Constructing the axial stiffness of longitudinally vibrating rod from fundamental mode shape

2001 ◽  
Vol 38 (19) ◽  
pp. 3443-3452 ◽  
Author(s):  
Suleyman Candan ◽  
Isaac Elishakoff
Keyword(s):  
Mode Shape ◽  
Fundamental Mode ◽  
Axial Stiffness

scholarly journals A 10-MHz FREE-FREE BEAM MICROMECHANICAL RESONATOR FABRICATION PROCESS USING SURFACE-MICROMACHINED TECHNOLOGY

2022 ◽  
Vol 36 (06) ◽  
Author(s):  
TAN-LOC NGUYEN
Keyword(s):  
Mode Shape ◽  
Fundamental Mode ◽  
Layout Design ◽  
Fabrication Process ◽  
Q Value ◽  
Standard Process ◽  
Mems Resonator ◽  
Second Mode ◽  
Motional Resistance ◽  
Free Beam

The fabrication process for the designed MEMS resonator using surface-micromachined technology is presented in this paper. A 10-MHz Free-Free beam MEMS resonator is designed to vibrate in the second-mode shape, which is significant improvement compare to the fundamental mode. The design showed a Q value as high as 75,000, which is significant improvement compared to 8,400 VHF F-F beam MEMS resonator by K. Wang; and very low motional resistance (18kΩ). The surface-micromachined technology is used as the standard process for the design. The process is briefly described from the layout design to the experimental fabricated device.

A Simple Approach for Estimating the Fundamental Mode Shape of Layered Soil Profiles

2019 ◽  
Vol 13 (01) ◽  
pp. 1950003
Author(s):  
Haizhong Zhang ◽  
Yan-Gang Zhao
Keyword(s):  
Mode Shape ◽  
Fundamental Mode ◽  
Close Agreement ◽  
Site Response ◽  
Vertical Direction ◽  
Simple Approach ◽  
Layered Soil ◽  
Soil Profiles ◽  
Seismic Code ◽  
Response Parameter

The fundamental mode shape of layered soil profiles is a key site response parameter, it has been adopted into the Japanese seismic code to represent the shape of the soil displacement response along the vertical direction. In this study, a simple approach for estimating the fundamental mode shape of layered soil profiles is developed. The proposed approach can directly model the fundamental mode shape and can be conveniently implemented using arithmetic operations, thus making it suitable to be used by the engineers. The assessments of the proposed approach using a series of layered soil profiles demonstrate that it can produce results in close agreement with the actual results.

scholarly journals Probabilistic and Interval Analyses Contrasted in Impact Buckling of a Clamped Column

2012 ◽  
Vol 80 (1) ◽  
Author(s):  
Isaac Elishakoff ◽  
Wim Verhaeghe ◽  
David Moens
Keyword(s):  
Mode Shape ◽  
Fundamental Mode ◽  
Axial Loading ◽  
Initial Imperfection ◽  
Numerical Data ◽  
The Impact

In this study we contrast two competing methodologies for the impact buckling of a column that is clamped at both ends. The initial imperfection is postulated to be co-configurational with the fundamental mode shape of the column without the axial loading. A solution is also furnished for the case when the initial imperfection is proportional to the Filonenko-Borodich “cosinusoidal polynomial”. Probabilistic and interval analyses are conducted for each case; these are contrasted on some representative numerical data.

Fundamental mode shape estimation and element stiffness evaluation of girder bridges by using passing tractor-trailers

2022 ◽  
Vol 169 ◽  
pp. 108746
Author(s):  
Yang Yang ◽  
Huicheng Lu ◽  
Xiaokun Tan ◽  
Hwa Kian Chai ◽  
Ruiqiong Wang ◽  
...  
Keyword(s):  
Mode Shape ◽  
Fundamental Mode ◽  
Shape Estimation ◽  
Girder Bridges ◽  
Stiffness Evaluation

Polar Orthotropic Inhomogeneous Circular Plates: Vibration Tailoring

2010 ◽  
Vol 77 (3) ◽  
Author(s):  
Demetris Pentaras ◽  
Isaac Elishakoff
Keyword(s):  
Eigenvalue Problem ◽  
Closed Form ◽  
Circular Plate ◽  
Mode Shape ◽  
Fundamental Mode ◽  
Inverse Eigenvalue Problem ◽  
Static Deflection ◽  
Circular Plates ◽  
Inverse Eigenvalue ◽  
Polar Orthotropic

Problem of matching a desired fundamental natural frequency is solved in the closed form for the polar-orthotropic inhomogeneous circular plate, which is clamped along its circumference. The vibration tailoring is performed by posing a semi-inverse eigenvalue problem. To do this, the fundamental mode shape is postulated. Namely, the analytical expression due to Lekhnitskii, and pertaining to the static deflection of the homogeneous circular plate is demanded to serve as an exact mode shape of the inhomogeneous plate. The analytical and numerical results are reported for several ratios of orthotropic coefficient.

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