The dynamic equation of motion of a structure contains M, C and K as mass, damping and stiffness matrices of the structure, respectively. If F is an external load vector, then which option is correct about the equation?

All the forces are time-independent

M ( ddot{x} ) + K ( dot{x} ) + Cx = F

M ( ddot{x} ) is time-dependent

All the forces are time-independent

In matrix algebra, which option is not correct about an eigenvalue problem of the type Ax = Lx?

It has solution only if A non-singular

The unsteady natural axial oscillations of a bar are periodic, and they are determined by assuming a solution u(x, t) = U(x) e-iwt. Which option is not correct about the solution equation?

w denotes the natural frequency

u(x, t) denotes transverse displacements

15 + Mcqs in Eigen Value and Time Dependent Problems 2 in Finite Element Method Page 1 McqOptions

Explore topic-wise MCQs in Finite Element Method.

From the Timoshenko beam theory of natural vibrations, using cubic Hermite polynomials approximation, what is the 1st element of the mass matrix?

From the Euler-Bernoulli beam theory of natural vibrations, using cubic Hermite polynomials approximation, what is the 1st element of the stiffness matrix?

In matrix algebra, what is the value of a-b if the eigenvector of ( begin{pmatrix}1&1&1 1&1&1 1&1&1 end{pmatrix} ) corresponding to eigenvalue three is ( begin{pmatrix}a b a end{pmatrix} )?

In matrix algebra, what is the eigenvalue of the matrix ( begin{pmatrix} 1&1&1 1&1&1 1&1&1 end{pmatrix} )?

In matrix algebra, a matrix K equals ( begin{pmatrix} 1&0&0 0&1&0 0&0&3 end{pmatrix} ). What is the value of a, if K7 = ( begin{pmatrix} c&0&0 0&b&0 0&0&a end{pmatrix} )?

The dynamic equation of motion of a structure contains M, C and K as mass, damping and stiffness matrices of the structure, respectively. If F is an external load vector, then which option is correct about the equation?

In matrix algebra, which option is not correct about an eigenvalue problem of the type Ax = Lx?

The unsteady natural axial oscillations of a bar are periodic, and they are determined by assuming a solution u(x, t) = U(x) e-iwt. Which option is not correct about the solution equation?

The governing equation of an unsteady one-dimensional heat transfer problem is given below. It has a solution u(x,t) = U(x)exp( t). What is appropriately called? ( frac{- partial}{ partial x} (a frac{ partial u}{ partial x}) + b frac{ partial u}{ partial t} ) + cu = 0 for 0<x<L

In thermodynamics, the following equation represents a diffusion process. If k is thermal conductivity, p is density, and c is the specific heat at constant pressure, then what is ? ( frac{ partial^2 T}{ partial x^2} = frac{1}{ alpha} frac{ partial T}{ partial t} )

A plane wall was maintained initially at a temperature of 35 C. It is subjected to an ambient temperature of 45 C at one surface. If the heat transfer coefficient at the surfaces of the wall is assumed to be infinite, then what is the new temperature at the wall surface?

A plane wall was maintained initially at a temperature of T units. It is subjected to an ambient temperature of T units at one surface. If the heat transfer coefficient at the surfaces of the wall is assumed to be infinite, then what is the new temperature at the wall?

Suppose the following eigenvalue equation represents a bar problem, then the value of the parameters a and c0 should be EA and A, respectively. (- frac{d}{dx}(a frac{dU}{dx}) )= c0 U

From the Timoshenko beam theory of natural vibrations, using cubic Hermite polynomials approximation, what is the 1^st element of the mass matrix?

From the Euler-Bernoulli beam theory of natural vibrations, using cubic Hermite polynomials approximation, what is the 1^st element of the stiffness matrix?

In matrix algebra, a matrix K equals ( begin{pmatrix} 1&0&0 0&1&0 0&0&3 end{pmatrix} ). What is the value of a, if K⁷ = ( begin{pmatrix} c&0&0 0&b&0 0&0&a end{pmatrix} )?

The unsteady natural axial oscillations of a bar are periodic, and they are determined by assuming a solution u(x, t) = U(x) e^-iwt. Which option is not correct about the solution equation?

The governing equation of an unsteady one-dimensional heat transfer problem is given below. It has a solution u(x,t) = U(x)exp( t). What is appropriately called?
( frac{- partial}{ partial x} (a frac{ partial u}{ partial x}) + b frac{ partial u}{ partial t} ) + cu = 0 for 0<x<L

In thermodynamics, the following equation represents a diffusion process. If k is thermal conductivity, p is density, and c is the specific heat at constant pressure, then what is ?
( frac{ partial^2 T}{ partial x^2} = frac{1}{ alpha} frac{ partial T}{ partial t} )

Suppose the following eigenvalue equation represents a bar problem, then the value of the parameters a and c₀ should be EA and A, respectively.
(- frac{d}{dx}(a frac{dU}{dx}) )= c₀ U