dynamics_modal_analysis

Uses

- dynamics_helper
- iso_fortran_env
- dynamics_error_handling
- linalg

Interfaces

public interface modal_response

private pure subroutine modal_response_dense(mass, stiff, freqs, modeshapes)

Computes the modal frequencies and modes shapes for multi-degree-of-freedom system. The generalized eigenproblem is $K\boldsymbol{\phi}_i=\lambda_iM\boldsymbol{\phi}_i, \qquad \omega_i=\sqrt{\lambda_i}.$

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in),		dimension(:,:)	::	mass	The N-by-N mass matrix for the system. This matrix must be symmetric.
real(kind=real64),	intent(in),		dimension(:,:)	::	stiff	The N-by-N stiffness matrix for the system. This matrix must be symmetric.
real(kind=real64),	intent(out),		allocatable, dimension(:)	::	freqs	An allocatable N-element array where the modal frequencies will be returned in ascending order with units of rad/s.
real(kind=real64),	intent(out),	optional,	allocatable, dimension(:,:)	::	modeshapes	An optional, allocatable N-by-N matrix where the N mode shapes for the system will be returned. The mode shapes are stored in columns.

private subroutine modal_response_sparse(mass, stiff, nmodes, freqs, modeshapes)

Computes selected modal frequencies and mode shapes for a multi-degree-of-freedom system using CSR sparse matrices. The generalized eigenproblem is $K\boldsymbol{\phi}_i=\lambda_iM\boldsymbol{\phi}_i, \qquad \omega_i=\sqrt{\lambda_i}.$

Arguments

Type	Intent	Optional	Attributes		Name
type(csr_matrix),	intent(in)			::	mass	The N-by-N symmetric positive-definite mass matrix.
type(csr_matrix),	intent(in)			::	stiff	The N-by-N symmetric stiffness matrix.
integer(kind=int32),	intent(in)			::	nmodes	The number of lowest-frequency modes to compute. This value must be greater than zero and less than N.
real(kind=real64),	intent(out),		allocatable, dimension(:)	::	freqs	An allocatable NMODES-element array containing the modal frequencies in ascending order with units of rad/s.
real(kind=real64),	intent(out),	optional,	allocatable, dimension(:,:)	::	modeshapes	An optional, allocatable N-by-NMODES matrix containing one mode shape per column.

Functions

public pure elemental function compute_modal_damping(lambda, alpha, beta) result(rst)

Computes the modal damping factors $\zeta_i$ given the proportional damping terms $\alpha$ and $\beta$ where $\alpha + \beta \omega_{i}^2 = 2 \zeta_{i} \omega_{i}$ , $\lambda_{i} = \omega_{i}^2$ , and $\lambda_i$ is the $i^{th}$ eigenvalue of the system. Equivalently, $\zeta_i=(\alpha+\beta\omega_i^2)/(2\omega_i)$ .

Arguments

Type	Intent		Name
real(kind=real64),	intent(in)	::	lambda	The square of the modal frequency - the eigen value.
real(kind=real64),	intent(in)	::	alpha	The mass damping factor, $\alpha$ .
real(kind=real64),	intent(in)	::	beta	The stiffness damping factor, $\beta$ .

Return Value real(kind=real64)

The modal damping parameter.

Subroutines

public pure subroutine normalize_mode_shapes(x)

Normalizes mode shape vectors such that the largest magnitude value in the vector is one. For each column $\boldsymbol{\phi}_i$ , the operation is $\boldsymbol{\phi}_i\leftarrow \frac{\boldsymbol{\phi}_i}{\phi_{i,k}},\qquad k=\arg\max_j|\phi_{i,j}|.$

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(inout),		dimension(:,:)	::	x	The matrix of mode shape vectors with one vector per column.

dynamics_modal_analysis Module

Contents

Interfaces

Functions

Subroutines

Uses

Contents

Interfaces

Functions

Subroutines

Interfaces

public interface modal_response

private pure subroutine modal_response_dense(mass, stiff, freqs, modeshapes)

Arguments

private subroutine modal_response_sparse(mass, stiff, nmodes, freqs, modeshapes)

Arguments

Functions

public pure elemental function compute_modal_damping(lambda, alpha, beta) result(rst)

Arguments

Return Value real(kind=real64)

Subroutines

public pure subroutine normalize_mode_shapes(x)

Arguments