Find the natural frequency and mode shape of all edge fixed plate.
Answers
Answered by
1
vibration analysis of plates has been an active research subject of engineering field. The analytical solutions have been found for plates with specified forms of mass and stiffness modifications, but for the plates with uncertain mass and stiffness modifications have not been addressed confidently. The concept of uncertainty plays an important role in the design of practical mechanical system. So it becomes important to study its effects on mechanical system for different frequency domain i.e. low, medium and high frequency. Here in this paper structural element square plate with all edge fixed boundary condition is selected on which mass, stiffness and combination of it, uncertainty is taking in account. By using Finite Element Method technique finding out, how plate is dynamically behaves in vibration. During modal analysis natural frequency and mode shapes are find and compared the response of bare plate and the plate with mass, stiffness ,mass-stiffness combination uncertainty.
INTRODUCTION
Plates and plate-like components are widely used in engineering structures such as several machine structures, civil engineering structure, boards in electronic equipment. Vibration analysis of plates and plate-like components has been an active research subject and numerous technical papers have been published. For to calculating the natural frequencies and mode shapes of a structure Modal analysis method is used. This method determined the dynamic response of complicated structural dynamic problems. In general, applications of modal analysis today cover a broad range of objectives identification and evaluation of vibration phenomena, validation, structural integrity assessment, structural modification, and damage detection. In engineering design, it is important to calculate the response quantities such as the displacement, stress, vibration frequencies, and mode shapes of given set of design parameters. The study of mathematical models which involve physical and geometric parameters such as mass density ρ, elastic modulus E, Poisson’s ratio v, lengths, and cross-section shape characteristics. In many practical engineering applications, these parameters frequently do not have well-defined values due to non-homogeneity of the mass distribution geometric properties or physical errors, as well as variation arising from the assembly and manufacturing processes. In engineering design these uncertainties in material properties, geometric parameters and boundary conditions are often unavoidable and must be considered. This concept of uncertainty plays an important role in investigation of various engineering
II. MATHEMATICAL MODELING
All the Vehicles, aircraft and home appliances structures are made up of Plate or combination of Plates so it becomes necessary to study Plate vibration. Using the Lagrange- Rayleigh -Ritz technique [8], the equations of motion of a dynamic system in modal space can be derived. 3.1: Bare Square Plate: Considering the All Edge Fixed bare square plate (with no structural uncertainty). For this plate eigenfunction is described by sinusoidal mode shapes in the x and y directions, respectively.Lagrange’s equation results in the equation of motion of the bare plate as given below(1) The natural frequencies can then be obtained by eigenvalue analysis [9] 3.2: Uncertain Mass Loaded Plate: Now consider the uncertain mass loaded plate as shown in Fig 2 for this the equation of motion is
INTRODUCTION
Plates and plate-like components are widely used in engineering structures such as several machine structures, civil engineering structure, boards in electronic equipment. Vibration analysis of plates and plate-like components has been an active research subject and numerous technical papers have been published. For to calculating the natural frequencies and mode shapes of a structure Modal analysis method is used. This method determined the dynamic response of complicated structural dynamic problems. In general, applications of modal analysis today cover a broad range of objectives identification and evaluation of vibration phenomena, validation, structural integrity assessment, structural modification, and damage detection. In engineering design, it is important to calculate the response quantities such as the displacement, stress, vibration frequencies, and mode shapes of given set of design parameters. The study of mathematical models which involve physical and geometric parameters such as mass density ρ, elastic modulus E, Poisson’s ratio v, lengths, and cross-section shape characteristics. In many practical engineering applications, these parameters frequently do not have well-defined values due to non-homogeneity of the mass distribution geometric properties or physical errors, as well as variation arising from the assembly and manufacturing processes. In engineering design these uncertainties in material properties, geometric parameters and boundary conditions are often unavoidable and must be considered. This concept of uncertainty plays an important role in investigation of various engineering
II. MATHEMATICAL MODELING
All the Vehicles, aircraft and home appliances structures are made up of Plate or combination of Plates so it becomes necessary to study Plate vibration. Using the Lagrange- Rayleigh -Ritz technique [8], the equations of motion of a dynamic system in modal space can be derived. 3.1: Bare Square Plate: Considering the All Edge Fixed bare square plate (with no structural uncertainty). For this plate eigenfunction is described by sinusoidal mode shapes in the x and y directions, respectively.Lagrange’s equation results in the equation of motion of the bare plate as given below(1) The natural frequencies can then be obtained by eigenvalue analysis [9] 3.2: Uncertain Mass Loaded Plate: Now consider the uncertain mass loaded plate as shown in Fig 2 for this the equation of motion is
Similar questions