Abstract
The present analysis demonstrates the thermal effect on vibrations of a symmetric, non-homoge- neous trapezoidal plate with parabolically varying thickness in both directions. The variation in Young’s modulus and mass density is the main cause for the occurrence of non-homogeneity in plate’s material. In this consideration, density varies linearly in one direction. The governing differential equations have been derived by Rayleigh-Ritz method in order to attain fundamental frequencies. With C-S-C-S boundary condition, a two term deflection function has been considered. The effect of structural parameters such as taper constants, thermal gradient, aspect ratio and non-homogeneity constant has been investigated for first two modes of vibration. The obtained numerical results have been presented in tabular and graphical form.
Highlights
People became interested in vibration when the first musical instruments, probably whistles or drums were discovered
All results acquired by Equation (24) provide the values of frequency parameter for different values of taper constants, thermal gradient, aspect ratios and non-homogeneity constant
It is evident from the table that as taper constant β1 increases the values of frequency parameter increases for both the modes of vibration
Summary
People became interested in vibration when the first musical instruments, probably whistles or drums were discovered. Since people have applied ingenuity and critical investigation to study the phenomenon of vibra-. How to cite this paper: Kavita, Kumar, S. and Sharma, P. (2016) Study of Thermally Induced Vibration of Non-Homogeneous Trapezoidal Plate with Parabolically Thickness Variation in Both Directions. Many studies in existing period have been aggravated by the engineering applications of vibration, such as design of machines, foundations, structures, engines and turbine systems. Most major movers have vibrational problems because of the inbuilt unbalance in the engines. In spite of its detrimental effects, vibration can be utilized profitably in several industrial and consumer applications
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