
In order to validate the theoretical model and gain some insights into the effects of these geometrical constraints for improved control of DNA origami conformations, we used kinematic analysis to derive the theoretical internal angles within Bennett linkages details are provided in the Supporting Information , and then compared the results with the above experimental measurements.
The joints are all formed by two wedge-shaped DNA bundles connected through a shared edge. The mechanical properties of joints is influenced by the angle of the wedges. The joint formed by two obtuse-angle shaped wedges should be stronger than that formed by two acute-angle shaped wedges.
Further optimizations of the joints, especially aiming to increase the stiffness of the sharp connecting region by introducing more cross links to supporting the connecting ends, will be helpful toward improving motion control of the DNA origami mechanisms and nanomachines.
Based on these results and visualization of Bennett linkage model, we proposed potential approaches for improving the control of Bennett linkage conformation. After 1 min incubation, the excessive solution on grid was blotted with filter paper. The cryo-PS specimens were prepared following the procedure described by Zhang et al. The flash-frozen grids were transferred into liquid nitrogen for storage.
The cryo-EM specimens were prepared similarly to the cryo-PS specimen, but were not washed by uranyl formate before flash-frozen in liquid nitrogen as described before.
The acquired micrographs were Gaussian high-pass filtered to nm and low-pass filtered to 1 nm after the X-ray speckles were removed. At this magnification, the pixel size of the micrographs is 0. At this magnification the pixel size of the micrographs is 0. All tilt series were initially aligned using the IMOD 31 software package.
In this process, an ab initio 3D density map was directly back-projected in Fourier space and served as the initial model.
The refinement was then iteratively invoked to translationally align each tilted particle image to the computed projection. During the refinement, automatically generated Gaussian low-pass filters, soft-boundary circular masks and particle-shaped soft-boundary masks were sequentially applied to the tilt images and references to increase the alignment accuracy 5.
An improved model was then reconstructed based upon the refined alignment at the end of each refinement. The 3D map was then reconstructed by back-projection of filtered and masked particle tilt series.
The back projection was performed in Fourier space without weighting.
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Post 3D reconstruction processing was conducted using our newly developed interactive algorithm to estimate the data in the missing wedge.
The resolution was determined based on the FSC that was calculated based upon two reconstructions that were generated using odd and even halves of aligned particle tilt series. It is noteworthy that the generation of the FSC curve did not take into account the missing wedge, as the missing data were estimated in our approach.
The frequency at which the FSC curve first falls to a value of 0. We used the 0.
All of the IPET density maps in the presented figures were low-pass filtered to 8 nm. This information is quite useful in revealing the structural heterogeneous and dynamics. CanDo 17 , 19 was used to build an initial Bennett linkage model. Hence DOF also represents minimum number of coordinate systems required to denote the position of the mass at any instant of time.
An overhead tank is considered as an example. This can be modeled as a cantilever column with concentrated mass at top. If we want axial vibration, then only one coordinate y is sufficient. If only the flexural deformation is required then also only one co-ordinate x is required. If both are required, then two coordinates are required. Depending upon the co-ordinates to describe the motion, we have 1.
Single degree of freedom system SDoF. Multiple degree of freedom MDoF. Continuous system. Free Vibration of SDoF: An SDoF is one which needs only one co-ordinate to describe the motion. The single bay single storey rigid frame is taken as SDoF based on assumptions. Hence neglected. When this frame vibrates due to lateral load in horizontal direction, the force acting are inertial force, 2 damping force, 3 restoring force, and 4 External force.
If the external force is removed after initial disturbance, the free vibration occurs. Further it will be treated as free damped vibration, if damping is present and if damping is not present it is called free undamped vibration.
An SDoF is represented as shown in Figure. For this system, only one coordinate x is required translation. The solution of this equation gives response of an SDoF system.
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Free Undamped Vibration: In this case, is zero and C is zero because no damping. Since cosine and sine functions are periodic functions, motion defined by x will also be periodic motion repeats itself after certain interval of time. Reciprocal of T is the frequency which is nothing but number of times motion repeats itself in one second.
This reciprocal is represented as f and it is natural frequency of the system. For example: A in the above equation is the amplitude of motion. Angle is called phase angle. Equation 10 is harmonic in nature. Determine natural frequency of free vibration of weight. Calculate the natural angular frequency of the frame shown in figure. Compute also natural period of vibration. In this case, the restoring force in the form of spring force is provided by AB and CD which are columns.
The equivalent stiffness is computed on the basis that the spring actions of the two columns are in parallel. Find the natural frequency of the system shown. The mass of the beam is negligible in comparison to the suspended mass.
The beam has elastic behavior and hence has spring action. Further spring attached to the mass also has a restoring force. The deformation of the mass at the centre is equal to deformation of beam at midspan and that of attached spring.
This is a d. Hence following cases are possible. The system is said to be over damped.
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Hence in this case, there is no periodicity or harmonic motion but the damping is so huge, that the system just comes back slowly equilibrium from displaced position.
Case 2: Hence , are real, negative and equal. Even in this case, there is no oscillatory motion. The damping in the system is enough to bring it back to equilibrium.
System is said to be Critically Damped. Hence the roots are complex conjugate roots. Using these conditions, c1 and c2 can be computed. Equation 8 describes motion in undamped case.
The variation of the displacement under damped free vibration system is as shown.
The amplitude decreases in an exponential manner. This means that damped natural time periods is more that of undamped period. However, this increase in time period is very small and hence for all practical purposes, it is assumed that a small viscous damping will not affect time period of vibration. A platform of weight 18 KN is being supported by four equal columns which are clamped to the foundation.
Experimentally, it has been computed that a static force 5KN applied horizontally, to the platform produces a displacement of 2. Compute the following:For example: The flash-frozen grids were transferred into liquid nitrogen for storage. Seven representative tilt images of a targeted particle first column were gradually aligned via an iterative refinement process next five columns.
TUTORIAL NOTES: Structural Dynamics
Further it will be treated as free damped vibration, if damping is present and if damping is not present it is called free undamped vibration. A simple model belonging to this class is chosen with parameters which can be estimated theoretically, thereby making this type of model potentially useful during the design stages. Hence following cases are possible.
F t which is the dynamic load varies with time.