def setup(self):
# Define a mode shape with deflection x^2 in the y direction
self.x = x = arange(0, 10.1, 1)
self.L = self.x[-1]
zero = 0 * x
shapes = c_[zero, x**2, zero].reshape((len(x), 3, 1))
rotations = c_[zero, 2 * x, zero].reshape((len(x), 3, 1))
self.modes = ModalRepresentation(x,
freqs=[1],
shapes=shapes,
rotations=rotations)
def setup(self):
# Define a mode shape with deflection x^2 in the y direction
self.x = x = arange(0, 10.1, 1)
self.L = self.x[-1]
zero = 0*x
shapes = c_[zero, x**2, zero].reshape((len(x), 3, 1))
rotations = c_[zero, 2*x, zero].reshape((len(x), 3, 1))
self.modes = ModalRepresentation(x, freqs=[1], shapes=shapes,
rotations=rotations)
class ModalRepesentationWithNoModes_Tests:
def setup(self):
# Define a mode shape with deflection x^2 in the y direction
self.x = x = arange(0, 10.1, 1)
self.L = self.x[-1]
zero = 0 * x
shapes = c_[zero, x**2, zero].reshape((len(x), 3, 1))
rotations = c_[zero, 2 * x, zero].reshape((len(x), 3, 1))
self.modes = ModalRepresentation(x,
freqs=[1],
shapes=shapes,
rotations=rotations)
def _uniform_force(self, direction, magnitude):
P = zeros((len(self.x), 3))
P[:, direction] = magnitude
return P
def test_distributed_loading_for_uniform_axial_loading(self):
P = self._uniform_force(0, 3.4)
Qr, Qw, Qe = self.modes.distributed_loading(P, [0])
assert_aae(Qr, [3.4 * 10, 0, 0])
assert_aae(Qw, [0, 0, 0]) # axial so no moment
assert_aae(Qe, [0]) # axial so no strain force
def test_distributed_loading_uniform_loading_aligned_with_mode(self):
P = self._uniform_force(1, 3.4)
Qr, Qw, Qe = self.modes.distributed_loading(P, [0])
assert_aae(Qr, [0, 3.4 * 10, 0])
assert_aae(Qw, [0, 0, 3.4 * self.L**2 / 2])
# Generalised force should be integral of applied
# force and deflection. Integral of x^2 if L^3 / 3
assert_aae(Qe, [3.4 * trapz(self.x**2, self.x)])
def test_distributed_loading_uniform_loading_not_aligned_with_mode(self):
P = self._uniform_force(2, 3.4)
Qr, Qw, Qe = self.modes.distributed_loading(P, [0])
assert_aae(Qr, [0, 0, 3.4 * 10])
assert_aae(Qw, [0, -3.4 * self.L**2 / 2, 0])
assert_aae(Qe, [0])
class ModalRepesentationWithNoModes_Tests:
def setup(self):
# Define a mode shape with deflection x^2 in the y direction
self.x = x = arange(0, 10.1, 1)
self.L = self.x[-1]
zero = 0*x
shapes = c_[zero, x**2, zero].reshape((len(x), 3, 1))
rotations = c_[zero, 2*x, zero].reshape((len(x), 3, 1))
self.modes = ModalRepresentation(x, freqs=[1], shapes=shapes,
rotations=rotations)
def _uniform_force(self, direction, magnitude):
P = zeros((len(self.x), 3))
P[:, direction] = magnitude
return P
def test_distributed_loading_for_uniform_axial_loading(self):
P = self._uniform_force(0, 3.4)
Qr, Qw, Qe = self.modes.distributed_loading(P, [0])
assert_aae(Qr, [3.4 * 10, 0, 0])
assert_aae(Qw, [0, 0, 0]) # axial so no moment
assert_aae(Qe, [0]) # axial so no strain force
def test_distributed_loading_uniform_loading_aligned_with_mode(self):
P = self._uniform_force(1, 3.4)
Qr, Qw, Qe = self.modes.distributed_loading(P, [0])
assert_aae(Qr, [0, 3.4 * 10, 0])
assert_aae(Qw, [0, 0, 3.4 * self.L**2 / 2])
# Generalised force should be integral of applied
# force and deflection. Integral of x^2 if L^3 / 3
assert_aae(Qe, [3.4 * trapz(self.x**2, self.x)])
def test_distributed_loading_uniform_loading_not_aligned_with_mode(self):
P = self._uniform_force(2, 3.4)
Qr, Qw, Qe = self.modes.distributed_loading(P, [0])
assert_aae(Qr, [0, 0, 3.4 * 10])
assert_aae(Qw, [0, -3.4 * self.L**2 / 2, 0])
assert_aae(Qe, [0])
def setup(self):
x = linspace(0, self.length, 50)
density = self.mass / self.length
# One mode shape: linear in z direction.
shape = linspace(0, 1, 50)
rotation = -np.ones(50) / self.length
shapes = c_[0 * x, 0 * x, shape].reshape((len(x), 3, 1))
rotations = c_[0 * x, rotation, 0 * x].reshape((len(x), 3, 1))
# Natural frequency: w^2 = k/I
I0 = self.mass * (self.length**2 / 3) # inertia about end
freq = (self.stiffness / I0)**0.5
modes = ModalRepresentation(x, density, shapes, rotations, [freq])
self.beam = ModalElement('beam', modes)
class ModalRepesentationWithNoModes_Tests:
def setup(self):
self.x = arange(0, 10.1, 1)
self.L = self.x[-1]
self.modes = ModalRepresentation(self.x)
def _uniform_force(self, direction, magnitude):
P = zeros((len(self.x), 3))
P[:, direction] = magnitude
return P
def test_distributed_loading_for_uniform_axial_loading(self):
P = self._uniform_force(0, 3.4)
Qr, Qw, Qe = self.modes.distributed_loading(P, [])
assert_aae(Qr, [3.4 * self.L, 0, 0])
assert_aae(Qw, [0, 0, 0]) # axial so no moment
assert_equal(Qe.shape, (0,))
def test_distributed_loading_for_uniform_perpendicular_loading(self):
P = self._uniform_force(1, 3.4)
Qr, Qw, Qe = self.modes.distributed_loading(P, [])
assert_aae(Qr, [0, 3.4 * self.L, 0])
assert_aae(Qw, [0, 0, 3.4 * self.L**2 / 2])
assert_equal(Qe.shape, (0,))
class ModalRepesentationWithNoModes_Tests:
def setup(self):
self.x = arange(0, 10.1, 1)
self.L = self.x[-1]
self.modes = ModalRepresentation(self.x)
def _uniform_force(self, direction, magnitude):
P = zeros((len(self.x), 3))
P[:, direction] = magnitude
return P
def test_distributed_loading_for_uniform_axial_loading(self):
P = self._uniform_force(0, 3.4)
Qr, Qw, Qe = self.modes.distributed_loading(P, [])
assert_aae(Qr, [3.4 * self.L, 0, 0])
assert_aae(Qw, [0, 0, 0]) # axial so no moment
assert_equal(Qe.shape, (0, ))
def test_distributed_loading_for_uniform_perpendicular_loading(self):
P = self._uniform_force(1, 3.4)
Qr, Qw, Qe = self.modes.distributed_loading(P, [])
assert_aae(Qr, [0, 3.4 * self.L, 0])
assert_aae(Qw, [0, 0, 3.4 * self.L**2 / 2])
assert_equal(Qe.shape, (0, ))
def make_a_modal_beam(length, density=None, section_inertia=None):
x = linspace(0, length, 10)
modes = ModalRepresentation(x, density, section_inertia=section_inertia)
beam = ModalElement('beam', modes)
return beam
def _mock_rigid_uniform_modes(density, length):
"""Return empty modal representation of 20m long rigid beam"""
x = arange(0, length + 0.01)
return ModalRepresentation(x, density * ones_like(x))
def setup(self):
self.x = arange(0, 10.1, 1)
self.L = self.x[-1]
self.modes = ModalRepresentation(self.x)
def setup(self):
self.x = arange(0, 10.1, 1)
self.L = self.x[-1]
self.modes = ModalRepresentation(self.x)